From 68e52121396015322f679f5067e7a567211bbe3e Mon Sep 17 00:00:00 2001 From: wolf Date: Fri, 31 Aug 2001 19:47:58 +0000 Subject: [PATCH] FETools::lexicographic_to_hierarchic and other way round. git-svn-id: https://svn.dealii.org/trunk@4928 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/deal.II/include/fe/fe_tools.h | 74 +++- deal.II/deal.II/source/fe/fe_q.cc | 2 +- deal.II/deal.II/source/fe/fe_tools.cc | 416 +++++++++++++++++++++ deal.II/doc/news/2001/c-3-1.html | 12 + tests/fe/numbering.cc | 119 +++++- tests/fe/numbering.checked | 512 ++++++++++++++++++++++++++ 6 files changed, 1122 insertions(+), 13 deletions(-) diff --git a/deal.II/deal.II/include/fe/fe_tools.h b/deal.II/deal.II/include/fe/fe_tools.h index 963a011877..b063585bf9 100644 --- a/deal.II/deal.II/include/fe/fe_tools.h +++ b/deal.II/deal.II/include/fe/fe_tools.h @@ -19,6 +19,7 @@ template class FullMatrix; template class FiniteElement; template class DoFHandler; template class Vector; +template class FE_Q; #include @@ -193,8 +194,77 @@ class FETools const Vector &z1, const DoFHandler &dof2, Vector &z2); - - + + /** + * The numbering of the degrees + * of freedom in continous finite + * elements is hierarchic, + * i.e. in such a way that we + * first number the vertex dofs, + * in the order of the vertices + * as defined by the + * triangulation, then the line + * dofs in the order and + * respecting the direction of + * the lines, then the dofs on + * quads, etc. However, we could + * have, as well, numbered them + * in a lexicographic way, + * i.e. with indices first + * running in x-direction, then + * in y-direction and finally in + * z-direction. Discontinuous + * elements of class @ref{FE_DGQ} + * are numbered in this way, for + * example. + * + * This function constructs a + * table which lexicographic + * index each degree of freedom + * in the hierarchic numbering + * would have. It operates on the + * continuous finite element + * given as first argument, and + * outputs the lexicographic + * indices in the second. + * + * Note that since this function + * uses specifics of the + * continuous finite elements, it + * can only operate on objects of + * type @ref{FE_Q}. + * + * It is assumed that the size of + * the output argument already + * matches the correct size, + * which is equal to the number + * of degrees of freedom in the + * finite element. + */ + template + static void + hierarchic_to_lexicographic_numbering (const FE_Q &fe, + std::vector &h2l); + + /** + * This is the reverse function + * to the above one, generating + * the map from the lexicographic + * to the hierarchical + * numbering. All the remarks + * made about the above function + * are also valid here. + */ + template + static void + lexicographic_to_hierarchic_numbering (const FE_Q &fe, + std::vector &l2h); + + /** + * Exception + */ + DeclException0 (ExcInvalidFE); + /** * Exception */ diff --git a/deal.II/deal.II/source/fe/fe_q.cc b/deal.II/deal.II/source/fe/fe_q.cc index bc90a386c2..d6c9b9695f 100644 --- a/deal.II/deal.II/source/fe/fe_q.cc +++ b/deal.II/deal.II/source/fe/fe_q.cc @@ -25,7 +25,7 @@ -//TODO:[WB] move build_renumbering to FiniteElementData class +//TODO:[RH] move build_renumbering to FiniteElementData class template FE_Q::FE_Q (const unsigned int degree) diff --git a/deal.II/deal.II/source/fe/fe_tools.cc b/deal.II/deal.II/source/fe/fe_tools.cc index 339e1f7fc0..b986c74638 100644 --- a/deal.II/deal.II/source/fe/fe_tools.cc +++ b/deal.II/deal.II/source/fe/fe_tools.cc @@ -19,6 +19,7 @@ #include #include #include +#include #include #include #include @@ -299,6 +300,412 @@ void FETools::extrapolate(const DoFHandler &dof1, +template +void +FETools::hierarchic_to_lexicographic_numbering (const FE_Q &fe, + std::vector &h2l) +{ + Assert (fe.n_components() == 1, ExcInvalidFE()); + Assert (h2l.size() == fe.dofs_per_cell, + ExcDimensionMismatch (h2l.size(), fe.dofs_per_cell)); + + const unsigned int dofs_per_cell = fe.dofs_per_cell; + // polynomial degree + const unsigned int degree = fe.dofs_per_line+1; + // number of grid points in each + // direction + const unsigned int n = degree+1; + + // the following lines of code are + // somewhat odd, due to the way the + // hierarchic numbering is + // organized. if someone would + // really want to understand these + // lines, you better draw some + // pictures where you indicate the + // indices and orders of vertices, + // lines, etc, along with the + // numbers of the degrees of + // freedom in hierarchical and + // lexicographical order + switch (dim) + { + case 1: + { + h2l[0] = 0; + h2l[1] = dofs_per_cell-1; + for (unsigned int i=2; i +void +FETools::lexicographic_to_hierarchic_numbering (const FE_Q &fe, + std::vector &l2h) +{ + // note: this function does the + // reverse operation of the + // previous one. nevertheless, they + // have been written independently + // from each other. the test + // "fe/numbering" checks that the + // output of the two functions is + // indeed the reverse of each other + // by checking that the + // concatenation of the two maps is + // the identity operation + // + // The experienced code reader will + // note that this function was not + // written by the same author than + // the previous one (although the + // author of the previous function + // cleaned up this if-block a + // little bit by introducing the + // arrays of numbers). Therefore, + // both authors have experienced + // the downsides of the hierarchic + // numbering of degrees of freedom + // in deal.II. Just to also provide + // some fun while reading code, + // here is the rant of the author + // of this function about the + // author of the previous one: + // + // "Unfortunately, somebody + // switched the upper corner points + // of a quad. The same person + // decided to find a very creative + // numbering of the vertices of a + // hexahedron. Therefore, this code + // looks quite sophisticated." + // + // NB: The "accused" same person + // claims to have had good reasons + // then, but seems to have + // forgotten about them. At least, + // the numbering was discussed with + // the complaining person back then + // when all began :-) + Assert (fe.n_components() == 1, ExcInvalidFE()); + Assert (l2h.size() == fe.dofs_per_cell, + ExcDimensionMismatch (l2h.size(), fe.dofs_per_cell)); + // polynomial degree + const unsigned int degree = fe.dofs_per_line+1; + // number of grid points in each + // direction + const unsigned int n = degree+1; + + if (degree > 0) + { + Assert (fe.dofs_per_vertex == 1, ExcInternalError()); + for (unsigned int i=0; i::vertices_per_cell; ++i) + { + unsigned int index = 0; + // Find indices of vertices. + switch (dim) + { + case 1: + { + const unsigned int values[GeometryInfo<1>::vertices_per_cell] + = { 0, degree }; + index = values[i]; + break; + }; + + case 2: + { + const unsigned int values[GeometryInfo<2>::vertices_per_cell] + = { 0, degree, n*degree+degree, n*degree }; + index = values[i]; + break; + }; + + case 3: + { + const unsigned int values[GeometryInfo<3>::vertices_per_cell] + = { 0, degree, + n*n*degree + degree, n*n*degree, + n*degree, n*degree+degree, + n*n*degree + n*degree+degree, n*n*degree + n*degree}; + index = values[i]; + break; + }; + + default: + Assert(false, ExcNotImplemented()); + } + + l2h[index] = i; + } + }; + + // for degree 2 and higher: Lines, + // quads, hexes etc also carry + // degrees of freedom + if (degree > 1) + { + Assert (fe.dofs_per_line == degree-1, ExcInternalError()); + Assert ((fe.dofs_per_quad == (degree-1)*(degree-1)) || + (dim < 2), ExcInternalError()); + Assert ((fe.dofs_per_hex == (degree-1)*(degree-1)*(degree-1)) || + (dim < 3), ExcInternalError()); + + for (int i=0; i(GeometryInfo::lines_per_cell); ++i) + { + unsigned int index = fe.first_line_index + i*fe.dofs_per_line; + unsigned int incr = 0; + unsigned int tensorstart = 0; + // This again looks quite + // strange because of the odd + // numbering scheme. + switch (i+100*dim) + { + // lines in x-direction + case 100: + case 200: case 202: + case 300: case 302: case 304: case 306: + incr = 1; + break; + // lines in y-direction + case 201: case 203: + case 308: case 309: case 310: case 311: + incr = n; + break; + // lines in z-direction + case 301: case 303: case 305: case 307: + incr = n*n; + break; + default: + Assert(false, ExcNotImplemented()); + } + switch (i+100*dim) + { + // x=y=z=0 + case 100: + case 200: case 203: + case 300: case 303: case 308: + tensorstart = 0; + break; + // x=1 y=z=0 + case 201: + case 301: case 309: + tensorstart = degree; + break; + // y=1 x=z=0 + case 202: + case 304: case 307: + tensorstart = n*degree; + break; + // x=z=1 y=0 + case 310: + tensorstart = n*n*degree+degree; + break; + // z=1 x=y=0 + case 302: case 311: + tensorstart = n*n*degree; + break; + // x=y=1 z=0 + case 305: + tensorstart = n*degree+degree; + break; + // y=z=1 x=0 + case 306: + tensorstart = n*n*n-n; + break; + default: + Assert(false, ExcNotImplemented()); + } + + for (unsigned int jx = 1; jx(GeometryInfo::quads_per_cell); ++i) + { + unsigned int index = fe.first_quad_index+i*fe.dofs_per_quad; + unsigned int tensorstart = 0; + unsigned int incx = 0; + unsigned int incy = 0; + switch (i) + { + case 0: + tensorstart = 0; incx = 1; + if (dim==2) + incy = n; + else + incy = n*n; + break; + case 1: + tensorstart = n*degree; incx = 1; incy = n*n; + break; + case 2: + tensorstart = 0; incx = 1; incy = n; + break; + case 3: + tensorstart = degree; incx = n; incy = n*n; + break; + case 4: + tensorstart = n*n*degree; incx = 1; incy = n; + break; + case 5: + tensorstart = 0; incx = n; incy = n*n; + break; + default: + Assert(false, ExcNotImplemented()); + } + + for (unsigned int jy = 1; jy(GeometryInfo::hexes_per_cell); ++i) + { + unsigned int index = fe.first_hex_index; + + for (unsigned int jz = 1; jz &, const Vector &, const DoFHandler &, Vector &); +template +void +FETools::hierarchic_to_lexicographic_numbering (const FE_Q &fe, + std::vector &h2l); +template +void +FETools::lexicographic_to_hierarchic_numbering (const FE_Q &fe, + std::vector &h2l); + /*---------------------------- fe_tools.cc ---------------------------*/ diff --git a/deal.II/doc/news/2001/c-3-1.html b/deal.II/doc/news/2001/c-3-1.html index b81d6ad75f..532206ed11 100644 --- a/deal.II/doc/news/2001/c-3-1.html +++ b/deal.II/doc/news/2001/c-3-1.html @@ -573,6 +573,18 @@ documentation, etc.

deal.II

    +

  1. + New: There are now two functions + FETools::hierarchic_to_lexicographic_numbering + and FETools::lexicographic_to_hierarchic_numbering + which map the hierarchical numbering used in continuous finite + element classes to a lexicographical numbering and back. +
    + (WB 2001/08/31) +

    +

  2. New: ConstraintMatrix::close now simply returns instead of throwing an exception, if the diff --git a/tests/fe/numbering.cc b/tests/fe/numbering.cc index faa2277643..273e6498ba 100644 --- a/tests/fe/numbering.cc +++ b/tests/fe/numbering.cc @@ -1,11 +1,13 @@ // $Id$ // Author: Wolfgang Bangerth, 2001 // -// Check the numbering of finite elements +// Check the numbering of continuous Lagrange finite elements. it +// constructs and independent numbering and compares it with the +// result of two functions from the library #include #include -#include +#include #include #include @@ -59,7 +61,8 @@ void check (const FE_Q &fe) for (unsigned int i=0; i &fe) break; }; + case 3: + { + unsigned int next_index = 0; + // first the eight vertices + hierarchic_to_lexicographic_numbering[next_index++] = 0; + hierarchic_to_lexicographic_numbering[next_index++] = n-1; + hierarchic_to_lexicographic_numbering[next_index++] = (n-1)*(n*n+1); + hierarchic_to_lexicographic_numbering[next_index++] = (n-1)*n*n; + hierarchic_to_lexicographic_numbering[next_index++] = n*(n-1); + hierarchic_to_lexicographic_numbering[next_index++] = n*n-1; + hierarchic_to_lexicographic_numbering[next_index++] = n*n*n-1; + hierarchic_to_lexicographic_numbering[next_index++] = (n-1)*(n*n+n); + + for (unsigned int i=0; i & - lexicographic_to_hierarchical_numbering = fe.get_renumber(); + // now check with data from the + // lib: there we have the mapping + // the other way round, and we + // check that the concatenation of + // the two mappings is the + // identity. output the two maps to + // generate some output for + // automatic comparison + std::vector l2h (fe.dofs_per_cell); + FETools::lexicographic_to_hierarchic_numbering (fe, l2h); for (unsigned int i=0; i h2l (fe.dofs_per_cell); + FETools::hierarchic_to_lexicographic_numbering (fe, h2l); + Assert (hierarchic_to_lexicographic_numbering == h2l, + ExcInternalError()); }; @@ -92,7 +190,7 @@ void check (const FE_Q &fe) template void check_dim () { - for (unsigned int degree=1; degree<4; ++degree) + for (unsigned int degree=1; degree<6; ++degree) { FE_Q fe(degree); check (fe); @@ -109,6 +207,7 @@ int main () check_dim<1> (); check_dim<2> (); + check_dim<3> (); }; diff --git a/tests/fe/numbering.checked b/tests/fe/numbering.checked index 446d3561d3..d2ea63be45 100644 --- a/tests/fe/numbering.checked +++ b/tests/fe/numbering.checked @@ -8,6 +8,17 @@ 1d, degree=3: 2 3 1d, degree=3: 3 1 1d, degree=3: 1 2 +1d, degree=4: 0 0 +1d, degree=4: 2 4 +1d, degree=4: 3 1 +1d, degree=4: 4 2 +1d, degree=4: 1 3 +1d, degree=5: 0 0 +1d, degree=5: 2 5 +1d, degree=5: 3 1 +1d, degree=5: 4 2 +1d, degree=5: 5 3 +1d, degree=5: 1 4 2d, degree=1: 0 0 2d, degree=1: 1 1 2d, degree=1: 3 3 @@ -37,3 +48,504 @@ 2d, degree=3: 8 6 2d, degree=3: 9 9 2d, degree=3: 2 10 +2d, degree=4: 0 0 +2d, degree=4: 4 4 +2d, degree=4: 5 24 +2d, degree=4: 6 20 +2d, degree=4: 1 1 +2d, degree=4: 13 2 +2d, degree=4: 16 3 +2d, degree=4: 17 9 +2d, degree=4: 18 14 +2d, degree=4: 7 19 +2d, degree=4: 14 21 +2d, degree=4: 19 22 +2d, degree=4: 20 23 +2d, degree=4: 21 5 +2d, degree=4: 8 10 +2d, degree=4: 15 15 +2d, degree=4: 22 6 +2d, degree=4: 23 7 +2d, degree=4: 24 8 +2d, degree=4: 9 11 +2d, degree=4: 3 12 +2d, degree=4: 10 13 +2d, degree=4: 11 16 +2d, degree=4: 12 17 +2d, degree=4: 2 18 +2d, degree=5: 0 0 +2d, degree=5: 4 5 +2d, degree=5: 5 35 +2d, degree=5: 6 30 +2d, degree=5: 7 1 +2d, degree=5: 1 2 +2d, degree=5: 16 3 +2d, degree=5: 20 4 +2d, degree=5: 21 11 +2d, degree=5: 22 17 +2d, degree=5: 23 23 +2d, degree=5: 8 29 +2d, degree=5: 17 31 +2d, degree=5: 24 32 +2d, degree=5: 25 33 +2d, degree=5: 26 34 +2d, degree=5: 27 6 +2d, degree=5: 9 12 +2d, degree=5: 18 18 +2d, degree=5: 28 24 +2d, degree=5: 29 7 +2d, degree=5: 30 8 +2d, degree=5: 31 9 +2d, degree=5: 10 10 +2d, degree=5: 19 13 +2d, degree=5: 32 14 +2d, degree=5: 33 15 +2d, degree=5: 34 16 +2d, degree=5: 35 19 +2d, degree=5: 11 20 +2d, degree=5: 3 21 +2d, degree=5: 12 22 +2d, degree=5: 13 25 +2d, degree=5: 14 26 +2d, degree=5: 15 27 +2d, degree=5: 2 28 +3d, degree=1: 0 0 +3d, degree=1: 1 1 +3d, degree=1: 4 5 +3d, degree=1: 5 4 +3d, degree=1: 3 2 +3d, degree=1: 2 3 +3d, degree=1: 7 7 +3d, degree=1: 6 6 +3d, degree=2: 0 0 +3d, degree=2: 8 2 +3d, degree=2: 1 20 +3d, degree=2: 16 18 +3d, degree=2: 22 6 +3d, degree=2: 17 8 +3d, degree=2: 4 26 +3d, degree=2: 12 24 +3d, degree=2: 5 1 +3d, degree=2: 11 11 +3d, degree=2: 20 19 +3d, degree=2: 9 9 +3d, degree=2: 25 7 +3d, degree=2: 26 17 +3d, degree=2: 23 25 +3d, degree=2: 15 15 +3d, degree=2: 21 3 +3d, degree=2: 13 5 +3d, degree=2: 3 23 +3d, degree=2: 10 21 +3d, degree=2: 2 10 +3d, degree=2: 19 16 +3d, degree=2: 24 4 +3d, degree=2: 18 14 +3d, degree=2: 7 22 +3d, degree=2: 14 12 +3d, degree=2: 6 13 +3d, degree=3: 0 0 +3d, degree=3: 8 3 +3d, degree=3: 9 51 +3d, degree=3: 1 48 +3d, degree=3: 24 12 +3d, degree=3: 40 15 +3d, degree=3: 41 63 +3d, degree=3: 26 60 +3d, degree=3: 25 1 +3d, degree=3: 42 2 +3d, degree=3: 43 19 +3d, degree=3: 27 35 +3d, degree=3: 4 49 +3d, degree=3: 16 50 +3d, degree=3: 17 16 +3d, degree=3: 5 32 +3d, degree=3: 14 13 +3d, degree=3: 32 14 +3d, degree=3: 33 31 +3d, degree=3: 10 47 +3d, degree=3: 52 61 +3d, degree=3: 56 62 +3d, degree=3: 57 28 +3d, degree=3: 44 44 +3d, degree=3: 53 4 +3d, degree=3: 58 8 +3d, degree=3: 59 7 +3d, degree=3: 45 11 +3d, degree=3: 22 55 +3d, degree=3: 36 59 +3d, degree=3: 37 52 +3d, degree=3: 18 56 +3d, degree=3: 15 17 +3d, degree=3: 34 18 +3d, degree=3: 35 33 +3d, degree=3: 11 34 +3d, degree=3: 54 29 +3d, degree=3: 60 30 +3d, degree=3: 61 45 +3d, degree=3: 46 46 +3d, degree=3: 55 5 +3d, degree=3: 62 6 +3d, degree=3: 63 9 +3d, degree=3: 47 10 +3d, degree=3: 23 23 +3d, degree=3: 38 27 +3d, degree=3: 39 39 +3d, degree=3: 19 43 +3d, degree=3: 3 53 +3d, degree=3: 12 54 +3d, degree=3: 13 57 +3d, degree=3: 2 58 +3d, degree=3: 30 20 +3d, degree=3: 48 24 +3d, degree=3: 49 36 +3d, degree=3: 28 40 +3d, degree=3: 31 21 +3d, degree=3: 50 22 +3d, degree=3: 51 25 +3d, degree=3: 29 26 +3d, degree=3: 7 37 +3d, degree=3: 20 38 +3d, degree=3: 21 41 +3d, degree=3: 6 42 +3d, degree=4: 0 0 +3d, degree=4: 8 4 +3d, degree=4: 9 104 +3d, degree=4: 10 100 +3d, degree=4: 1 20 +3d, degree=4: 32 24 +3d, degree=4: 62 124 +3d, degree=4: 63 120 +3d, degree=4: 64 1 +3d, degree=4: 35 2 +3d, degree=4: 33 3 +3d, degree=4: 65 29 +3d, degree=4: 66 54 +3d, degree=4: 67 79 +3d, degree=4: 36 101 +3d, degree=4: 34 102 +3d, degree=4: 68 103 +3d, degree=4: 69 25 +3d, degree=4: 70 50 +3d, degree=4: 37 75 +3d, degree=4: 4 21 +3d, degree=4: 20 22 +3d, degree=4: 21 23 +3d, degree=4: 22 49 +3d, degree=4: 5 74 +3d, degree=4: 17 99 +3d, degree=4: 44 121 +3d, degree=4: 45 122 +3d, degree=4: 46 123 +3d, degree=4: 11 45 +3d, degree=4: 89 70 +3d, degree=4: 98 95 +3d, degree=4: 99 5 +3d, degree=4: 100 10 +3d, degree=4: 71 15 +3d, degree=4: 90 9 +3d, degree=4: 101 14 +3d, degree=4: 102 19 +3d, degree=4: 103 109 +3d, degree=4: 72 114 +3d, degree=4: 91 119 +3d, degree=4: 104 105 +3d, degree=4: 105 110 +3d, degree=4: 106 115 +3d, degree=4: 73 26 +3d, degree=4: 29 27 +3d, degree=4: 53 28 +3d, degree=4: 54 51 +3d, degree=4: 55 52 +3d, degree=4: 23 53 +3d, degree=4: 18 76 +3d, degree=4: 47 77 +3d, degree=4: 48 78 +3d, degree=4: 49 46 +3d, degree=4: 12 47 +3d, degree=4: 92 48 +3d, degree=4: 107 71 +3d, degree=4: 108 72 +3d, degree=4: 109 73 +3d, degree=4: 74 96 +3d, degree=4: 93 97 +3d, degree=4: 110 98 +3d, degree=4: 111 6 +3d, degree=4: 112 7 +3d, degree=4: 75 8 +3d, degree=4: 94 11 +3d, degree=4: 113 12 +3d, degree=4: 114 13 +3d, degree=4: 115 16 +3d, degree=4: 76 17 +3d, degree=4: 30 18 +3d, degree=4: 56 34 +3d, degree=4: 57 39 +3d, degree=4: 58 44 +3d, degree=4: 24 59 +3d, degree=4: 19 64 +3d, degree=4: 50 69 +3d, degree=4: 51 84 +3d, degree=4: 52 89 +3d, degree=4: 13 94 +3d, degree=4: 95 106 +3d, degree=4: 116 107 +3d, degree=4: 117 108 +3d, degree=4: 118 111 +3d, degree=4: 77 112 +3d, degree=4: 96 113 +3d, degree=4: 119 116 +3d, degree=4: 120 117 +3d, degree=4: 121 118 +3d, degree=4: 78 30 +3d, degree=4: 97 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