/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
>>
>
>
