ok, I finally got it. Looks like a good solution, but would require some
work for us to implement.
/Anders
Matthew Knepley wrote:
> On 7/9/07, Anders Logg <logg@xxxxxxxxx> wrote:
>>
>>
>> Matthew Knepley wrote:
>> > On 7/9/07, Anders Logg <logg@xxxxxxxxx> wrote:
>> >> It looks to me like the (quad) cell which first has vertices 1-2-5-4
>> >> after the surgery has vertices 1-(0)-(2)-3. What are then the
>> >
>> > Yes.
>> >
>> >> coordinates of vertices (0) and (2)? Same as for 0 and 2, or same as
>> >> original 2 and 5?
>> >
>> > Same as (0) and (2) since no other vertices actually exist in the mesh.
>> > Those are vertices 0 and 2. I put them in parens to emphasize that I
>> > was writing them twice, but they exist only once. Next time I will just
>> > write the Sieves. Much clearer :)
>> >
>> > Matt
>>
>> It still doesn't make sense to me, but maybe I'm just getting tired...
>>
>> If the coordinates of (0) and (2) are the same as those of 0 and 2,
>> won't we get the wrong geometry for the cells on the boundary? Imagine
>> having a much finer grid. Then the cells on the right boundary will
>> stretch all the way back to touch the left boundary.
>
> Yes, but that is why I put in the explanation for calculation of J. With
> the
> exception of coordinate functions (which we can talk about after this),
> you only need J or functions of it. Now, the Jacobian only depends on
> coordinate differences. So you just need something like
>
> dx = (x_1 - x_0) mod L
>
> where L is the periodic length.
>
> Matt
>
>> /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
>> >> >>
>> >> >
>> >> >
>> >>
>> >
>> >
>>
>
>
