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[Branch ~yade-pkg/yade/git-trunk] Rev 3605: Ning Guo's FEMxDEM package added to trunk

To: Yade developers <yade-dev@xxxxxxxxxxxxxxxxxxx>
From: noreply@xxxxxxxxxxxxx
Date: Tue, 03 Mar 2015 22:21:21 -0000
Reply-to: noreply@xxxxxxxxxxxxx
Sender: bounces@xxxxxxxxxxxxx

------------------------------------------------------------
revno: 3605
author: Ning GUO <ceguo@xxxxxxxxxxxxxx>
committer: Bruno Chareyre <bruno.chareyre@xxxxxxxxxxx>
timestamp: Tue 2015-03-03 20:06:49 +0100
message:
  Ning Guo's FEMxDEM package added to trunk
added:
  examples/FEMxDEM/
  examples/FEMxDEM/biaxialSmooth.py
  examples/FEMxDEM/footing.msh
  examples/FEMxDEM/footing.py
  examples/FEMxDEM/readme
  examples/FEMxDEM/retainingSmooth.py
  examples/FEMxDEM/triaxialRough.py
  examples/FEMxDEM/undrain.py
  py/FEMxDEM/
  py/FEMxDEM/mpipool.py
  py/FEMxDEM/msFEM2D.py
  py/FEMxDEM/msFEM3D.py
  py/FEMxDEM/msFEMup.py
  py/FEMxDEM/saveGauss.py
  py/FEMxDEM/simDEM.py
modified:
  pkg/dem/Shop.hpp
  pkg/dem/Shop_02.cpp
  py/CMakeLists.txt
  py/_utils.cpp


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=== added directory 'examples/FEMxDEM'
=== added file 'examples/FEMxDEM/biaxialSmooth.py'
--- examples/FEMxDEM/biaxialSmooth.py	1970-01-01 00:00:00 +0000
+++ examples/FEMxDEM/biaxialSmooth.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,82 @@
+""" Author: Ning Guo <ceguo@xxxxxxxxxxxxxx>
+    run `mv biaxialSmooth.yade.gz 0.yade.gz`
+    to generate initial RVE packing
+"""
+from esys.escript import *
+from esys.finley import Rectangle
+from esys.weipa import saveVTK
+from esys.escript.pdetools import Projector
+from msFEM2D import MultiScale
+from saveGauss import saveGauss2D
+import time
+
+vel = -0.0001; confining=-1.e5;
+lx = 0.05; ly = 0.1; # sample size, 50mm by 100mm
+nx = 8; ny = 16; # sample discretization, 8 by 16 quadrilateral elements
+mydomain = Rectangle(l0=lx,l1=ly,n0=nx,n1=ny,order=2,integrationOrder=2)
+dim = mydomain.getDim()
+k = kronecker(mydomain)
+numg = 4*nx*ny; # number of Gauss points, 4 GP each element (reduced integration)
+nump = 16; # number of processes for multiprocessing
+
+prob = MultiScale(domain=mydomain,ng=numg,np=nump,random=False,rtol=1e-2,usePert=False,pert=-2.e-5,verbose=True)
+
+disp = Vector(0.,Solution(mydomain))
+
+t=0
+
+stress = prob.getCurrentStress() # initial stress
+proj = Projector(mydomain)
+sig = proj(stress) # project Gauss point value to nodal value
+sig_bounda = interpolate(sig,FunctionOnBoundary(mydomain)) # interpolate
+traction = matrix_mult(sig_bounda,mydomain.getNormal()) # boundary traction
+x = mydomain.getX() # nodal coordinate
+bx = FunctionOnBoundary(mydomain).getX()
+topSurf = whereZero(bx[1]-sup(bx[1]))
+tractTop = traction*topSurf # traction at top surface
+forceTop = integrate(tractTop,where=FunctionOnBoundary(mydomain)) # resultant force at top
+lengthTop = integrate(topSurf,where=FunctionOnBoundary(mydomain)) # length of top surface
+fout=file('./result/biaxial_surf.dat','w')
+fout.write('0 '+str(forceTop[1])+' '+str(lengthTop)+'\n')
+# Dirichlet BC positions, smooth at bottom and top, fixed at the center of bottom
+Dbc = whereZero(x[1])*[0,1]+whereZero(x[1]-ly)*[0,1]+whereZero(x[1])*whereZero(x[0]-.5*lx)*[1,1]
+# Dirichlet BC values
+Vbc = whereZero(x[1])*[0,0]+whereZero(x[1]-ly)*[0,vel]+whereZero(x[1])*whereZero(x[0]-.5*lx)*[0,0]
+# Neumann BC, constant confining pressure
+Nbc = whereZero(bx[0])*[-confining,0]+whereZero(bx[0]-lx)*[confining,0]
+
+time_start = time.time()
+while t < 100: # apply 100 load steps
+
+   prob.initialize(f=Nbc, specified_u_mask=Dbc, specified_u_val=Vbc) # initialize BC
+   t += 1
+   du=prob.solve(iter_max=100) # get solution: nodal displacement
+
+   disp += du
+   stress=prob.getCurrentStress()
+   
+   dom = prob.getDomain() # domain is updated Lagrangian formulation
+   proj = Projector(dom)
+   sig = proj(stress)
+
+   sig_bounda = interpolate(sig,FunctionOnBoundary(dom))
+   traction = matrix_mult(sig_bounda,dom.getNormal())
+   tractTop = traction*topSurf
+   forceTop = integrate(tractTop,where=FunctionOnBoundary(dom))
+   lengthTop = integrate(topSurf,where=FunctionOnBoundary(dom))
+   fout.write(str(t*vel/ly)+' '+str(forceTop[1])+' '+str(lengthTop)+'\n')
+      
+   vR=prob.getLocalVoidRatio()
+   fabric=prob.getLocalFabric()
+   strain = prob.getCurrentStrain()
+   saveGauss2D(name='./result/gauss/time_'+str(t)+'.dat',strain=strain,stress=stress,fabric=fabric)
+   volume_strain = trace(strain)
+   dev_strain = symmetric(strain) - volume_strain*k/dim
+   shear = sqrt(2*inner(dev_strain,dev_strain))
+   saveVTK("./result/vtk/biaxialSmooth_%d.vtu"%t,disp=disp,shear=shear,e=vR)
+
+prob.getCurrentPacking(pos=(),time=t,prefix='./result/packing/')
+time_elapse = time.time() - time_start
+fout.write("#Elapsed time in hours: "+str(time_elapse/3600.)+'\n')   
+fout.close()
+prob.exitSimulation()

=== added file 'examples/FEMxDEM/footing.msh'
--- examples/FEMxDEM/footing.msh	1970-01-01 00:00:00 +0000
+++ examples/FEMxDEM/footing.msh	2015-03-03 19:06:49 +0000
@@ -0,0 +1,7894 @@
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+$EndElements

=== added file 'examples/FEMxDEM/footing.py'
--- examples/FEMxDEM/footing.py	1970-01-01 00:00:00 +0000
+++ examples/FEMxDEM/footing.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,81 @@
+""" Author: Ning Guo <ceguo@xxxxxxxxxxxxxx>
+    run `mv footing.yade.gz 0.yade.gz`
+    to generate initial RVE packing
+"""
+from esys.escript import *
+from esys.finley import ReadGmsh
+from esys.weipa import saveVTK
+from esys.escript.pdetools import Projector
+from msFEM import MultiScale
+from saveGauss import saveGauss2D
+import time
+
+vel = -0.00025; surcharge=-20.e3; # surcharge equals to the initial vertical stress of the RVE packing
+dim = 2; B = 0.05; L = 0.6; H = 0.4;
+mydomain = ReadGmsh('footing.msh',numDim=dim,integrationOrder=2)  # read Gmsh mesh with 6-node triangle element (2500 tri6); each element has 3 Gauss points
+k = kronecker(mydomain)
+numg = 3*2500; # number of Gauss points
+nump = 16; # number of processes in multiprocessing
+packNo=range(0,numg,50)
+
+prob = MultiScale(domain=mydomain,ng=numg,np=nump,random=False,rtol=1e-2,usePert=False,pert=-2.e-5,verbose=False)
+
+disp = Vector(0.,Solution(mydomain))
+
+t=0
+stress = prob.getCurrentStress()
+proj = Projector(mydomain)
+sig = proj(stress)
+sig_bounda = interpolate(sig,FunctionOnBoundary(mydomain))
+traction = matrix_mult(sig_bounda,mydomain.getNormal())
+x = mydomain.getX()
+bx = FunctionOnBoundary(mydomain).getX()
+footingBase = whereZero(bx[1]-sup(bx[1]))*whereNonPositive(bx[0]-B)
+tractFoot = traction*footingBase
+forceFoot = integrate(tractFoot,where=FunctionOnBoundary(mydomain))
+lengthFoot = integrate(footingBase,where=FunctionOnBoundary(mydomain))
+fout=file('./result/bearing.dat','w')
+fout.write('0 '+str(forceFoot[0])+' '+str(forceFoot[1])+' '+str(lengthFoot)+'\n')
+
+# Dirichlet BC, rollers at left and right, fixties at bottom, rigid and rough footing
+Dbc = whereZero(x[0])*[1,0]+whereZero(x[0]-sup(x[0]))*[1,0]+whereZero(x[1]-inf(x[1]))*[1,1]+whereZero(x[1]-sup(x[1]))*whereNonPositive(x[0]-B)*[1,1]
+Vbc = whereZero(x[0])*[0,0]+whereZero(x[0]-sup(x[0]))*[0,0]+whereZero(x[1]-inf(x[1]))*[0,0]+whereZero(x[1]-sup(x[1]))*whereNonPositive(x[0]-B)*[0,vel]
+# Neumann BC, surcharge at the rest area of the top surface
+Nbc = whereZero(bx[1]-sup(bx[1]))*wherePositive(bx[0]-B)*[0,surcharge]
+
+time_start = time.time()
+while t < 58: # apply 58 loading step; further loading would abort the program due to severe mesh distortion
+
+   prob.initialize(f=Nbc, specified_u_mask=Dbc, specified_u_val=Vbc)
+   t += 1
+   du=prob.solve(iter_max=100)
+
+   disp += du
+   stress=prob.getCurrentStress()
+   
+   dom = prob.getDomain() # domain updated (Lagrangian)
+   proj = Projector(dom)
+   sig = proj(stress)
+
+   sig_bounda = interpolate(sig,FunctionOnBoundary(dom))
+   traction = matrix_mult(sig_bounda,dom.getNormal())
+   tractFoot = traction*footingBase
+   forceFoot = integrate(tractFoot,where=FunctionOnBoundary(dom))
+   lengthFoot = integrate(footingBase,where=FunctionOnBoundary(dom))
+   fout.write(str(t*vel)+' '+str(forceFoot[0])+' '+str(forceFoot[1])+' '+str(lengthFoot)+'\n')
+      
+   vR=prob.getLocalVoidRatio()
+   rotation=prob.getLocalAvgRotation()
+   fabric=prob.getLocalFabric()
+   strain = prob.getCurrentStrain()
+   saveGauss2D(name='./result/gauss/time_'+str(t)+'.dat',strain=strain,stress=stress,fabric=fabric)
+   volume_strain = trace(strain)
+   dev_strain = symmetric(strain) - volume_strain*k/dim
+   shear = sqrt(2*inner(dev_strain,dev_strain))
+   saveVTK("./result/vtk/footing_%d.vtu"%t,disp=disp,stress=stress,shear=shear,e=vR,rot=rotation)
+
+prob.getCurrentPacking(pos=packNo,time=t,prefix='./result/packing/') # output packing
+time_elapse = time.time() - time_start
+fout.write("#Elapsed time in hours: "+str(time_elapse/3600.)+'\n')   
+fout.close()
+prob.exitSimulation()

=== added file 'examples/FEMxDEM/readme'
--- examples/FEMxDEM/readme	1970-01-01 00:00:00 +0000
+++ examples/FEMxDEM/readme	2015-03-03 19:06:49 +0000
@@ -0,0 +1,26 @@
+The code is built upon two open source packages: Yade (https://launchpad.net/yade) for DEM modules and Escript (https://launchpad.net/escript-finley) for FEM modules. It implements the hierarchical multiscale model for simulating the boundary value problem (BVP) for granular media. FEM is used to discretize the problem domain. Each Gauss point of the FEM mesh is embedded a representative volume element (RVE) packing simulated by DEM. As hundreds to thousands of RVEs are involved in a medium-sized problem which is critically time consuming, parallelization is achieved in the code through either multiprocessing on a supercomputer or mpi4py on a HPC cluster (more efficient but only experimental).
+For the usage of the code please refer to `GuoFEMxDEM.pdf` (https://www.yade-dem.org/w/images/e/e5/GuoFEMxDEM.pdf) and the example scripts in this folder.
+
+Copyright (C) 2015 Ning Guo. Feel free to use and redistribute. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+
+The MPI implementation in the multiscale model is quite experimental. The mpipool.py is contributed by Lisandro Dalcín, the author of mpi4py package, which is used in the code to provide MPI functionality (require MPICH or Open MPI). The mpipool.py file is available from this thread (also included in the code):
+ 
+ https://groups.google.com/forum/#!searchin/mpi4py/mpipool/mpi4py/OJG5eZ2f-Pg/8j-zO5CMGlEJ
+
+Alternatively, I found another package playdoh (https://github.com/rossant/playdoh) is also suitable and easy to use for the distributed computation. It also provides the map function similar to that provided by multiprocessing and mpipool. Thus, it might be conveneitly adapted in the current code. Contributions are welcome to improve the MPI functionality, as it is crucial to extend the multiscale simulation for real large-scale problems. We appreciate it if you find better solutions and contact Ning <ceguo@xxxxxxxxxxxxxx>.
+
+The code is part of the work presented in the following papers:
+
+1. Guo, N. and Zhao, J. (2014) A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media. International Journal for Numerical Methods in Engineering 99(11), 789-818. DOI: 10.1002/nme.4702.
+
+2. Guo, N. (2014) Multiscale characterization of the shear behavior of granular media. PhD Thesis, The Hong Kong University of Science and Technology, Hong Kong.
+
+3. Zhao, J. and Guo, N. (2015) The interplay between anisotropy and strain localisation in granular soils: a multiscale insight. Géotechnique, under review.
+
+4. Guo, N. and Zhao, J. (2015) Multiscale insights into classic geomechanics problems. International Journal for Numerical and Analytical Methods in Geomechanics, under review.
+
+5. Guo, N. and Zhao, J. (2015) Parallel hierarchical multiscale modelling of hydro-mechanical problems for saturated granular soil. International Journal for Numerical Methods in Engineering, in preparation.
+
+6. Guo, N. and Zhao, J. (2015) 3D multiscale analysis of strain localization in granular media. International Journal of Solids and Structures, in preparation.
+
+We appreciate it if you use the code in your publication and cite one or two above references.

=== added file 'examples/FEMxDEM/retainingSmooth.py'
--- examples/FEMxDEM/retainingSmooth.py	1970-01-01 00:00:00 +0000
+++ examples/FEMxDEM/retainingSmooth.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,89 @@
+""" Author: Ning Guo <ceguo@xxxxxxxxxxxxxx>
+    run `mv retainingSmooth.yade.gz 0.yade.gz`
+    to generate initial RVE packing
+"""
+from esys.escript import *
+from esys.finley import Rectangle
+from esys.weipa import saveVTK
+from esys.escript.pdetools import Projector
+from msFEM2D import MultiScale
+from saveGauss import saveGauss2D
+import time
+
+vel = -0.00017; surcharge=-2.e4; # surcharge equals to the initial vertical stress of the RVE packing; vel<0 passive failure; vel>0 active failure
+B = 0.4; H = 0.2; wallH = 0.17; baseH = H-wallH; # setup dimensions
+nx = 40; ny = 20 # discretization with 40x20 quads
+mydomain = Rectangle(l0=B,l1=H,n0=nx,n1=ny,order=2,integrationOrder=2)
+dim = mydomain.getDim()
+k = kronecker(mydomain)
+numg = 4*nx*ny; nump = 16;
+packNo=range(0,numg,16)
+
+disp = Vector(0.,Solution(mydomain))
+
+prob = MultiScale(domain=mydomain,ng=numg,np=nump,random=False,rtol=1e-2,usePert=False,pert=-2.e-5,verbose=True)
+
+t=0
+time_start = time.time()
+
+x = mydomain.getX()
+bx = FunctionOnBoundary(mydomain).getX()
+left = whereZero(x[0])
+right = whereZero(x[0]-B)
+bottom = whereZero(x[1])
+top = whereZero(bx[1]-H)
+base = whereZero(x[0]-B)*whereNegative(x[1]-baseH)
+wall = whereZero(x[0]-B)*whereNonNegative(x[1]-baseH)
+wallBF = whereZero(bx[0]-B)*whereNonNegative(bx[1]-baseH)
+# Dirichlet BC, all fixed in space except wall (only fixed in x direction, smooth)
+Dbc = left*[1,1]+base*[1,1]+bottom*[1,1]+wall*[1,0]
+Vbc = left*[0,0]+base*[0,0]+bottom*[0,0]+wall*[vel,0]
+# Neumann BC, apply surcharge at the top surface
+Nbc = top*[0,surcharge]
+
+stress = prob.getCurrentStress()
+proj = Projector(mydomain)
+sig = proj(stress)
+sig_bounda = interpolate(sig,FunctionOnBoundary(mydomain))
+traction = matrix_mult(sig_bounda,mydomain.getNormal())
+tract = traction*wallBF # traction on wall
+forceWall = integrate(tract,where=FunctionOnBoundary(mydomain)) # force on wall
+lengthWall = integrate(wallBF,where=FunctionOnBoundary(mydomain))
+fout=file('./result/pressure.dat','w')
+fout.write('0 '+str(forceWall[0])+' '+str(lengthWall)+'\n')
+
+while t < 100:
+
+   prob.initialize(f=Nbc,specified_u_mask=Dbc,specified_u_val=Vbc)
+   t += 1
+   du=prob.solve(iter_max=100)
+
+   disp += du
+   stress=prob.getCurrentStress()
+   
+   dom = prob.getDomain()
+   proj = Projector(dom)
+   sig = proj(stress)
+
+   sig_bounda = interpolate(sig,FunctionOnBoundary(dom))
+   traction = matrix_mult(sig_bounda,dom.getNormal())
+   tract = traction*wallBF
+   forceWall = integrate(tract,where=FunctionOnBoundary(dom))
+   lengthWall = integrate(wallBF,where=FunctionOnBoundary(dom))
+   fout.write(str(t*vel)+' '+str(forceWall[0])+' '+str(lengthWall)+'\n')
+      
+   vR=prob.getLocalVoidRatio()
+   rotation=prob.getLocalAvgRotation()
+   fabric=prob.getLocalFabric()
+   strain = prob.getCurrentStrain()
+   saveGauss2D(name='./result/gauss/time_'+str(t)+'.dat',strain=strain,stress=stress,fabric=fabric)
+   volume_strain = trace(strain)
+   dev_strain = symmetric(strain) - volume_strain*k/dim
+   shear = sqrt(2*inner(dev_strain,dev_strain))
+   saveVTK("./result/vtk/retainingSmooth_%d.vtu"%t,disp=disp,stress=stress,shear=shear,e=vR,rot=rotation)
+
+prob.getCurrentPacking(pos=packNo,time=t,prefix='./result/packing/')
+time_elapse = time.time() - time_start
+fout.write("#Elapsed time in hours: "+str(time_elapse/3600.)+'\n')
+fout.close()
+prob.exitSimulation()

=== added file 'examples/FEMxDEM/triaxialRough.py'
--- examples/FEMxDEM/triaxialRough.py	1970-01-01 00:00:00 +0000
+++ examples/FEMxDEM/triaxialRough.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,81 @@
+""" Author: Ning Guo <ceguo@xxxxxxxxxxxxxx>
+    run `mv triaxialRough.yade.gz 0.yade.gz`
+    to generate initial RVE packing
+"""
+from esys.escript import *
+from esys.finley import Brick
+from esys.weipa import saveVTK
+from esys.escript.pdetools import Projector
+from msFEM3D import MultiScale
+from saveGauss import saveGauss3D
+import time
+
+vel = -0.0001; confining=-1.e5;
+lx = 0.05; ly = 0.05; lz = 0.1; # sample dimension
+nx = 8; ny = 8; nz = 16; # discretization
+mydomain = Brick(l0=lx,l1=ly,l2=lz,n0=nx,n1=ny,n2=nz,order=2,integrationOrder=2) # 20-noded,8-Gauss hexahedral element
+dim = 3; k = kronecker(mydomain)
+numg = 8*nx*ny*nz; # number of Gauss points
+packNo=range(0,numg,8)
+
+prob = MultiScale(domain=mydomain,ng=numg,useMPI=True,rtol=1e-2) # mpi is activated
+
+disp = Vector(0.,Solution(mydomain))
+
+t=0
+stress = prob.getCurrentStress()
+proj = Projector(mydomain)
+sig = proj(stress)
+sig_bounda = interpolate(sig,FunctionOnBoundary(mydomain))
+traction = matrix_mult(sig_bounda,mydomain.getNormal()) # traction on boundary
+x = mydomain.getX()
+bx = FunctionOnBoundary(mydomain).getX()
+topSurf = whereZero(bx[2]-lz)
+tractTop = traction*topSurf # traction on top surface
+forceTop = integrate(tractTop,where=FunctionOnBoundary(mydomain)) # force on top
+areaTop = integrate(topSurf,where=FunctionOnBoundary(mydomain))
+fout=file('./result/resultant.dat','w')
+fout.write('0 '+str(forceTop[2])+' '+str(areaTop)+'\n')
+
+# Dirichlet BC, rough loading ends
+Dbc = whereZero(x[2])*[1,1,1]+whereZero(x[2]-lz)*[1,1,1]
+Vbc = whereZero(x[2])*[0,0,0]+whereZero(x[2]-lz)*[0,0,vel]
+# Neumann BC, constant lateral confining
+Nbc = whereZero(bx[0])*[-confining,0,0]+whereZero(bx[0]-sup(bx[0]))*[confining,0,0]+whereZero(bx[1])*[0,-confining,0]+whereZero(bx[1]-sup(bx[1]))*[0,confining,0]
+
+time_start = time.time()
+while t < 100:
+
+   prob.initialize(f=Nbc, specified_u_mask=Dbc, specified_u_val=Vbc)
+   t += 1
+   du=prob.solve(iter_max=100)
+
+   disp += du
+   stress=prob.getCurrentStress()
+   
+   dom = prob.getDomain()
+   proj = Projector(dom)
+   sig = proj(stress)
+
+   sig_bounda = interpolate(sig,FunctionOnBoundary(dom))
+   traction = matrix_mult(sig_bounda,dom.getNormal())
+   tractTop = traction*topSurf
+   forceTop = integrate(tractTop,where=FunctionOnBoundary(dom))
+   areaTop = integrate(topSurf,where=FunctionOnBoundary(dom))
+   fout.write(str(t*vel/lz)+' '+str(forceTop[2])+' '+str(areaTop)+'\n')
+      
+   vR=prob.getLocalVoidRatio()
+   rotation=prob.getLocalAvgRotation()
+   fabric=prob.getLocalFabric()
+   strain = prob.getCurrentStrain()
+   saveGauss3D(name='./result/gauss/time_'+str(t)+'.dat',strain=strain,stress=stress,fabric=fabric)
+   volume_strain = trace(strain)
+   dev_strain = symmetric(strain) - volume_strain*k/dim
+   shear = sqrt(2./3.*inner(dev_strain,dev_strain))
+   saveVTK("./result/vtk/triaxialRough_%d.vtu"%t,disp=disp,shear=shear,e=vR,rot=rotation)
+   
+prob.getCurrentPacking(pos=packNo,time=t,prefix='./result/packing/')
+time_elapse = time.time() - time_start
+fout.write("#Elapsed time in hours: "+str(time_elapse/3600.)+'\n')   
+fout.close()
+prob.exitSimulation()

=== added file 'examples/FEMxDEM/undrain.py'
--- examples/FEMxDEM/undrain.py	1970-01-01 00:00:00 +0000
+++ examples/FEMxDEM/undrain.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,86 @@
+""" Author: Ning Guo <ceguo@xxxxxxxxxxxxxx>
+    run `mv undrain.yade.gz 0.yade.gz`
+    to generate initial RVE packing
+"""
+from esys.escript import *
+from esys.finley import Rectangle
+from esys.weipa import saveVTK
+from esys.escript.pdetools import Projector
+from msFEMup import MultiScale
+from saveGauss import saveGauss2D
+import time
+
+confining = -2.e5; pore = 1.e5 # initial pore pressure
+perm = 0.001**2/(180.*8.9e-4); # unscaled permeability, using KC equation
+kf = 2.2e9 # fluid bulk modulus
+dt = .1; vel = -0.0001 # time step and loading speed
+lx = 0.05; ly = 0.1 # sample dimension
+nx = 8; ny = 16 # discretization
+mydomain = Rectangle(l0=lx,l1=ly,n0=nx,n1=ny,order=2,integrationOrder=2)
+k = kronecker(mydomain); dim = 2.
+numg = 4*nx*ny; # no. of Gauss points
+mpi = True # use MPI
+
+prob = MultiScale(domain=mydomain,pore0=pore,perm=perm,kf=kf,dt=dt,ng=numg,useMPI=mpi,rtol=1.e-2)
+disp = Vector(0.,Solution(mydomain))
+t = 0
+ux = mydomain.getX() # disp. node coordinate
+px = ReducedSolution(mydomain).getX() # press. node coordinate
+bx = FunctionOnBoundary(mydomain).getX()
+topSurf = whereZero(bx[1]-ly)
+uDbc = whereZero(ux[1])*[0,1]+whereZero(ux[0]-lx/2.)*whereZero(ux[1])*[1,1]+whereZero(ux[1]-ly)*[0,1] # disp. Dirichlet BC mask
+vDbc = whereZero(ux[1])*[0,0]+whereZero(ux[0]-lx/2.)*whereZero(ux[1])*[0,0]+whereZero(ux[1]-ly)*[0,vel*dt] # disp. Dirichlet BC value
+uNbc = whereZero(bx[0])*[-confining,0]+whereZero(bx[0]-lx)*[confining,0] # disp. Neumann BC
+
+stress = prob.getCurrentStress() # effective stress at GP
+proj = Projector(mydomain)
+sig = proj(stress) # effective stress at node (reduced)
+sig_bound = interpolate(sig,FunctionOnBoundary(mydomain))
+traction = matrix_mult(sig_bound,mydomain.getNormal())
+tractTop = traction*topSurf
+forceTop = integrate(tractTop,where=FunctionOnBoundary(mydomain))
+lengthTop = integrate(topSurf,where=FunctionOnBoundary(mydomain))
+fout = file('./result/resultantForce.dat','w')
+fout.write('0 '+str(forceTop[1])+' '+str(lengthTop)+'\n')
+
+time_start = time.time()
+while t < 400:
+   prob.initialize(f=uNbc,umsk=uDbc,uvalue=vDbc)
+   t += 1
+   du = prob.solve(globalIter=10,solidIter=50)
+   disp += du
+   pore = prob.getCurrentPore() # pore pressure at node (reduced)
+   flux = prob.getCurrentFlux() # Darcy flux at GP
+   stress = prob.getCurrentStress() # effective stress at GP
+   strain = prob.getCurrentStrain() # disp. grad at GP
+   volume_strain = trace(strain) # volumetric strain
+   dev_strain = symmetric(strain) - volume_strain*k/dim # deviatoric strain
+   shear = sqrt(2.*inner(dev_strain,dev_strain)) # shear strain
+   fab = prob.getLocalFabric() # fabric tensor at GP
+   dev_fab = 4.*(fab-trace(fab)/dim*k)
+   anis = sqrt(.5*inner(dev_fab,dev_fab))
+   p = prob.getEquivalentPorosity() # porosity at GP
+   rot = prob.getLocalAvgRotation() # average rotation at GP
+   saveGauss2D(name='./result/gauss/time_'+str(t)+'.dat',strain=strain,fabric=fab,stress=stress)
+   dom = prob.getDomain() # domain updated (Lagrangian)
+   proj = Projector(dom)
+   flux = proj(flux) # Darcy flux at node (reduced)
+   p = proj(p) # porosity at node (reduced)
+   shear = proj(shear) # shear strain at node (reduced)
+   anis = proj(anis)
+   rot = proj(rot)
+   saveVTK("./result/vtk/undrain_%d.vtu"%t,disp=disp,pore=pore,flux=flux,shear=shear,p=p,anis=anis,rot=rot)
+   sig = proj(stress) # effective stress at node (reduced)
+   sig_bound = interpolate(sig,FunctionOnBoundary(dom))
+   traction = matrix_mult(sig_bound,dom.getNormal())
+   tractTop = traction*topSurf
+   forceTop = integrate(tractTop,where=FunctionOnBoundary(dom))
+   lengthTop = integrate(topSurf,where=FunctionOnBoundary(dom))
+   fout.write(str(t*vel*dt/ly)+' '+str(forceTop[1])+' '+str(lengthTop)+'\n')
+
+prob.getCurrentPacking(time=t,prefix='./result/packing/')
+time_elapse = time.time() - time_start
+fout.write('#Elapsed time in hours: '+str(time_elapse/3600.)+'\n')
+fout.close()
+prob.exitSimulation()
+

=== modified file 'pkg/dem/Shop.hpp'
--- pkg/dem/Shop.hpp	2015-02-06 17:07:21 +0000
+++ pkg/dem/Shop.hpp	2015-03-03 19:06:49 +0000
@@ -149,5 +149,11 @@
 		
 		/* \todo implement groupMask */
 		static py::tuple aabbExtrema(Real cutoff=0.0, bool centers=false);
+		
+		//! evaluation of 2D quantities
+		static Real getSpheresVolume2D(const shared_ptr<Scene>& rb=shared_ptr<Scene>(), int mask=-1);
+		static Real getVoidRatio2D(const shared_ptr<Scene>& rb=shared_ptr<Scene>(),Real zlen=1);
+		//! get stress tensor and tangent operator tensor for FEMxDEM coupling. By Ning Guo
+		static py::tuple getStressAndTangent(Real volume=0, bool symmetry=true);
 };
 

=== modified file 'pkg/dem/Shop_02.cpp'
--- pkg/dem/Shop_02.cpp	2015-02-06 17:07:21 +0000
+++ pkg/dem/Shop_02.cpp	2015-03-03 19:06:49 +0000
@@ -622,3 +622,93 @@
 	Vector3r dim=maximum-minimum;
 	return py::make_tuple(Vector3r(minimum+.5*cutoff*dim),Vector3r(maximum-.5*cutoff*dim));
 }
+
+/*! Added function for 2D calculation: sphere volume. Optional. By Ning Guo */
+Real Shop::getSpheresVolume2D(const shared_ptr<Scene>& _scene, int mask){
+	const shared_ptr<Scene> scene=(_scene?_scene:Omega::instance().getScene());
+	Real vol=0;
+	FOREACH(shared_ptr<Body> b, *scene->bodies){
+		if (!b || !b->isDynamic()) continue;
+		Sphere* s=dynamic_cast<Sphere*>(b->shape.get());
+		if((!s) or ((mask>0) and ((b->groupMask & mask)==0))) continue;
+		vol += Mathr::PI*pow(s->radius,2);
+	}
+	return vol;
+}
+
+/*! Added function for 2D calculation: void ratio. Optional. By Ning Guo */
+Real Shop::getVoidRatio2D(const shared_ptr<Scene>& _scene, Real _zlen){
+	const shared_ptr<Scene> scene=(_scene?_scene:Omega::instance().getScene());
+	Real V;
+	if(!scene->isPeriodic){
+		throw std::invalid_argument("utils.voidratio2D applies only to aperiodic simulations.");
+	} else {
+		V=scene->cell->getVolume()/_zlen;
+	}
+	Real Vs=Shop::getSpheresVolume2D();
+	return (V-Vs)/Vs;
+}
+
+/*! Added function to get stress tensor and tangent operator tensor. By Ning Guo */
+py::tuple Shop::getStressAndTangent(Real volume, bool symmetry){
+	Scene* scene=Omega::instance().getScene().get();
+	if (volume==0) volume = scene->isPeriodic?scene->cell->hSize.determinant():1;
+	Matrix3r stress = Matrix3r::Zero();
+	Matrix6r tangent = Matrix6r::Zero();
+	const bool isPeriodic = scene->isPeriodic;
+	FOREACH(const shared_ptr<Interaction>& I, *scene->interactions){
+		if(!I->isReal()) continue;
+		shared_ptr<Body> b1 = Body::byId(I->getId1(),scene);
+		shared_ptr<Body> b2 = Body::byId(I->getId2(),scene);
+		Vector3r pos1 = Vector3r::Zero();
+		Vector3r pos2 = Vector3r::Zero();
+		if(b1->isClumpMember()) {
+			pos1 = Body::byId(b1->clumpId,scene)->state->pos;
+		}
+		else {
+			pos1 = b1->state->pos;
+		}
+		if(b2->isClumpMember()) {
+			pos2 = Body::byId(b2->clumpId,scene)->state->pos;
+		}
+		else {
+			pos2 = b2->state->pos;
+		}
+		Vector3r branch=pos1 - pos2;
+		if (isPeriodic) branch -= scene->cell->hSize*I->cellDist.cast<Real>();
+		NormShearPhys* nsi=YADE_CAST<NormShearPhys*>(I->phys.get());
+		Real kN=nsi->kn; Real kT=nsi->ks;
+		GenericSpheresContact* geom=YADE_CAST<GenericSpheresContact*>(I->geom.get());
+		const Vector3r& n=geom->normal;
+		const Vector3r& fT=nsi->shearForce;
+		const Vector3r& fTotal=nsi->normalForce+nsi->shearForce;
+		Real T=fT.norm();
+		bool hasShear=(T>0);
+		Vector3r t(Vector3r::Zero()); if(hasShear) t=fT/T;
+		stress += fTotal*branch.transpose();
+		tangent(0,0) += kN*n[0]*branch[0]*n[0]*branch[0]+kT*t[0]*branch[0]*t[0]*branch[0];
+		tangent(0,1) += kN*n[0]*branch[0]*n[1]*branch[1]+kT*t[0]*branch[0]*t[1]*branch[1];
+		tangent(0,2) += kN*n[0]*branch[0]*n[2]*branch[2]+kT*t[0]*branch[0]*t[2]*branch[2];
+                tangent(0,3) += kN*n[0]*branch[0]*(n[1]*branch[2]+n[2]*branch[1])*0.5+kT*t[0]*branch[0]*(t[1]*branch[2]+t[2]*branch[1])*0.5;
+                tangent(0,4) += kN*n[0]*branch[0]*(n[0]*branch[2]+n[2]*branch[0])*0.5+kT*t[0]*branch[0]*(t[0]*branch[2]+t[2]*branch[0])*0.5;
+                tangent(0,5) += kN*n[0]*branch[0]*(n[0]*branch[1]+n[1]*branch[0])*0.5+kT*t[0]*branch[0]*(t[0]*branch[1]+t[1]*branch[0])*0.5;
+		tangent(1,1) += kN*n[1]*branch[1]*n[1]*branch[1]+kT*t[1]*branch[1]*t[1]*branch[1];
+		tangent(1,2) += kN*n[1]*branch[1]*n[2]*branch[2]+kT*t[1]*branch[1]*t[2]*branch[2];
+                tangent(1,3) += kN*n[1]*branch[1]*(n[1]*branch[2]+n[2]*branch[1])*0.5+kT*t[1]*branch[1]*(t[1]*branch[2]+t[2]*branch[1])*0.5;
+                tangent(1,4) += kN*n[1]*branch[1]*(n[0]*branch[2]+n[2]*branch[0])*0.5+kT*t[1]*branch[1]*(t[0]*branch[2]+t[2]*branch[0])*0.5;
+                tangent(1,5) += kN*n[1]*branch[1]*(n[0]*branch[1]+n[1]*branch[0])*0.5+kT*t[1]*branch[1]*(t[0]*branch[1]+t[1]*branch[0])*0.5;
+		tangent(2,2) += kN*n[2]*branch[2]*n[2]*branch[2]+kT*t[2]*branch[2]*t[2]*branch[2];
+                tangent(2,3) += kN*n[2]*branch[2]*(n[1]*branch[2]+n[2]*branch[1])*0.5+kT*t[2]*branch[2]*(t[1]*branch[2]+t[2]*branch[1])*0.5;
+                tangent(2,4) += kN*n[2]*branch[2]*(n[0]*branch[2]+n[2]*branch[0])*0.5+kT*t[2]*branch[2]*(t[0]*branch[2]+t[2]*branch[0])*0.5;
+                tangent(2,5) += kN*n[2]*branch[2]*(n[0]*branch[1]+n[1]*branch[0])*0.5+kT*t[2]*branch[2]*(t[0]*branch[1]+t[1]*branch[0])*0.5;
+                tangent(3,3) += kN*(n[1]*branch[2]*n[1]*branch[2]+n[1]*branch[2]*n[2]*branch[1]*2+n[2]*branch[1]*n[2]*branch[1])*0.25+kT*(t[1]*branch[2]*t[1]*branch[2]+t[1]*branch[2]*t[2]*branch[1]*2+t[2]*branch[1]*t[2]*branch[1])*0.25;
+                tangent(3,4) += kN*(n[1]*branch[2]*n[0]*branch[2]+n[1]*branch[2]*n[2]*branch[0]+n[2]*branch[1]*n[0]*branch[2]+n[2]*branch[1]*n[2]*branch[0])*0.25+kT*(t[1]*branch[2]*t[0]*branch[2]+t[1]*branch[2]*t[2]*branch[0]+t[2]*branch[1]*t[0]*branch[2]+t[2]*branch[1]*t[2]*branch[0])*0.25;
+                tangent(3,5) += kN*(n[1]*branch[2]*n[0]*branch[1]+n[1]*branch[2]*n[1]*branch[0]+n[2]*branch[1]*n[0]*branch[1]+n[2]*branch[1]*n[1]*branch[0])*0.25+kT*(t[1]*branch[2]*t[0]*branch[1]+t[1]*branch[2]*t[1]*branch[0]+t[2]*branch[1]*t[0]*branch[1]+t[2]*branch[1]*t[1]*branch[0])*0.25;
+                tangent(4,4) += kN*(n[0]*branch[2]*n[0]*branch[2]+n[0]*branch[2]*n[2]*branch[0]*2+n[2]*branch[0]*n[2]*branch[0])*0.25+kT*(t[0]*branch[2]*t[0]*branch[2]+t[0]*branch[2]*t[2]*branch[0]*2+t[2]*branch[0]*t[2]*branch[0])*0.25;
+                tangent(4,5) += kN*(n[0]*branch[2]*n[0]*branch[1]+n[0]*branch[2]*n[1]*branch[0]+n[2]*branch[0]*n[0]*branch[1]+n[2]*branch[0]*n[1]*branch[0])*0.25+kT*(t[0]*branch[2]*t[0]*branch[1]+t[0]*branch[2]*t[1]*branch[0]+t[2]*branch[0]*t[0]*branch[1]+t[2]*branch[0]*t[1]*branch[0])*0.25;
+                tangent(5,5) += kN*(n[0]*branch[1]*n[0]*branch[1]+n[0]*branch[1]*n[1]*branch[0]*2+n[1]*branch[0]*n[1]*branch[0])*0.25+kT*(t[0]*branch[1]*t[0]*branch[1]+t[0]*branch[1]*t[1]*branch[0]*2+t[1]*branch[0]*t[1]*branch[0])*0.25;
+	}
+	stress/=volume;
+	tangent/=volume;
+	return py::make_tuple(stress,tangent);
+}

=== modified file 'py/CMakeLists.txt'
--- py/CMakeLists.txt	2014-08-04 16:38:31 +0000
+++ py/CMakeLists.txt	2015-03-03 19:06:49 +0000
@@ -26,6 +26,8 @@
 INSTALL(FILES ${filesPYTests} DESTINATION ${YADE_PY_PATH}/yade/tests)
 FILE(GLOB filesPYPerf "${CMAKE_CURRENT_SOURCE_DIR}/../examples/test/performance/*")
 INSTALL(FILES ${filesPYPerf} DESTINATION ${YADE_PY_PATH}/yade/tests/checks/performance)
+FILE(GLOB filesFEMxDEM "${CMAKE_CURRENT_SOURCE_DIR}/FEMxDEM/*.py")
+INSTALL(FILES ${filesFEMxDEM} DESTINATION ${YADE_PY_PATH}/yade/FEMxDEM)
 ADD_LIBRARY(WeightedAverage2d SHARED "${CMAKE_CURRENT_SOURCE_DIR}/WeightedAverage2d.cpp")
 SET_TARGET_PROPERTIES(WeightedAverage2d PROPERTIES PREFIX "")
 INSTALL(TARGETS WeightedAverage2d DESTINATION "${YADE_PY_PATH}/yade/")

=== added directory 'py/FEMxDEM'
=== added file 'py/FEMxDEM/mpipool.py'
--- py/FEMxDEM/mpipool.py	1970-01-01 00:00:00 +0000
+++ py/FEMxDEM/mpipool.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,69 @@
+__contributor__="Lisandro Dalcín"
+""" MPIPool wrapped using mpi4py """
+#import mpi4py
+#mpi4py.rc.threaded = False
+from mpi4py import MPI
+
+class MPIPool(object):
+
+    def __init__(self, comm=None, master=0):
+        self.comm = MPI.COMM_WORLD if comm is None else comm
+        self.master = master
+        self.workers = set(range(self.comm.size))
+        self.workers.discard(self.master)
+
+    def is_master(self):
+        return self.master == self.comm.rank
+
+    def is_worker(self):
+        return self.comm.rank in self.workers
+
+    def map(self, function, iterable):
+        assert self.is_master()
+
+        comm = self.comm
+        workerset = self.workers.copy()
+        tasklist = [(tid, (function, arg)) for tid, arg in enumerate(iterable)]
+        resultlist = [None] * len(tasklist)
+        pending = len(tasklist)
+
+        while pending:
+
+            if workerset and tasklist:
+                worker = workerset.pop()
+                taskid, task = tasklist.pop()
+                comm.send(task, dest=worker, tag=taskid)
+
+            if tasklist:
+                flag = comm.Iprobe(source=MPI.ANY_SOURCE, tag=MPI.ANY_TAG)
+                if not flag: continue
+            else:
+                comm.Probe(source=MPI.ANY_SOURCE, tag=MPI.ANY_TAG)
+
+            status = MPI.Status()
+            result = comm.recv(source=MPI.ANY_SOURCE, tag=MPI.ANY_TAG, status=status)
+            worker = status.source
+            workerset.add(worker)
+            taskid = status.tag
+            resultlist[taskid] = result
+            pending -= 1
+
+        return resultlist
+
+    def start(self):
+        if not self.is_worker(): return
+        comm = self.comm
+        master = self.master
+        status = MPI.Status()
+        while True:
+            task = comm.recv(source=master, tag=MPI.ANY_TAG, status=status)
+            if task is None: break
+            function, arg = task
+            result = function(arg)
+            comm.ssend(result, master, status.tag)
+
+    def close(self):
+        if not self.is_master(): return
+        for worker in self.workers:
+            self.comm.send(None, worker, 0)
+

=== added file 'py/FEMxDEM/msFEM2D.py'
--- py/FEMxDEM/msFEM2D.py	1970-01-01 00:00:00 +0000
+++ py/FEMxDEM/msFEM2D.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,261 @@
+__author__="Ning Guo, ceguo@xxxxxxxxxxxxxx"
+__supervisor__="Jidong Zhao, jzhao@xxxxxx"
+__institution__="The Hong Kong University of Science and Technology"
+
+""" 2D model for multiscale simulation
+which implements a Newton-Raphson scheme
+into FEM framework to solve the nonlinear
+problem where the tangent operator is obtained
+from DEM simulation by calling simDEM modules"""
+
+# import Escript modules
+import esys.escript as escript
+from esys.escript import util
+from esys.escript.linearPDEs import LinearPDE,SolverOptions
+# import YADE modules
+from simDEM import *
+# other python modules
+from itertools import repeat
+
+""" function to return pool for parallelization
+    supporting both MPI (experimental) on distributed
+    memory and multiprocessing on shared memory.
+"""
+def get_pool(mpi=False,threads=1):
+   if mpi: # using MPI
+      from mpipool import MPIPool
+      pool = MPIPool()
+      pool.start()
+      if not pool.is_master():
+         sys.exit(0)
+   elif threads>1: # using multiprocessing
+      from multiprocessing import Pool
+      pool = Pool(processes=threads)
+   else:
+      raise RuntimeError,"Wrong arguments: either mpi=True or threads>1."
+   return pool
+
+class MultiScale(object):
+   """
+   problem description:
+   -(A_{ijkl} u_{k,l})_{,j} = -X_{ij,j} + Y_i
+   Neumann boundary: n_j A_{ijkl} u_{k,l} = n_j X_{ij} + y_i
+   Dirichlet boundary: u_i = r_i where q_i > 0
+   :var u: unknown vector, displacement
+   :var A: elastic tensor / tangent operator
+   :var X: old/current stress tensor
+   :var Y: vector, body force
+   :var y: vector, Neumann bc traction
+   :var q: vector, Dirichlet bc mask
+   :var r: vector, Dirichlet bc value
+   """
+   def __init__(self,domain,ng=1,useMPI=False,np=1,random=False,rtol=1.e-2,usePert=False,pert=-2.e-6,verbose=False):
+      """
+      initialization of the problem, i.e. model constructor
+      :param domain: type Domain, domain of the problem
+      :param ng: type integer, number of Gauss points
+      :param useMPI: type boolean, use MPI or not
+      :param np: type integer, number of processors
+      :param random: type boolean, if or not use random density field
+      :param rtol: type float, relevative tolerance for global convergence
+      :param usePert: type boolean, if or not use perturbation method
+      :param pert: type float, perturbated strain applied to DEM to obtain tangent operator
+      :param verbose: type boolean, if or not print messages during calculation
+      """
+      self.__domain=domain
+      self.__pde=LinearPDE(domain,numEquations=self.__domain.getDim(),numSolutions=self.__domain.getDim())
+      self.__pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
+      self.__pde.setSymmetryOn()
+      #self.__pde.getSolverOptions().setTolerance(rtol**2)
+      #self.__pde.getSolverOptions().setPackage(SolverOptions.UMFPACK)
+      self.__numGaussPoints=ng
+      self.__rtol=rtol
+      self.__usepert=usePert
+      self.__pert=pert
+      self.__verbose=verbose
+      self.__pool=get_pool(mpi=useMPI,threads=np)
+      self.__scenes=self.__pool.map(initLoad,range(ng))
+      self.__strain=escript.Tensor(0,escript.Function(self.__domain))
+      self.__stress=escript.Tensor(0,escript.Function(self.__domain))
+      self.__S=escript.Tensor4(0,escript.Function(self.__domain))
+      
+      if self.__usepert:
+         s = self.__pool.map(getStressTensor,self.__scenes)
+         t = self.__pool.map(getTangentOperator,zip(self.__scenes,repeat(pert)))
+         for i in xrange(ng):
+            self.__stress.setValueOfDataPoint(i,s[i])
+            self.__S.setValueOfDataPoint(i,t[i])
+      else:
+         st = self.__pool.map(getStressAndTangent2D,self.__scenes)
+         for i in xrange(ng):
+            self.__stress.setValueOfDataPoint(i,st[i][0])
+            self.__S.setValueOfDataPoint(i,st[i][1])
+                     
+   def initialize(self, b=escript.Data(), f=escript.Data(), specified_u_mask=escript.Data(), specified_u_val=escript.Data()):
+      """
+      initialize the model for each time step, e.g. assign parameters
+      :param b: type vector, body force on FunctionSpace, e.g. gravity
+      :param f: type vector, boundary traction on FunctionSpace (FunctionOnBoundary)
+      :param specified_u_mask: type vector, mask of location for Dirichlet boundary
+      :param specified_u_val: type vector, specified displacement for Dirichlet boundary
+      """
+      self.__pde.setValue(Y=b,y=f,q=specified_u_mask,r=specified_u_val)
+      
+   def getDomain(self):
+      """
+      return model domain
+      """
+      return self.__domain
+      
+   def getRelTolerance(self):
+      """
+      return relative tolerance for convergence
+      type float
+      """
+      return self.__rtol
+  
+   def getCurrentPacking(self,pos=(),time=0,prefix=''):
+      if len(pos) == 0:
+         # output all Gauss points packings
+         self.__pool.map(outputPack,zip(self.__scenes,repeat(time),repeat(prefix)))
+      else:
+         # output selected Gauss points packings
+         scene = [self.__scenes[i] for i in pos]
+         self.__pool.map(outputPack,zip(scene,repeat(time),repeat(prefix)))
+   
+   def getLocalVoidRatio(self):
+      void=escript.Scalar(0,escript.Function(self.__domain))
+      e = self.__pool.map(getVoidRatio2D,self.__scenes)
+      for i in xrange(self.__numGaussPoints):
+         void.setValueOfDataPoint(i,e[i])
+      return void
+   
+   def getLocalAvgRotation(self):
+      rot=escript.Scalar(0,escript.Function(self.__domain))
+      r = self.__pool.map(avgRotation2D,self.__scenes)
+      for i in xrange(self.__numGaussPoints):
+         rot.setValueOfDataPoint(i,r[i])
+      return rot
+   
+   def getLocalFabric(self):
+      fabric=escript.Tensor(0,escript.Function(self.__domain))
+      f = self.__pool.map(getFabric2D,self.__scenes)
+      for i in xrange(self.__numGaussPoints):
+         fabric.setValueOfDataPoint(i,f[i])
+      return fabric
+   
+   """ used for clumped particle model only
+   def getLocalParOriFab(self):
+      fabric=escript.Tensor(0,escript.Function(self.__domain))
+      f = self.__pool.map(getParOriFabric,self.__scenes)
+      for i in xrange(self.__numGaussPoints):
+         fabric.setValueOfDataPoint(i,f[i])
+      return fabric
+   """
+   
+   """ used for cohesive particle model only
+   def getLocalBondBreakage(self,oriIntr=[]):
+      debond = escript.Scalar(0,escript.Function(self.__domain))
+      num = self.__pool.map(getDebondingNumber,zip(self.__scenes,repeat(oriIntr)))
+      for i in xrange(self.__numGaussPoints):
+         debond.setValueOfDataPoint(i,num[i])
+      return debond
+   """
+      
+   def getCurrentTangent(self):
+      """
+      return current tangent operator
+      type Tensor4 on FunctionSpace
+      """
+      return self.__S
+      
+   def getCurrentStress(self):
+      """
+      return current stress
+      type: Tensor on FunctionSpace
+      """
+      return self.__stress
+      
+   def getCurrentStrain(self):
+      """
+      return current strain
+      type: Tensor on FunctionSpace
+      """
+      return self.__strain
+   
+   def exitSimulation(self):
+      """finish the whole simulation, exit"""
+      self.__pool.close()
+   
+   def solve(self, iter_max=100):
+      """
+      solve the equation using Newton-Ralphson scheme
+      """
+      iterate=0
+      rtol=self.getRelTolerance()
+      stress=self.getCurrentStress()
+      s=self.getCurrentTangent()
+      x_safe=self.__domain.getX()
+      self.__pde.setValue(A=s, X=-stress)
+      #residual0=util.L2(self.__pde.getRightHandSide()) # using force error
+      u=self.__pde.getSolution()  # trial solution, displacement
+      D=util.grad(u)              # trial strain tensor
+      # !!!!!! obtain stress and tangent operator from DEM part
+      update_stress,update_s,update_scenes=self.applyStrain_getStressTangentDEM(st=D)
+      err=1.0 # initial error before iteration
+      converged=(err<rtol)
+      while (not converged) and (iterate<iter_max):
+         if self.__verbose:
+            print "Not converged after %d iteration(s)! Relative error: %e"%(iterate,err)
+         iterate+=1
+         self.__domain.setX(x_safe+u)
+         self.__pde.setValue(A=update_s,X=-update_stress,r=escript.Data())
+         #residual=util.L2(self.__pde.getRightHandSide())
+         du=self.__pde.getSolution()
+         u+=du
+         l,d=util.L2(u),util.L2(du)
+         err=d/l # displacement error, alternatively using force error 'residual'
+         converged=(err<rtol)
+         if err>rtol*0.001: # only update DEM parts when error is large enough
+            self.__domain.setX(x_safe)
+            D=util.grad(u)
+            update_stress,update_s,update_scenes=self.applyStrain_getStressTangentDEM(st=D)
+
+         #if err>err_safe: # to ensure consistent convergence, however this may not be achieved due to fluctuation!
+         #   raise RuntimeError,"No improvement of convergence with iterations! Relative error: %e"%err
+      """
+      update 'domain geometry', 'stress', 'tangent operator',
+      'accumulated strain' and 'simulation scenes'.
+      """
+      self.__domain.setX(x_safe+u)
+      self.__stress=update_stress
+      self.__S=update_s
+      self.__strain+=D
+      self.__scenes=update_scenes
+      if self.__verbose:
+         print "Convergence reached after %d iteration(s)! Relative error: %e"%(iterate,err)
+      return u
+      
+   """
+   apply strain to DEM packing,
+   get stress and tangent operator (including two methods)
+   """
+   def applyStrain_getStressTangentDEM(self,st=escript.Data()):
+      st = st.toListOfTuples()
+      st = numpy.array(st).reshape(-1,4)
+      stress = escript.Tensor(0,escript.Function(self.__domain))
+      S = escript.Tensor4(0,escript.Function(self.__domain))
+      scenes = self.__pool.map(shear2D,zip(self.__scenes,st))
+      if self.__usepert:
+         s = self.__pool.map(getStressTensor,scenes)
+         t = self.__pool.map(getTangentOperator,zip(scenes,repeat(self.__pert)))
+         for i in xrange(self.__numGaussPoints):
+            stress.setValueOfDataPoint(i,s[i])
+            S.setValueOfDataPoint(i,t[i])
+      else:
+         ST = self.__pool.map(getStressAndTangent2D,scenes)
+         for i in xrange(self.__numGaussPoints):
+            stress.setValueOfDataPoint(i,ST[i][0])
+            S.setValueOfDataPoint(i,ST[i][1])
+      return stress,S,scenes
+      

=== added file 'py/FEMxDEM/msFEM3D.py'
--- py/FEMxDEM/msFEM3D.py	1970-01-01 00:00:00 +0000
+++ py/FEMxDEM/msFEM3D.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,223 @@
+__author__="Ning Guo, ceguo@xxxxxxxxxxxxxx"
+__supervisor__="Jidong Zhao, jzhao@xxxxxx"
+__institution__="The Hong Kong University of Science and Technology"
+
+""" 3D model for multiscale simulation
+which implements a Newton-Raphson scheme
+into FEM framework to solve the nonlinear
+problem where the tangent operator is obtained
+from DEM simulation by calling simDEM modules"""
+
+""" import Escript modules """
+import esys.escript as escript
+from esys.escript import util
+from esys.escript.linearPDEs import LinearPDE,SolverOptions
+from simDEM import *
+from itertools import repeat
+
+""" function to return pool for parallelization
+    supporting both MPI (experimental) on distributed
+    memory and multiprocessing on shared memory.
+"""
+def get_pool(mpi=False,threads=1):
+   if mpi: # using MPI
+      from mpipool import MPIPool
+      pool = MPIPool()
+      pool.start()
+      if not pool.is_master():
+         sys.exit(0)
+   elif threads>1: # using multiprocessing
+      from multiprocessing import Pool
+      pool = Pool(processes=threads)
+   else:
+      raise RuntimeError,"Wrong arguments: either mpi=True or threads>1."
+   return pool
+
+class MultiScale(object):
+   """
+   problem description:
+   -(A_{ijkl} u_{k,l})_{,j} = -X_{ij,j} + Y_i
+   Neumann boundary: n_j A_{ijkl} u_{k,l} = n_j X_{ij} + y_i
+   Dirichlet boundary: u_i = r_i where q_i > 0
+   :var u: unknown vector, displacement
+   :var A: elastic tensor / tangent operator
+   :var X: old/current stress tensor
+   :var Y: vector, body force
+   :var y: vector, Neumann bc traction
+   :var q: vector, Dirichlet bc mask
+   :var r: vector, Dirichlet bc value
+   """
+   def __init__(self,domain,ng=1,useMPI=False,np=1,random=False,rtol=1.e-2,verbose=False):
+      """
+      initialization of the problem, i.e. model constructor
+      :param domain: type Domain, domain of the problem
+      :param ng: type integer, number of Gauss points
+      :param useMPI: type boolean, use MPI or not
+      :param np: type integer, number of processors
+      :param random: type boolean, if or not use random density field
+      :param rtol: type float, relevant tolerance for global convergence
+      :param verbose: type boolean, if or not print messages during calculation
+      """
+      self.__domain=domain
+      self.__pde=LinearPDE(domain,numEquations=self.__domain.getDim(),numSolutions=self.__domain.getDim())
+      self.__pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
+      self.__pde.setSymmetryOn()
+      #self.__pde.getSolverOptions().setTolerance(rtol**2)
+      #self.__pde.getSolverOptions().setPackage(SolverOptions.UMFPACK)
+      self.__numGaussPoints=ng
+      self.__rtol=rtol
+      self.__verbose=verbose
+      self.__pool=get_pool(mpi=useMPI,threads=np)
+      self.__scenes=self.__pool.map(initLoad,range(ng))
+      self.__strain=escript.Tensor(0,escript.Function(self.__domain))
+      self.__stress=escript.Tensor(0,escript.Function(self.__domain))
+      self.__S=escript.Tensor4(0,escript.Function(self.__domain))
+      
+      st = self.__pool.map(getStressAndTangent,self.__scenes)
+      for i in xrange(ng):
+         self.__stress.setValueOfDataPoint(i,st[i][0])
+         self.__S.setValueOfDataPoint(i,st[i][1])
+                     
+   def initialize(self, b=escript.Data(), f=escript.Data(), specified_u_mask=escript.Data(), specified_u_val=escript.Data()):
+      """
+      initialize the model for each time step, e.g. assign parameters
+      :param b: type vector, body force on FunctionSpace, e.g. gravity
+      :param f: type vector, boundary traction on FunctionSpace (FunctionOnBoundary)
+      :param specified_u_mask: type vector, mask of location for Dirichlet boundary
+      :param specified_u_val: type vector, specified displacement for Dirichlet boundary
+      """
+      self.__pde.setValue(Y=b,y=f,q=specified_u_mask,r=specified_u_val)
+      
+   def getDomain(self):
+      """
+      return model domain
+      """
+      return self.__domain
+      
+   def getRelTolerance(self):
+      """
+      return relative tolerance for convergence
+      type float
+      """
+      return self.__rtol
+  
+   def getCurrentPacking(self,pos=(),time=0,prefix=''):
+      if len(pos) == 0:
+         # output all Gauss points packings
+         self.__pool.map(outputPack,zip(self.__scenes,repeat(time),repeat(prefix)))
+      else:
+         # output selected Gauss points packings
+         scene = [self.__scenes[i] for i in pos]
+         self.__pool.map(outputPack,zip(scene,repeat(time),repeat(prefix)))
+   
+   def getLocalVoidRatio(self):
+      void=escript.Scalar(0,escript.Function(self.__domain))
+      e = self.__pool.map(getVoidRatio,self.__scenes)
+      for i in xrange(self.__numGaussPoints):
+         void.setValueOfDataPoint(i,e[i])
+      return void
+   
+   def getLocalAvgRotation(self):
+      rot=escript.Vector(0,escript.Function(self.__domain))
+      r = self.__pool.map(avgRotation,self.__scenes)
+      for i in xrange(self.__numGaussPoints):
+         rot.setValueOfDataPoint(i,r[i])
+      return rot
+
+   def getLocalFabric(self):
+      fabric=escript.Tensor(0,escript.Function(self.__domain))
+      f = self.__pool.map(getFabric,self.__scenes)
+      for i in xrange(self.__numGaussPoints):
+         fabric.setValueOfDataPoint(i,f[i])
+      return fabric
+ 
+   def getCurrentTangent(self):
+      """
+      return current tangent operator
+      type Tensor4 on FunctionSpace
+      """
+      return self.__S
+      
+   def getCurrentStress(self):
+      """
+      return current stress
+      type: Tensor on FunctionSpace
+      """
+      return self.__stress
+      
+   def getCurrentStrain(self):
+      """
+      return current strain
+      type: Tensor on FunctionSpace
+      """
+      return self.__strain
+   
+   def exitSimulation(self):
+      """finish the whole simulation, exit"""
+      self.__pool.close()
+   
+   def solve(self, iter_max=100):
+      """
+      solve the equation using Newton-Ralphson scheme
+      """
+      iterate=0
+      rtol=self.getRelTolerance()
+      stress=self.getCurrentStress()
+      s=self.getCurrentTangent()
+      x_safe=self.__domain.getX()
+      self.__pde.setValue(A=s, X=-stress)
+      #residual0=util.L2(self.__pde.getRightHandSide()) # using force error
+      u=self.__pde.getSolution()  # trial solution, displacement
+      D=util.grad(u)              # trial strain tensor
+      # !!!!!! obtain stress and tangent operator from DEM part
+      update_stress,update_s,update_scenes=self.applyStrain_getStressTangentDEM(st=D)
+      err=1.0 # initial error before iteration
+      converged=(err<rtol)
+      while (not converged) and (iterate<iter_max):
+         if self.__verbose:
+            print "Not converged after %d iteration(s)! Relative error: %e"%(iterate,err)
+         iterate+=1
+         self.__domain.setX(x_safe+u)
+         self.__pde.setValue(A=update_s,X=-update_stress,r=escript.Data())
+         #residual=util.L2(self.__pde.getRightHandSide())
+         du=self.__pde.getSolution()
+         u+=du
+         l,d=util.L2(u),util.L2(du)
+         err=d/l # displacement error, alternatively using force error 'residual'
+         converged=(err<rtol)
+         if err>rtol*0.001: # only update DEM parts when error is large enough
+            self.__domain.setX(x_safe)
+            D=util.grad(u)
+            update_stress,update_s,update_scenes=self.applyStrain_getStressTangentDEM(st=D)
+
+         #if err>err_safe: # to ensure consistent convergence, however this may not be achieved due to fluctuation!
+         #   raise RuntimeError,"No improvement of convergence with iterations! Relative error: %e"%err
+      """
+      update 'domain geometry', 'stress', 'tangent operator',
+      'accumulated strain' and 'simulation scenes'.
+      """
+      self.__domain.setX(x_safe+u)
+      self.__stress=update_stress
+      self.__S=update_s
+      self.__strain+=D
+      self.__scenes=update_scenes
+      if self.__verbose:
+         print "Convergence reached after %d iteration(s)! Relative error: %e"%(iterate,err)
+      return u
+      
+   """
+   apply strain to DEM packing,
+   get stress and tangent operator (including two methods)
+   """
+   def applyStrain_getStressTangentDEM(self,st=escript.Data()):
+      st = st.toListOfTuples()
+      st = numpy.array(st).reshape(-1,9)
+      stress = escript.Tensor(0,escript.Function(self.__domain))
+      S = escript.Tensor4(0,escript.Function(self.__domain))
+      scenes = self.__pool.map(shear,zip(self.__scenes,st))
+      st = self.__pool.map(getStressAndTangent,scenes)      
+      for i in xrange(self.__numGaussPoints):
+         stress.setValueOfDataPoint(i,st[i][0])
+         S.setValueOfDataPoint(i,st[i][1])
+      return stress,S,scenes
+      

=== added file 'py/FEMxDEM/msFEMup.py'
--- py/FEMxDEM/msFEMup.py	1970-01-01 00:00:00 +0000
+++ py/FEMxDEM/msFEMup.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,293 @@
+__author__="Ning Guo, ceguo@xxxxxxxxxxxxxx"
+__supervisor__="Jidong Zhao, jzhao@xxxxxx"
+__institution__="The Hong Kong University of Science and Technology"
+
+""" 2D model for multiscale simulation of a 
+hydromechanical system based on u-p formulation;
+iterative scheme (fixed-stress split) is used for
+the coupled PDEs; Newton-Raphson scheme is used to
+solve the nonlinear PDE for displacement, pore
+pressure is solved from the mass conservation equation;
+total stress is a superposition of the effective stress
+and pore pressure."""
+
+# import Escript modules
+import esys.escript as escript
+from esys.escript import util
+from esys.escript.linearPDEs import LinearPDE,SolverOptions
+from simDEM import *
+from itertools import repeat
+
+""" function to return pool for parallelization
+    supporting both MPI (experimental) on distributed
+    memory and multiprocessing on shared memory.
+"""
+def get_pool(mpi=False,threads=1):
+   if mpi: # using MPI
+      from mpipool import MPIPool
+      pool = MPIPool()
+      pool.start()
+      if not pool.is_master():
+         sys.exit(0)
+   elif threads>1: # using multiprocessing
+      from multiprocessing import Pool
+      pool = Pool(processes=threads)
+   else:
+      raise RuntimeError,"Wrong arguments: either mpi=True or threads>1."
+   return pool
+
+class MultiScale(object):
+   """
+   problem description
+   1. displacement:
+   -(A_{ijkl} u_{k,l})_{,j} = -X_{ij,j} + Y_i
+   Neumann boundary: n_j A_{ijkl} u_{k,l} = n_j X_{ij} + y_i
+   Dirichlet boundary: u_i = r_i where q_i > 0
+   :var u: unknown vector, displacement
+   :var A: elastic tensor / tangent operator
+   :var X: tensor, minus old stress
+   :var Y: vector, gamma - grad(p)
+   :var y: vector, Neumann bc traction
+   :var q: vector, Dirichlet bc mask
+   :var r: vector, Dirichlet bc value
+   2. pore pressure:
+   -(A_{ij} p_{,j})_{,i} + D p = Y
+   Neumann boundary: n_j A_{jl} p_{,l} = y
+   Dirichlet boundary: p = r where q > 0
+   :var p: unknown scalar, pore pressure
+   :var A: permeability tensor
+   :var D: scalar, n / (K_f dt)
+   :var Y: scalar, -dot(u)_{i,i} + n p_pre / (K_f dt)
+   :var y: scalar, Neumann bc flux
+   :var q: scalar, Dirichlet bc mask
+   :var r: scalar, Dirichlet bc value
+   """
+   def __init__(self,domain,pore0=0.,perm=1.e-5,kf=2.2e9,dt=0.001,ng=1,useMPI=False,np=1,rtol=1.e-2):
+      """
+      initialization of the problem, i.e. model constructor
+      :param domain: type Domain, domain of the problem
+      :param pore0: type float, initial pore pressure
+      :param perm: type float, d^2/(150 mu_f) in KC equation
+      :param kf: type float, bulk modulus of the fluid
+      :param dt: type float, time step for calculation
+      :param ng: type integer, number of Gauss points
+      :param useMPI: type boolean, use MPI or not
+      :param np: type integer, number of processors
+      :param rtol: type float, relevative tolerance for global convergence
+      """
+      self.__domain=domain
+      self.__upde=LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim())
+      self.__ppde=LinearPDE(domain,numEquations=1,numSolutions=1)
+      # use reduced interpolation for pore pressure
+      self.__ppde.setReducedOrderOn()
+      
+      self.__upde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
+      self.__ppde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
+      self.__upde.setSymmetryOn()
+      self.__ppde.setSymmetryOn()
+      
+      self.__dt=dt
+      self.__bulkFluid=kf
+      self.__numGaussPoints=ng
+      self.__rtol=rtol
+      self.__stress=escript.Tensor(0,escript.Function(domain))
+      self.__S=escript.Tensor4(0,escript.Function(domain))
+      self.__pool=get_pool(mpi=useMPI,threads=np)
+      self.__scenes=self.__pool.map(initLoad,range(ng))
+      st = self.__pool.map(getStressAndTangent2D,self.__scenes)
+      for i in xrange(ng):
+         self.__stress.setValueOfDataPoint(i,st[i][0])
+         self.__S.setValueOfDataPoint(i,st[i][1])
+      self.__strain=escript.Tensor(0,escript.Function(domain))
+      self.__pore=escript.Scalar(pore0,escript.ReducedSolution(domain))
+      self.__pgauss=util.interpolate(pore0,escript.Function(domain))
+      self.__permeability=perm
+      self.__meanStressRate=escript.Scalar(0,escript.Function(domain))
+      self.__r=escript.Vector(0,escript.Solution(domain)) #Dirichlet BC for u
+
+   def initialize(self, b=escript.Data(), f=escript.Data(), umsk=escript.Data(), uvalue=escript.Data(), flux=escript.Data(), pmsk=escript.Data(), pvalue=escript.Data()):
+      """
+      initialize the model for each time step, e.g. assign parameters
+      :param b: type vector, body force on FunctionSpace, e.g. gravity
+      :param f: type vector, boundary traction on FunctionSpace (FunctionOnBoundary)
+      :param umsk: type vector, mask of location for Dirichlet boundary
+      :param uvalue: type vector, specified displacement for Dirichlet boundary
+      """
+      self.__upde.setValue(Y=b,y=f,q=umsk,r=uvalue)
+      self.__ppde.setValue(y=flux,q=pmsk,r=pvalue)
+      self.__r=uvalue                  
+   
+   def getDomain(self):
+      """
+      return model domain
+      """
+      return self.__domain
+      
+   def setTimeStep(self,dt=1.0):
+      self.__dt = dt
+
+   def getCurrentPacking(self,pos=(),time=0,prefix=''):
+      if len(pos) == 0: # output all Gauss points packings
+         self.__pool.map(outputPack,zip(self.__scenes,repeat(time),repeat(prefix)))
+      else: # output selected Gauss points packings
+         scene = [self.__scenes[i] for i in pos]
+         self.__pool.map(outputPack,zip(scene,repeat(time),repeat(prefix)))
+   
+   def getEquivalentPorosity(self):
+      porosity=escript.Scalar(0,escript.Function(self.__domain))
+      p = self.__pool.map(getEquivalentPorosity,self.__scenes)
+      for i in xrange(self.__numGaussPoints):
+         porosity.setValueOfDataPoint(i,p[i])
+      return porosity
+   
+   def getLocalAvgRotation(self):
+      rot=escript.Scalar(0,escript.Function(self.__domain))
+      r = self.__pool.map(avgRotation2D,self.__scenes)
+      for i in xrange(self.__numGaussPoints):
+         rot.setValueOfDataPoint(i,r[i])
+      return rot
+   
+   def getLocalFabric(self):
+      fabric=escript.Tensor(0,escript.Function(self.__domain))
+      f = self.__pool.map(getFabric2D,self.__scenes)
+      for i in xrange(self.__numGaussPoints):
+         fabric.setValueOfDataPoint(i,f[i])
+      return fabric
+   
+   def getCurrentTangent(self):
+      """
+      return current tangent operator
+      type Tensor4 on FunctionSpace
+      """
+      return self.__S
+      
+   def getCurrentStress(self):
+      """
+      return current stress (effective)
+      type: Tensor on FunctionSpace
+      """
+      return self.__stress
+      
+   def getCurrentPore(self):
+      """
+      return current pore pressure
+      type: Scalar on ReducedSolution
+      """
+      return self.__pore
+      
+   def getCurrentStrain(self):
+      """
+      return current strain
+      type: Tensor on FunctionSpace
+      """
+      return self.__strain
+
+   def getCurrentFlux(self):
+      """
+      return current Darcy flux
+      type: Vector on FunctionSpace
+      """
+      n=self.getEquivalentPorosity()
+      perm=self.__permeability*n**3/(1.-n)**2
+      flux=-perm*util.grad(self.__pore)
+      return flux
+   
+   def exitSimulation(self):
+      """finish the whole simulation, exit"""
+      self.__pool.close()
+   
+   def solveSolid(self, p_iter_gauss=escript.Data(), iter_max=50):
+      """
+      solve the pde for displacement using Newton-Ralphson scheme
+      """
+      k=util.kronecker(self.__domain)
+      p=p_iter_gauss*k
+      iterate=0
+      rtol=self.__rtol
+      stress_safe=self.__stress
+      s_safe=self.__S
+      x_safe=self.__domain.getX()
+      self.__upde.setValue(A=s_safe, X=-stress_safe+p, r=self.__r)
+      #residual0=util.L2(self.__pde.getRightHandSide()) # using force error
+      u=self.__upde.getSolution()  # trial solution, displacement
+      D=util.grad(u)               # trial strain tensor
+      # !!!!!! obtain stress and tangent operator from DEM part
+      update_stress,update_s,update_scenes=self.applyStrain_getStressTangentDEM(st=D)
+      err=util.Lsup(u) # initial error before iteration
+      converged=(err<1.e-12)
+      while (not converged) and (iterate<iter_max):
+         #if iterate>iter_max:
+         #   raise RuntimeError,"Convergence for Newton-Raphson failed after %s steps."%(iter_max)
+         iterate+=1
+         self.__domain.setX(x_safe+u)
+         self.__upde.setValue(A=update_s,X=-update_stress+p,r=escript.Data())
+         #residual=util.L2(self.__pde.getRightHandSide())
+         du=self.__upde.getSolution()
+         u+=du
+         l,d=util.L2(u),util.L2(du)
+         err=d/l # displacement error, alternatively using force error 'residual'
+         converged=(err<rtol)
+         if err>rtol**3: # only update DEM parts when error is large enough
+            self.__domain.setX(x_safe)
+            D=util.grad(u)
+            update_stress,update_s,update_scenes=self.applyStrain_getStressTangentDEM(st=D)
+      """reset domain geometry to original until global convergence"""
+      self.__domain.setX(x_safe)
+      return u,D,update_stress,update_s,update_scenes
+   
+   def solve(self, globalIter=10, solidIter=50):
+      """
+      solve the coupled PDE using fixed-stress split method,
+      call solveSolid to get displacement
+      """
+      rtol=self.__rtol
+      x_safe=self.__domain.getX()
+      k=util.kronecker(self.__domain)
+      kdr=util.inner(k,util.tensor_mult(self.__S,k))/4.
+      n=self.getEquivalentPorosity()
+      perm=self.__permeability*n**3/(1.-n)**2*k
+      kf=self.__bulkFluid
+      dt=self.__dt
+      self.__ppde.setValue(A=perm,D=(n/kf+1./kdr)/dt,Y=(n/kf+1./kdr)/dt*self.__pgauss-self.__meanStressRate/kdr)
+      p_iter_old=self.__ppde.getSolution()
+      p_iter_gauss=util.interpolate(p_iter_old,escript.Function(self.__domain))
+      u_old,D,sig,s,scene=self.solveSolid(p_iter_gauss=p_iter_gauss,iter_max=solidIter)
+      converge=False
+      iterate=0
+      while (not converge) and (iterate<globalIter):
+         iterate += 1
+         self.__ppde.setValue(Y=n/kf/dt*self.__pgauss+1./kdr/dt*p_iter_gauss-util.trace(D)/dt)
+         p_iter=self.__ppde.getSolution()
+         p_err=util.L2(p_iter-p_iter_old)/util.L2(p_iter)
+         p_iter_old=p_iter
+         p_iter_gauss=util.interpolate(p_iter,escript.Function(self.__domain))
+         u,D,sig,s,scene=self.solveSolid(p_iter_gauss=p_iter_gauss,iter_max=solidIter)
+         u_err=util.L2(u-u_old)/util.L2(u)
+         u_old=u
+         converge=(u_err<=rtol and p_err <= rtol*.1)
+      self.__meanStressRate=(util.trace(sig-self.__stress)/2.-p_iter_gauss+self.__pgauss)/dt
+      self.__pore=p_iter_old
+      self.__pgauss=p_iter_gauss
+      self.__domain.setX(x_safe+u_old)
+      self.__strain+=D
+      self.__stress=sig
+      self.__S=s
+      self.__scenes=scene
+      return u_old
+
+   """
+   apply strain to DEM packing,
+   get stress and tangent operator
+   """
+   def applyStrain_getStressTangentDEM(self,st=escript.Data()):
+      st = st.toListOfTuples()
+      st = numpy.array(st).reshape(-1,4)
+      stress = escript.Tensor(0,escript.Function(self.__domain))
+      S = escript.Tensor4(0,escript.Function(self.__domain))
+      scenes = self.__pool.map(shear2D,zip(self.__scenes,st))
+      ST = self.__pool.map(getStressAndTangent2D,scenes)
+      for i in xrange(self.__numGaussPoints):
+         stress.setValueOfDataPoint(i,ST[i][0])
+         S.setValueOfDataPoint(i,ST[i][1])
+      return stress,S,scenes
+      

=== added file 'py/FEMxDEM/saveGauss.py'
--- py/FEMxDEM/saveGauss.py	1970-01-01 00:00:00 +0000
+++ py/FEMxDEM/saveGauss.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,32 @@
+"""
+2D/3D Function to output Gauss point tensorial quantities, e.g. stress, strain, fabric.
+Author: Ning Guo <ceguo@xxxxxxxxxxxxxx>
+"""
+def saveGauss2D(name='',pos=(),**kwargs):
+   fout = file(name,'w')
+   for key in kwargs:
+      data = kwargs[key].toListOfTuples()
+      if len(pos)==0:
+         fout.write('%s '%key+str(len(data))+'\n')
+         for i in xrange(len(data)):
+            fout.write(' '.join('%s %s'%x for x in data[i])+'\n')
+      else:
+         fout.write('%s '%key+str(len(pos))+'\n')
+         for i in pos:
+            fout.write(' '.join('%s %s'%x for x in data[i])+'\n')
+   fout.close()
+   
+def saveGauss3D(name='',pos=(),**kwargs):
+   fout = file(name,'w')
+   for key in kwargs:
+      data = kwargs[key].toListOfTuples()
+      if len(pos)==0:
+         fout.write('%s '%key+str(len(data))+'\n')
+         for i in xrange(len(data)):
+            fout.write(' '.join('%s %s %s'%x for x in data[i])+'\n')
+      else:
+         fout.write('%s '%key+str(len(pos))+'\n')
+         for i in pos:
+            fout.write(' '.join('%s %s %s'%x for x in data[i])+'\n')
+   fout.close()
+   

=== added file 'py/FEMxDEM/simDEM.py'
--- py/FEMxDEM/simDEM.py	1970-01-01 00:00:00 +0000
+++ py/FEMxDEM/simDEM.py	2015-03-03 19:06:49 +0000
@@ -0,0 +1,255 @@
+__author__="Ning Guo, ceguo@xxxxxxxxxxxxxx"
+__supervisor__="Jidong Zhao, jzhao@xxxxxx"
+__institution__="The Hong Kong University of Science and Technology"
+
+"""
+DEM part for multiscale simulation which sets up a packing representing
+a material point (RVE) at the Gauss point of the FEM domain and returns
+constitutive responses (updated stress and tangent operator) at this point.
+"""
+# import yade modules
+import sys
+from os.path import expanduser
+sys.path.append(expanduser('~')+'/yade/bin') # path where you have yadeimport.py
+# yadeimport.py is generated by `ln yade-versionNo yadeimport.py`
+from yadeimport import *
+import numpy
+
+def initLoad(ID=0): # where ID identifies the Gauss point location
+   if 1:
+      # All Gauss points import 0.yade.gz resulting in a uniform sample (default)
+      Omega().load('0.yade.gz')
+   else:
+      # Otherwise load different packings to generate random field
+      # resulting in an inherently heterogeneous sample
+      Omega().load(str(ID)+'.yade.gz')
+   Omega().tags['id']=str(ID)
+   return Omega().sceneToString()
+
+def outputPack(param):
+   if len(param) != 3:
+      raise RuntimeError,"No. of param. should be exactly 3. 0: RVE scene; 1: step count; 2: name prefix"
+   Omega().stringToScene(param[0])
+   pos = Omega().tags['id']
+   Omega().save(param[2]+'packing_'+pos+'_'+str(param[1])+'.yade.gz')
+
+def numOfParticles(scene):
+   Omega().stringToScene(scene)
+   return len(Omega().bodies) # !!! for spherical particle packing only
+
+# Apply deformation on 2D DEM packing
+def shear2D(param):
+   if len(param) != 2:
+      raise RuntimeError,"No. of param. should be exactly 2. 0: RVE scene; 1: strain."
+   Omega().stringToScene(param[0])
+   ns=int(max(1e5*numpy.max(numpy.abs(param[1])),2))
+   dstrain = utils.Matrix3(param[1][0],param[1][1],0, param[1][2],param[1][3],0, 0,0,0)
+   Omega().cell.velGrad=dstrain/(ns*Omega().dt)
+   Omega().run(ns,True)
+   Omega().cell.velGrad=utils.Matrix3.Zero
+   return Omega().sceneToString()
+
+# Apply deformation on 3D DEM packing
+def shear3D(param):
+   if len(param) != 2:
+      raise RuntimeError,"No. of param. should be exactly 2. 0: RVE scene; 1: strain."
+   Omega().stringToScene(param[0])
+   ns=int(max(1e5*numpy.max(numpy.abs(param[1])),2))
+   dstrain = utils.Matrix3(param[1][0],param[1][1],param[1][2], param[1][3],param[1][4],param[1][5], param[1][6],param[1][7],param[1][8])
+   Omega().cell.velGrad=dstrain/(ns*Omega().dt)
+   Omega().run(ns,True)
+   Omega().cell.velGrad=utils.Matrix3.Zero
+   return Omega().sceneToString()
+
+""" Used for perturbation method only (2D), deprecated
+def getStressTensor(scene):
+   Omega().stringToScene(scene)
+   stress = utils.getStress()
+   stress = .5*(stress+stress.transpose())
+   return [[stress[0],stress[1]],[stress[3],stress[4]]]
+"""
+
+# get contact normal based fabric tensor
+def getFabric2D(scene):
+   Omega().stringToScene(scene)
+   f = utils.fabricTensor(splitTensor=False,revertSign=False)[0]
+   return [[f[0,0],f[0,1]],[f[1,0],f[1,1]]]
+
+def getFabric3D(scene):
+   Omega().stringToScene(scene)
+   f = utils.fabricTensor(splitTensor=False,revertSign=False)[0]
+   return [[f[0,0],f[0,1],f[0,2]],[f[1,0],f[1,1],f[1,2]],[f[2,0],f[2,1],f[2,2]]]
+
+""" # Used for clumped particle model only
+    # get particle orientation based fabric tensor
+def getParOriFabric(scene):
+   Omega().stringToScene(scene)
+   fab = utils.Matrix3.Zero
+   numPar = 0
+   for b in Omega().bodies:
+      if b.isClump:
+         numPar += 1
+         keys = b.shape.members.keys()
+         pos1 = Omega().bodies[keys[0]].state.pos
+         pos2 = Omega().bodies[keys[1]].state.pos
+         ori = (pos1-pos2).normalized()
+         fab += ori.outer(ori)
+   fab /= numPar
+   return [[fab[0],fab[1]],[fab[3],fab[4]]]
+"""
+
+""" # Used for cohesive particle model only
+    # get the bond breakage number within a packing
+def getDebondingNumber(param):
+   Omega().stringToScene(param[0])
+   num = 0
+   for id1,id2 in param[1]:
+      try:
+         i = Omega().interactions[id1,id2]
+         if not i.isReal():
+            num += 1
+         elif i.phys.cohesionBroken:
+            num += 1
+      except IndexError:
+         num += 1
+   return num
+"""
+
+# get updated stress tensor and tangent operator as a tuple
+# utils.getStressAndTangent() is implemented in Shop.cpp
+def getStressAndTangent2D(scene):
+   Omega().stringToScene(scene)
+   st = utils.getStressAndTangent(symmetry=True)
+   s = st[0]
+   s = .5*(s+s.transpose())
+   t=[[[[0,0],[0,0]],[[0,0],[0,0]]],[[[0,0],[0,0]],[[0,0],[0,0]]]]
+   t[0][0][0][0]=st[1][0,0]
+   t[1][1][0][0]=t[0][0][1][1]=st[1][0,1]
+   t[0][1][0][0]=t[0][0][0][1]=t[1][0][0][0]=t[0][0][1][0]=st[1][0,5]
+   t[1][1][1][1]=st[1][1,1]
+   t[1][1][0][1]=t[0][1][1][1]=t[1][1][1][0]=t[1][0][1][1]=st[1][1,5]
+   t[0][1][0][1]=t[0][1][1][0]=t[1][0][0][1]=t[1][0][1][0]=st[1][5,5]
+   return [[s[0,0],s[0,1]],[s[1,0],s[1,1]]],t
+
+def getStressAndTangent3D(scene):
+   Omega().stringToScene(scene)
+   st = utils.getStressAndTangent(symmetry=True)
+   s = st[0]
+   s = .5*(s+s.transpose())
+   t = numpy.zeros((3,3,3,3))
+   t[0][0][0][0]=st[1][0,0]
+   t[0][0][1][1]=t[1][1][0][0]=st[1][0,1]
+   t[0][0][2][2]=t[2][2][0][0]=st[1][0,2]
+   t[0][0][1][2]=t[0][0][2][1]=t[1][2][0][0]=t[2][1][0][0]=st[1][0,3]
+   t[0][0][0][2]=t[0][0][2][0]=t[0][2][0][0]=t[2][0][0][0]=st[1][0,4]
+   t[0][0][0][1]=t[0][0][1][0]=t[0][1][0][0]=t[1][0][0][0]=st[1][0,5]
+   t[1][1][1][1]=st[1][1,1]
+   t[1][1][2][2]=t[2][2][1][1]=st[1][1,2]
+   t[1][1][1][2]=t[1][1][2][1]=t[1][2][1][1]=t[2][1][1][1]=st[1][1,3]
+   t[1][1][0][2]=t[1][1][2][0]=t[0][2][1][1]=t[2][0][1][1]=st[1][1,4]
+   t[1][1][0][1]=t[1][1][1][0]=t[0][1][1][1]=t[1][0][1][1]=st[1][1,5]
+   t[2][2][2][2]=st[1][2,2]
+   t[2][2][1][2]=t[2][2][2][1]=t[1][2][2][2]=t[2][1][2][2]=st[1][2,3]
+   t[2][2][0][2]=t[2][2][2][0]=t[0][2][2][2]=t[2][0][2][2]=st[1][2,4]
+   t[2][2][0][1]=t[2][2][1][0]=t[0][1][2][2]=t[1][0][2][2]=st[1][2,5]
+   t[1][2][1][2]=t[1][2][2][1]=t[2][1][1][2]=t[2][1][2][1]=st[1][3,3]
+   t[1][2][0][2]=t[1][2][2][0]=t[2][1][0][2]=t[2][1][2][0]=t[0][2][1][2]=t[2][0][1][2]=t[0][2][2][1]=t[2][0][2][1]=st[1][3,4]
+   t[1][2][0][1]=t[1][2][1][0]=t[2][1][0][1]=t[2][1][1][0]=t[0][1][1][2]=t[1][0][1][2]=t[0][1][2][1]=t[1][0][2][1]=st[1][3,5]
+   t[0][2][0][2]=t[2][0][0][2]=t[0][2][2][0]=t[2][0][2][0]=st[1][4,4]
+   t[0][2][0][1]=t[0][2][1][0]=t[2][0][0][1]=t[2][0][1][0]=t[0][1][0][2]=t[1][0][0][2]=t[0][1][2][0]=t[1][0][2][0]=st[1][4,5]
+   t[0][1][0][1]=t[0][1][1][0]=t[1][0][0][1]=t[1][0][1][0]=st[1][5,5]
+   return [[s[0,0],s[0,1],s[0,2]],[s[1,0],s[1,1],s[1,2]],[s[2,0],s[2,1],s[2,2]]],t
+
+# utils.voidratio2D() is implemented in Shop.cpp
+# to get plane void ratio (for 2D test only)   
+def getVoidRatio2D(scene):
+   Omega().stringToScene(scene)
+   zSize = Omega().cell.hSize[2,2]
+   return utils.voidratio2D(zlen=zSize)
+
+def getEquivalentPorosity(scene):
+   Omega().stringToScene(scene)
+   zSize = Omega().cell.hSize[2,2]
+   e = utils.voidratio2D(zlen=zSize)
+   return e/(1.+e)
+   
+def getVoidRatio3D(scene):
+   Omega().stringToScene(scene)
+   p = utils.porosity()
+   return p/(1.0-p)
+
+# get average rotation of the particles within a packing
+def avgRotation2D(scene):
+   Omega().stringToScene(scene)
+   rot = 0.0
+   for b in Omega().bodies:
+      rot += b.state.rot()[2]
+   rot /= len(Omega().bodies)
+   return rot
+   
+def avgRotation3D(scene):
+   Omega().stringToScene(scene)
+   rot = utils.Vector3.Zero
+   for b in Omega().bodies:
+      rot += b.state.rot()
+   rot /= len(Omega().bodies)
+   return [rot[0],rot[1],rot[2]]
+
+""" Used for perturbation method only (2D), deprecated   
+def getTangentOperator(param):
+   if len(param)!=2:
+      raise RuntimeError,"No. of param. should be exactly 2. 0: RVE scene; 1: perturbation."
+   Omega().stringToScene(param[0])
+   pos = Omega().tags['id']
+   perturbation = param[1]
+   t=[[[[0,0],[0,0]],[[0,0],[0,0]]],[[[0,0],[0,0]],[[0,0],[0,0]]]]
+   ns=int(max(1e5*abs(perturbation),2))
+   stress0 = utils.getStress()
+   stress0 = .5*(stress0+stress0.transpose())
+   #00
+   strain=utils.Matrix3(perturbation,0,0, 0,0,0, 0,0,0)
+   Omega().cell.velGrad=strain/(ns*Omega().dt)
+   Omega().run(ns,True)
+   stress1 = utils.getStress()
+   stress1 = .5*(stress1+stress1.transpose())
+   t[0][0][0][0]=(stress1[0]-stress0[0])/perturbation
+   t[1][1][0][0]=(stress1[4]-stress0[4])/perturbation
+   t[0][1][0][0]=t[1][0][0][0]=(stress1[1]-stress0[1])/perturbation
+   Omega().stringToScene(param[0])
+   #11
+   strain=utils.Matrix3(0,0,0, 0,perturbation,0, 0,0,0)
+   Omega().cell.velGrad=strain/(ns*Omega().dt)
+   Omega().run(ns,True)
+   stress1=utils.getStress()
+   stress1=.5*(stress1+stress1.transpose())
+   t[0][0][1][1]=(stress1[0]-stress0[0])/perturbation
+   t[1][1][1][1]=(stress1[4]-stress0[4])/perturbation
+   t[0][1][1][1]=t[1][0][1][1]=(stress1[1]-stress0[1])/perturbation
+   Omega().stringToScene(param[0])
+   #01
+   strain=utils.Matrix3(0,perturbation,0, 0,0,0, 0,0,0)
+   Omega().cell.velGrad=strain/(ns*Omega().dt)
+   Omega().run(ns,True)
+   stress1=utils.getStress()
+   stress1=.5*(stress1+stress1.transpose())
+   t[0][0][0][1]=(stress1[0]-stress0[0])/perturbation
+   t[1][1][0][1]=(stress1[4]-stress0[4])/perturbation
+   t[0][1][0][1]=t[1][0][0][1]=(stress1[1]-stress0[1])/perturbation
+   Omega().stringToScene(param[0])
+   #10
+   strain=utils.Matrix3(0,0,0, perturbation,0,0, 0,0,0)
+   Omega().cell.velGrad=strain/(ns*Omega().dt)
+   Omega().run(ns,True)
+   stress1=utils.getStress()
+   stress1=.5*(stress1+stress1.transpose())
+   t[0][0][1][0]=(stress1[0]-stress0[0])/perturbation
+   t[1][1][1][0]=(stress1[4]-stress0[4])/perturbation
+   t[0][1][1][0]=t[1][0][1][0]=(stress1[1]-stress0[1])/perturbation
+   #symmetrize
+   t[0][0][1][1]=t[1][1][0][0]=(t[0][0][1][1]+t[1][1][0][0])*0.5
+   t[0][1][0][0]=t[1][0][0][0]=t[0][0][1][0]=t[0][0][0][1]=(t[0][1][0][0]*2+t[0][0][0][1]+t[0][0][1][0])*0.25
+   t[0][1][0][1]=t[0][1][1][0]=t[1][0][0][1]=t[1][0][1][0]=(t[0][1][1][0]+t[0][1][0][1])*0.5
+   t[0][1][1][1]=t[1][0][1][1]=t[1][1][0][1]=t[1][1][1][0]=(t[0][1][1][1]*2+t[1][1][0][1]+t[1][1][1][0])*0.25
+   return t
+"""
+

=== modified file 'py/_utils.cpp'
--- py/_utils.cpp	2015-02-06 18:24:54 +0000
+++ py/_utils.cpp	2015-03-03 19:06:49 +0000
@@ -410,6 +410,10 @@
 	return ret;
 }
 
+Real Shop__getSpheresVolume2D(int mask=-1){ return Shop::getSpheresVolume2D(Omega::instance().getScene(), mask=mask);}
+Real Shop__getVoidRatio2D(Real zlen=1){ return Shop::getVoidRatio2D(Omega::instance().getScene(),zlen);}
+py::tuple Shop__getStressAndTangent(Real volume=0, bool symmetry=true){return Shop::getStressAndTangent(volume,symmetry);}
+
 BOOST_PYTHON_MODULE(_utils){
 	// http://numpy.scipy.org/numpydoc/numpy-13.html mentions this must be done in module init, otherwise we will crash
 	import_array();
@@ -474,4 +478,7 @@
 	py::def("TetrahedronWithLocalAxesPrincipal",TetrahedronWithLocalAxesPrincipal,"TODO");
 	py::def("momentum",Shop::momentum,"TODO");
 	py::def("angularMomentum",Shop::angularMomentum,(py::args("origin")=Vector3r(Vector3r::Zero())),"TODO");
+	py::def("getSpheresVolume2D",Shop__getSpheresVolume2D,(py::arg("mask")=-1),"Compute the total volume of discs in the simulation (might crash for now if dynamic bodies are not discs), mask parameter is considered");
+	py::def("voidratio2D",Shop__getVoidRatio2D,(py::arg("zlen")=1),"Compute 2D packing void ratio $\\frac{V-V_s}{V_s}$ where $V$ is overall volume and $V_s$ is volume of disks.\n\n:param float zlen: length in the third direction.\n");
+	py::def("getStressAndTangent",Shop__getStressAndTangent,(py::args("volume")=0,py::args("symmetry")=true),"Compute overall stress of periodic cell using the same equation as function getStress. In addition, the tangent operator is calculated using the equation published in [Kruyt and Rothenburg1998]_:\n\n.. math:: S_{ijkl}=\\frac{1}{V}\\sum_{c}(k_n n_i l_j n_k l_l + k_t t_i l_j t_k l_l)\n\n:param float volume: same as in function getStress\n:param bool symmetry: make the tensors symmetric.\n\n:return: macroscopic stress tensor and tangent operator as py::tuple");
 }