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Commit 2cc1ac29 authored by Matti Pellika's avatar Matti Pellika
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Update demo

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/*********************************************************************
*
* Gmsh tutorial 10
* Gmsh tutorial
*
* Homology computation
* Homology and cohomology computation
*
*********************************************************************/
// Homology computation in Gmsh finds representative chains of
// (relative) homology spaces using a mesh of a model. Those
// representatives generate the (relative) homology spaces of the
// model. Alternatively, Gmsh can only look for the ranks of the
// (relative) homology spaces, the Betti numbers of the model.
// The generators chains are stored in a given .msh-file as physical
// groups, whose mesh elements are oriented such that their
// coefficients are 1 in the generator chain.
// (relative) (co)homology space bases using a mesh of a model.
// The representative basis chains are stored in the mesh as
// physical groups of Gmsh, one for each chain.
// Create an example geometry
......@@ -134,27 +129,40 @@ Physical Surface(74) = {46, 18, 20, 52, 22, 50, 24, 48, 66, 63, 60, 58, 56, 54};
Physical Surface(75) = {46, 63, 66, 52, 50, 48, 54, 60, 58, 56};
// Create a mesh of the model
Mesh 3;
// Find generators of relative homology spaces of the domain modulo the
// four terminals.
// Save the generator chains to t10_hom.msh.
HomGen("t10_hom.msh") = {{69}, {70, 71, 72, 73}};
// Find bases for relative homology spaces of
// the domain modulo the four terminals.
Homology {{69}, {70, 71, 72, 73}};
// Find the corresponding thin cuts,
// generators of relative homology spaces modulo the
// non-terminal domain surface.
// Save the cut chains to t10_hom.msh.
HomGen("t10_hom.msh") = {{69}, {75}};
// Find homology space bases isomorphic to the previous bases:
// homology spaces modulo the non-terminal domain surface,
// a.k.a the thin cuts.
Homology {{69}, {75}};
// Find the corresponding thick cuts.
// Save the cut chains to t10_hom.msh.
HomCut("t10_hom.msh") = {{69}, {70, 71, 72, 73}};
// Find cohomology space bases isomorphic to the previous bases:
// cohomology spaces of the domain modulo the four terminals,
// a.k.a the thick cuts.
Cohomology {{69}, {70, 71, 72, 73}};
// More examples (uncomment):
// HomGen("t10_hom.msh") = {{69}, {}};
// HomGen("t10_hom.msh") = {{}, {}};
// HomGen("t10_hom.msh") = {{69}, {74}};
// HomGen("t10_hom.msh") = {{}, {74}};
// Homology = {{69}, {}};
// Homology {{69}, {74}};
// Homology {{74}, {70, 71, 72, 73}};
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