/Anders
>> /Anders
>>
>>
>> Matthew Knepley wrote:
>> > Not quite. I am suggesting changing the grid. For instance, lets use
>> > the 3-lines mesh as an example. You start with
>> >
>> > 6--7--8
>> > | | |
>> > 3--4--5
>> > | | |
>> > 0--1--2
>> >
>> > and I suggest doing surgery to produce
>> >
>> > 4--5--(4)
>> > | | |
>> > 2--3--(2)
>> > | | |
>> > 0--1--(0)
>> >
>> > Notice that the edges on the far right are being shown twice. Thus,
>> in the
>> > second mesh there are 6 vertices, 10 edges, and 8 triangles. Then we
>> > discretize on that mesh with my prescription for J.
>> >
>> > Matt
>> >
>> > On 7/9/07, Anders Logg <logg@xxxxxxxxx> wrote:
>> >> Matthew Knepley wrote:
>> >> > On 7/9/07, Anders Logg <logg@xxxxxxxxx> wrote:
>> >> >> Matthew Knepley wrote:
>> >> >> > On 7/9/07, Anders Logg <logg@xxxxxxxxx> wrote:
>> >> >> >> Good point, but I don't see how to do this in DOLFIN without
>> a few
>> >> >> major
>> >> >> >> changes. For example, we assume that each vertex is
>> associated to
>> >> >> >> exactly one coordinate and the local-to-global mappings
that FFC
>> >> >> >> generate are computed in terms of the global number of
vertices,
>> >> edges
>> >> >> >> etc.
>> >> >> >
>> >> >> > I think we can preserve those. Imagine discretizing a
>> cylinder, but
>> >> >> with
>> >> >> > Cartesian coordinates.The connectivity will give the correct
>> >> assembly.
>> >> >>
>> >> >> ok so far...
>> >> >>
>> >> >> > Our only problem is calculation of the Jacobian (I will ignore
>> >> >> coordinate
>> >> >> > functions for now). Since J only depends on coordinate
>> >> differences, it
>> >> >> > is enough to take differences mod L = \pi d. I have
>> implemented this
>> >> >> > for my thesis. It works well and I think its simpler to think
>> about.
>> >> >>
>> >> >> But what about when it's not a cylinder? Say a mesh of the unit
>> square
>> >> >> and its not embedded in 3D.
>> >> >
>> >> > Not sure what you mean here. Everything I said goes through for a
>> >> > discretization of
>> >> >
>> >> > R^k \times S^{n-k}
>> >> >
>> >> > So basically the product of a box and a torus. Do you have
something
>> >> > more complicated?
>> >> >
>> >> > Matt
>> >>
>> >> I'm just thinking of the very simple case of the unit square and
you
>> >> want u(0, y) = u(1, y). Then I think what you suggest is to let's
>> number
>> >> the vertices vertices (and edges) at x = 0 with the same indices as
>> the
>> >> vertices and edges at x = 1. Is this what you suggest?
>> >>
>> >> /Anders
>> >>
>> >>
>> >> >> /Anders
>> >> >>
>> >> >>
>> >> >> > Matt
>> >> >> >
>> >> >> >> Perhaps one could postprocess the system to remove the rows
>> with a
>> >> >> >> single 1 on the diagonal (Dirichlet BCs) and the rows with
a 1
>> >> and -1
>> >> >> >> (periodic BCs)?
>> >> >> >>
>> >> >> >> /Anders
>> >> >> >>
>> >> >> >>
>> >> >> >> Matthew Knepley wrote:
>> >> >> >> > This seems weird to me. When I want periodic boundary
>> conditions,
>> >> >> >> > I just make a periodic mesh. Anything else messes with the
>> system
>> >> >> >> > too much. Making a periodic mesh from a flat one is simple
>> >> surgery.
>> >> >> >> > I agree that you have to modify the computation of element
>> >> geometry,
>> >> >> >> > but that seems to right place to me to account for the
>> embedding.
>> >> >> >> >
>> >> >> >> > Matt
>> >> >> >> >
>> >> >> >> > On 7/9/07, Garth N. Wells <g.n.wells@xxxxxxxxxx> wrote:
>> >> >> >> >>
>> >> >> >> >> Quoting DOLFIN <dolfin@xxxxxxxxxx>:
>> >> >> >> >>
>> >> >> >> >> > One or more new changesets pushed to the primary dolfin
>> >> >> repository.
>> >> >> >> >> > A short summary of the last three changesets is included
>> >> below.
>> >> >> >> >> >
>> >> >> >> >> > changeset:
3306:c70033cb881cb98ef8f177ebf0cb95348de96aa7
>> >> >> >> >> > tag: tip
>> >> >> >> >> > user: "Anders Logg <logg@xxxxxxxxx>"
>> >> >> >> >> > date: Mon Jul 09 19:24:50 2007 +0200
>> >> >> >> >> > files: Makefile.in aclocal.m4 configure
>> src/Makefile.in
>> >> >> >> >> > src/bench/Makefile.in src/bench/fem/Makefile.in
>> >> >> >> >> src/bench/la/Makefile.in
>> >> >> >> >> > src/bench/ode/Makefile.in src/demo/Makefile.in
>> >> >> >> src/greeting/Makefile.in
>> >> >> >> >> > src/kernel/Makefile.in src/kernel/common/Makefile.in
>> >> >> >> >> > src/kernel/common/dolfin/Makefile.in
>> >> >> src/kernel/elements/Makefile.in
>> >> >> >> >> > src/kernel/elements/dolfin/Makefile.in
>> >> >> >> >> src/kernel/fem/BoundaryCondition.cpp
>> >> >> >> >> > src/kernel/fem/Makefile.am src/kernel/fem/Makefile.in
>> >> >> >> >> > src/kernel/fem/PeriodicBoundaryCondition.cpp
>> >> >> >> >> > src/kernel/fem/dolfin/BoundaryCondition.h
>> >> >> >> >> src/kernel/fem/dolfin/Makefile.am
>> >> >> >> >> > src/kernel/fem/dolfin/Makefile.in
>> >> >> >> >> > src/kernel/fem/dolfin/PeriodicBoundaryCondition.h
>> >> >> >> >> > src/kernel/fem/dolfin/dolfin_fem.h
>> >> >> src/kernel/function/Makefile.in
>> >> >> >> >> > src/kernel/function/dolfin/Makefile.in
>> >> >> src/kernel/graph/Makefile.in
>> >> >> >> >> > src/kernel/graph/dolfin/Makefile.in
>> src/kernel/io/Makefile.in
>> >> >> >> >> > src/kernel/io/dolfin/Makefile.in
src/kernel/la/Makefile.in
>> >> >> >> >> > src/kernel/la/dolfin/Makefile.in
src/kernel/log/Makefile.in
>> >> >> >> src/kernel
>> >> >> >> >> > /log/dolfin/Makefile.in src/kernel/main/Makefile.in
>> >> >> >> >> > src/kernel/main/dolfin/Makefile.in
>> src/kernel/math/Makefile.in
>> >> >> >> >> > src/kernel/math/dolfin/Makefile.in
>> src/kernel/mesh/Makefile.in
>> >> >> >> >> > src/kernel/mesh/SubDomain.cpp
>> >> src/kernel/mesh/dolfin/Makefile.in
>> >> >> >> >> > src/kernel/mesh/dolfin/SubDomain.h
>> src/kernel/mf/Makefile.in
>> >> >> >> >> > src/kernel/mf/dolfin/Makefile.in
src/kernel/nls/Makefile.in
>> >> >> >> >> > src/kernel/nls/dolfin/Makefile.in
>> src/kernel/ode/Makefile.in
>> >> >> >> >> > src/kernel/ode/dolfin/Makefile.in
>> >> >> src/kernel/parameter/Makefile.in
>> >> >> >> >> > src/kernel/parameter/dolfin/Makefile.in
>> >> >> src/kernel/pde/Makefile.in
>> >> >> >> >> > src/kernel/pde/dolfin/Makefile.in
>> src/kernel/plot/Makefile.in
>> >> >> >> >> > src/kernel/plot/dolfin/Makefile.in
>> >> >> src/kernel/quadrature/Makefile.in
>> >> >> >> >> > src/kernel/quadrature/dolfin/Makefile.in
>> src/lib/Makefile.in
>> >> >> >> >> > src/pydolfin/Makefile.in src/test/Makefile.in
>> >> >> src/utils/Makefile.in
>> >> >> >> >> > src/utils/convert/Makefile.in
src/utils/inp2dx/Makefile.in
>> >> >> >> >> > src/utils/swig/Makefile.in
>> >> >> >> >> > description:
>> >> >> >> >> > Add support for setting periodic boundary conditions.
>> >> >> >> >> >
>> >> >> >> >> > To set a periodic boundary condition, specify a pair of
>> >> domains
>> >> >> >> >> > G and H by a SubDomain. The inside() function should
>> >> specify the
>> >> >> >> >> > points of G and the map() function should specify a
mapping
>> >> F : H
>> >> >> >> >> --> G.
>> >> >> >> >> >
>> >> >> >> >> > Then create a PeriodicBoundaryCondition and apply() it
>> to the
>> >> >> linear
>> >> >> >> >> system.
>> >> >> >> >> >
>> >> >> >> >> > Bugs/features:
>> >> >> >> >> >
>> >> >> >> >> > 1. Only works for scalar subsystems, so it needs to be
>> done
>> >> >> >> once for
>> >> >> >> >> > each subsystem of a vector function.
>> >> >> >> >> >
>> >> >> >> >> > 2. Setting the entries in the matrix can perhaps be
>> >> optimized.
>> >> >> >> >> >
>> >> >> >> >> > 3. PeriodicBoundaryCondition is not a subclass of
>> >> >> >> BoundaryCondition,
>> >> >> >> >> > so it does not work to give a
>> PeriodicBoundaryCondition as
>> >> >> >> argument
>> >> >> >> >> > to LinearPDE.
>> >> >> >> >> >
>> >> >> >> >> > To fix 3, should we rename BoundaryCondition -->
>> DirichletBC
>> >> >> >> >> > and have PeriodicBC and DirichletBC as subclasses of
>> >> >> >> BoundaryCondition?
>> >> >> >> >> >
>> >> >> >> >>
>> >> >> >> >> Yes, sounds good.
>> >> >> >> >>
>> >> >> >> >> Garth
>> >> >> >> >>
>> >> >> >> >> >
>> >> >> >> >> > changeset:
3305:4564fa57c9159e7dbe287ba121324ec84afd4d00
>> >> >> >> >> > user: "Garth N. Wells <g.n.wells@xxxxxxxxxx>"
>> >> >> >> >> > date: Thu Jul 05 22:24:27 2007 +0200
>> >> >> >> >> > files: src/kernel/la/PETScLUSolver.cpp
>> >> >> >> >> src/kernel/nls/NewtonSolver.cpp
>> >> >> >> >> > src/kernel/nls/dolfin/NewtonSolver.h
>> >> src/kernel/pde/LinearPDE.cpp
>> >> >> >> >> > description:
>> >> >> >> >> > Fix use of PETSc with UMFPACK.
>> >> >> >> >> >
>> >> >> >> >> >
>> >> >> >> >> > changeset:
3304:1a95bb6095dd1b91e462f62a630035defd37c8c6
>> >> >> >> >> > parent:
3303:a324e9cb2c73b27ecd636fcee5b1a08cc01a0da8
>> >> >> >> >> > parent:
3302:cd19d9eeddaa68d14d8c6fafe4de490ff17c1f5a
>> >> >> >> >> > user: "Garth N. Wells <g.n.wells@xxxxxxxxxx>"
>> >> >> >> >> > date: Wed Jul 04 14:38:37 2007 +0200
>> >> >> >> >> > files:
>> >> >> >> >> > description:
>> >> >> >> >> > merge.
>> >> >> >> >> >
>> >> >> >> >> >
>> >> >> >>
>> >>
----------------------------------------------------------------------
>> >> >> >> >> > For more details, visit http://www.fenics.org/hg/dolfin
>> >> >> >> >> > _______________________________________________
>> >> >> >> >> > DOLFIN-dev mailing list
>> >> >> >> >> > DOLFIN-dev@xxxxxxxxxx
>> >> >> >> >> > http://www.fenics.org/mailman/listinfo/dolfin-dev
>> >> >> >> >> >
>> >> >> >> >> _______________________________________________
>> >> >> >> >> DOLFIN-dev mailing list
>> >> >> >> >> DOLFIN-dev@xxxxxxxxxx
>> >> >> >> >> http://www.fenics.org/mailman/listinfo/dolfin-dev
>> >> >> >> >>
>> >> >> >> >
>> >> >> >> >
>> >> >> >>
>> >> >> >>
>> >> >> >
>> >> >> >
>> >> >> _______________________________________________
>> >> >> DOLFIN-dev mailing list
>> >> >> DOLFIN-dev@xxxxxxxxxx
>> >> >> http://www.fenics.org/mailman/listinfo/dolfin-dev
>> >> >>
>> >> >
>> >> >
>> >> _______________________________________________
>> >> DOLFIN-dev mailing list
>> >> DOLFIN-dev@xxxxxxxxxx
>> >> http://www.fenics.org/mailman/listinfo/dolfin-dev
>> >>
>> >
>> >
>>
>
>
