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Add iso element on a tetrahedron #688

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merged 9 commits into from
Aug 17, 2023
Merged

Add iso element on a tetrahedron #688

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15299d6
Hard code degree 1 macro polynomials on a triangle
mscroggs Aug 15, 2023
0c652c0
cell types for iso
mscroggs Aug 16, 2023
0531620
correct basis functions
mscroggs Aug 16, 2023
0eb4882
decimals not std::sqrt
mscroggs Aug 16, 2023
4c90290
Add degree 2 macro edge polyset on a triangle
mscroggs Aug 16, 2023
8bdbfdb
Start working on iso on a tet
mscroggs Aug 16, 2023
4dcd147
Merge branch 'main' into mscroggs/macro-tet
mscroggs Aug 16, 2023
ac6d5da
Update README
mscroggs Aug 16, 2023
357f3d7
correct polyset
mscroggs Aug 17, 2023
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2 changes: 2 additions & 0 deletions README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -92,6 +92,7 @@ The following elements are supported on a triangle:
- [Crouzeix-Raviart](https://defelement.com/elements/crouzeix-raviart.html)
- [Bubble](https://defelement.com/elements/bubble.html)
- [Hermite](https://defelement.com/elements/hermite.html)
- [iso](https://defelement.com/elements/p1-iso-p2.html)


### Quadrilateral
Expand Down Expand Up @@ -132,6 +133,7 @@ The following elements are supported on a tetrahedron:
- [Crouzeix-Raviart](https://defelement.com/elements/crouzeix-raviart.html)
- [Bubble](https://defelement.com/elements/bubble.html)
- [Hermite](https://defelement.com/elements/hermite.html)
- [iso](https://defelement.com/elements/p1-iso-p2.html)


### Hexahedron
Expand Down
339 changes: 339 additions & 0 deletions cpp/basix/polyset.cpp
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Expand Up @@ -931,6 +931,340 @@ void tabulate_polyset_triangle_macroedge_derivs(
}
//-----------------------------------------------------------------------------
/// Compute the complete set of derivatives from 0 to nderiv, for all
/// the piecewise polynomials up to order n on a tetrahedron split into 8 by
/// splitting each edge into two parts
template <typename T>
void tabulate_polyset_tetrahedron_macroedge_derivs(
stdex::mdspan<T, stdex::dextents<std::size_t, 3>> P, std::size_t n,
std::size_t nderiv,
stdex::mdspan<const T, stdex::dextents<std::size_t, 2>> x)
{
assert(x.extent(0) > 0);
assert(P.extent(0) == nderiv + 1);
assert(P.extent(1) == (n + 1) * (2 * n + 1) * (2 * n + 3) / 3);
assert(P.extent(2) == x.extent(0));

auto x0 = stdex::submdspan(x, stdex::full_extent, 0);
auto x1 = stdex::submdspan(x, stdex::full_extent, 1);
auto x2 = stdex::submdspan(x, stdex::full_extent, 2);

std::fill(P.data_handle(), P.data_handle() + P.size(), 0.0);

if (n == 0)
{
for (std::size_t p = 0; p < P.extent(2); ++p)
P(idx(0, 0), 0, p) = std::sqrt(6);
}
else if (n == 1)
{
for (std::size_t p = 0; p < P.extent(2); ++p)
{
if (x0[p] + x1[p] + x2[p] < 0.5)
{
P(idx(0, 0), 0, p) = 21.908902300206645 - 43.81780460041329 * x2[p]
- 43.81780460041329 * x1[p]
- 43.81780460041329 * x0[p];
P(idx(0, 0), 4, p) = -5.855400437691199 + 11.710800875382398 * x2[p]
+ 11.710800875382398 * x1[p]
+ 35.1324026261472 * x0[p];
P(idx(0, 0), 5, p) = -3.1326068447244277 + 6.2652136894488555 * x2[p]
+ 25.75698961217863 * x1[p]
- 0.6961348543832062 * x0[p];
P(idx(0, 0), 6, p) = -4.079436335011508 + 32.853642355761124 * x2[p]
+ 3.359535805303594 * x1[p]
+ 4.581185189050355 * x0[p];
P(idx(0, 0), 7, p) = 1.6490105505038288 - 7.300270809207225 * x2[p]
- 8.666892660787566 * x1[p]
- 0.5229420350434975 * x0[p];
P(idx(0, 0), 8, p) = 3.365373344712382 - 10.492441445989503 * x2[p]
- 11.258215021433038 * x1[p]
- 11.903076979701279 * x0[p];
P(idx(0, 0), 9, p) = 0.8017837257372732 + 2.6726124191242437 * x2[p]
- 5.3452248382484875 * x1[p]
- 5.3452248382484875 * x0[p];
if (nderiv >= 1)
{
P(idx(0, 0, 1), 0, p) = -43.81780460041329;
P(idx(0, 0, 1), 4, p) = 11.710800875382398;
P(idx(0, 0, 1), 5, p) = 6.2652136894488555;
P(idx(0, 0, 1), 6, p) = 32.853642355761124;
P(idx(0, 0, 1), 7, p) = -7.300270809207225;
P(idx(0, 0, 1), 8, p) = -10.492441445989503;
P(idx(0, 0, 1), 9, p) = 2.6726124191242437;
P(idx(0, 1, 0), 0, p) = -43.81780460041329;
P(idx(0, 1, 0), 4, p) = 11.710800875382398;
P(idx(0, 1, 0), 5, p) = 25.75698961217863;
P(idx(0, 1, 0), 6, p) = 3.359535805303594;
P(idx(0, 1, 0), 7, p) = -8.666892660787566;
P(idx(0, 1, 0), 8, p) = -11.258215021433038;
P(idx(0, 1, 0), 9, p) = -5.3452248382484875;
P(idx(1, 0, 0), 0, p) = -43.81780460041329;
P(idx(1, 0, 0), 4, p) = 35.1324026261472;
P(idx(1, 0, 0), 5, p) = -0.6961348543832062;
P(idx(1, 0, 0), 6, p) = 4.581185189050355;
P(idx(1, 0, 0), 7, p) = -0.5229420350434975;
P(idx(1, 0, 0), 8, p) = -11.903076979701279;
P(idx(1, 0, 0), 9, p) = -5.3452248382484875;
}
}
else if (x0[p] > 0.5)
{
P(idx(0, 0), 1, p) = -21.908902300206645 + 43.81780460041329 * x0[p];
P(idx(0, 0), 4, p) = 29.277002188455995 - 23.421601750764797 * x2[p]
- 23.421601750764797 * x1[p]
- 35.1324026261472 * x0[p];
P(idx(0, 0), 5, p) = -8.701685679790078 + 6.961348543832062 * x2[p]
+ 6.961348543832062 * x1[p]
+ 10.442022815748093 * x0[p];
P(idx(0, 0), 6, p) = -4.472109351215823 + 3.5776874809726587 * x2[p]
+ 3.5776874809726587 * x1[p]
+ 5.366531221458988 * x0[p];
P(idx(0, 0), 7, p) = 3.4688488324552 - 2.77507906596416 * x2[p]
- 2.77507906596416 * x1[p]
- 4.16261859894624 * x0[p];
P(idx(0, 0), 8, p) = -1.148660363165304 + 26.439340288997876 * x2[p]
+ 5.172330290276515 * x1[p]
- 2.8750095639459072 * x0[p];
P(idx(0, 0), 9, p) = 0.8017837257372732 + 29.398736610366683 * x1[p]
- 5.3452248382484875 * x0[p];
if (nderiv >= 1)
{
P(idx(0, 0, 1), 4, p) = -23.421601750764797;
P(idx(0, 0, 1), 5, p) = 6.961348543832062;
P(idx(0, 0, 1), 6, p) = 3.5776874809726587;
P(idx(0, 0, 1), 7, p) = -2.77507906596416;
P(idx(0, 0, 1), 8, p) = 26.439340288997876;
P(idx(0, 1, 0), 4, p) = -23.421601750764797;
P(idx(0, 1, 0), 5, p) = 6.961348543832062;
P(idx(0, 1, 0), 6, p) = 3.5776874809726587;
P(idx(0, 1, 0), 7, p) = -2.77507906596416;
P(idx(0, 1, 0), 8, p) = 5.172330290276515;
P(idx(0, 1, 0), 9, p) = 29.398736610366683;
P(idx(1, 0, 0), 1, p) = 43.81780460041329;
P(idx(1, 0, 0), 4, p) = -35.1324026261472;
P(idx(1, 0, 0), 5, p) = 10.442022815748093;
P(idx(1, 0, 0), 6, p) = 5.366531221458988;
P(idx(1, 0, 0), 7, p) = -4.16261859894624;
P(idx(1, 0, 0), 8, p) = -2.8750095639459072;
P(idx(1, 0, 0), 9, p) = -5.3452248382484875;
}
}
else if (x1[p] > 0.5)
{
P(idx(0, 0), 2, p) = -21.908902300206645 + 43.81780460041329 * x1[p];
P(idx(0, 0), 5, p) = 24.36471990341222 - 19.491775922729772 * x2[p]
- 29.237663884094662 * x1[p]
- 19.491775922729772 * x0[p];
P(idx(0, 0), 6, p) = -5.999171080899275 + 4.79933686471942 * x2[p]
+ 7.199005297079131 * x1[p]
+ 4.79933686471942 * x0[p];
P(idx(0, 0), 7, p) = -0.4985380734081343 + 30.219077065046907 * x2[p]
- 4.371795412963639 * x1[p]
+ 5.368871559779907 * x0[p];
P(idx(0, 0), 8, p) = -6.952417987579472 - 0.6448619582682409 * x2[p]
+ 9.377367643150668 * x1[p]
+ 4.527468332008274 * x0[p];
P(idx(0, 0), 9, p) = 0.8017837257372732 - 5.3452248382484875 * x1[p]
+ 29.398736610366683 * x0[p];
if (nderiv >= 1)
{
P(idx(0, 0, 1), 5, p) = -19.491775922729772;
P(idx(0, 0, 1), 6, p) = 4.79933686471942;
P(idx(0, 0, 1), 7, p) = 30.219077065046907;
P(idx(0, 0, 1), 8, p) = -0.6448619582682409;
P(idx(0, 1, 0), 2, p) = 43.81780460041329;
P(idx(0, 1, 0), 5, p) = -29.237663884094662;
P(idx(0, 1, 0), 6, p) = 7.199005297079131;
P(idx(0, 1, 0), 7, p) = -4.371795412963639;
P(idx(0, 1, 0), 8, p) = 9.377367643150668;
P(idx(0, 1, 0), 9, p) = -5.3452248382484875;
P(idx(1, 0, 0), 5, p) = -19.491775922729772;
P(idx(1, 0, 0), 6, p) = 4.79933686471942;
P(idx(1, 0, 0), 7, p) = 5.368871559779907;
P(idx(1, 0, 0), 8, p) = 4.527468332008274;
P(idx(1, 0, 0), 9, p) = 29.398736610366683;
}
}
else if (x2[p] > 0.5)
{
P(idx(0, 0), 3, p) = -21.908902300206645 + 43.81780460041329 * x2[p];
P(idx(0, 0), 6, p) = 30.868462107172636 - 37.04215452860716 * x2[p]
- 24.69476968573811 * x1[p]
- 24.69476968573811 * x0[p];
P(idx(0, 0), 7, p) = 1.209739241067291 - 6.421728190334149 * x2[p]
+ 28.85245521346657 * x1[p]
+ 4.002249708199567 * x0[p];
P(idx(0, 0), 8, p) = -0.6784485185947118 - 2.4047977193753147 * x2[p]
- 1.4106355337117769 * x1[p]
+ 25.0287047552861 * x0[p];
P(idx(0, 0), 9, p) = 3.474396144861517 - 2.6726124191242437 * x2[p]
- 8.017837257372731 * x1[p]
- 8.017837257372731 * x0[p];
if (nderiv >= 1)
{
P(idx(0, 0, 1), 3, p) = 43.81780460041329;
P(idx(0, 0, 1), 6, p) = -37.04215452860716;
P(idx(0, 0, 1), 7, p) = -6.421728190334149;
P(idx(0, 0, 1), 8, p) = -2.4047977193753147;
P(idx(0, 0, 1), 9, p) = -2.6726124191242437;
P(idx(0, 1, 0), 6, p) = -24.69476968573811;
P(idx(0, 1, 0), 7, p) = 28.85245521346657;
P(idx(0, 1, 0), 8, p) = -1.4106355337117769;
P(idx(0, 1, 0), 9, p) = -8.017837257372731;
P(idx(1, 0, 0), 6, p) = -24.69476968573811;
P(idx(1, 0, 0), 7, p) = 4.002249708199567;
P(idx(1, 0, 0), 8, p) = 25.0287047552861;
P(idx(1, 0, 0), 9, p) = -8.017837257372731;
}
}
else if (x1[p] + x2[p] < 0.5 && x0[p] + x1[p] < 0.5)
{
P(idx(0, 0), 4, p) = 11.710800875382398 - 23.421601750764797 * x2[p]
- 23.421601750764797 * x1[p];
P(idx(0, 0), 5, p) = -3.480674271916031 + 6.961348543832062 * x2[p]
+ 26.453124466561835 * x1[p];
P(idx(0, 0), 6, p) = 10.558541102382724 + 3.5776874809726587 * x2[p]
- 25.91641906948487 * x1[p]
- 24.69476968573811 * x0[p];
P(idx(0, 0), 7, p) = -0.6135853211177037 - 2.77507906596416 * x2[p]
- 4.1417009175445 * x1[p]
+ 4.002249708199567 * x0[p];
P(idx(0, 0), 8, p) = -15.100517522781306 + 26.439340288997876 * x2[p]
+ 25.67356671355434 * x1[p]
+ 25.0287047552861 * x0[p];
P(idx(0, 0), 9, p) = 2.138089935299395 - 8.017837257372731 * x1[p]
- 8.017837257372731 * x0[p];
if (nderiv >= 1)
{
P(idx(0, 0, 1), 4, p) = -23.421601750764797;
P(idx(0, 0, 1), 5, p) = 6.961348543832062;
P(idx(0, 0, 1), 6, p) = 3.5776874809726587;
P(idx(0, 0, 1), 7, p) = -2.77507906596416;
P(idx(0, 0, 1), 8, p) = 26.439340288997876;
P(idx(0, 1, 0), 4, p) = -23.421601750764797;
P(idx(0, 1, 0), 5, p) = 26.453124466561835;
P(idx(0, 1, 0), 6, p) = -25.91641906948487;
P(idx(0, 1, 0), 7, p) = -4.1417009175445;
P(idx(0, 1, 0), 8, p) = 25.67356671355434;
P(idx(0, 1, 0), 9, p) = -8.017837257372731;
P(idx(1, 0, 0), 6, p) = -24.69476968573811;
P(idx(1, 0, 0), 7, p) = 4.002249708199567;
P(idx(1, 0, 0), 8, p) = 25.0287047552861;
P(idx(1, 0, 0), 9, p) = -8.017837257372731;
}
}
else if (x1[p] + x2[p] < 0.5)
{
P(idx(0, 0), 4, p) = 11.710800875382398 - 23.421601750764797 * x2[p]
- 23.421601750764797 * x1[p];
P(idx(0, 0), 5, p) = 6.2652136894488555 + 6.961348543832062 * x2[p]
+ 6.961348543832062 * x1[p]
- 19.491775922729772 * x0[p];
P(idx(0, 0), 6, p) = -4.18851217284604 + 3.5776874809726587 * x2[p]
+ 3.5776874809726587 * x1[p]
+ 4.79933686471942 * x0[p];
P(idx(0, 0), 7, p) = -1.2968962469078738 - 2.77507906596416 * x2[p]
- 2.77507906596416 * x1[p]
+ 5.368871559779907 * x0[p];
P(idx(0, 0), 8, p) = -4.849899311142394 + 26.439340288997876 * x2[p]
+ 5.172330290276515 * x1[p]
+ 4.527468332008274 * x0[p];
P(idx(0, 0), 9, p) = -16.57019699857031 + 29.398736610366683 * x1[p]
+ 29.398736610366683 * x0[p];
if (nderiv >= 1)
{
P(idx(0, 0, 1), 4, p) = -23.421601750764797;
P(idx(0, 0, 1), 5, p) = 6.961348543832062;
P(idx(0, 0, 1), 6, p) = 3.5776874809726587;
P(idx(0, 0, 1), 7, p) = -2.77507906596416;
P(idx(0, 0, 1), 8, p) = 26.439340288997876;
P(idx(0, 1, 0), 4, p) = -23.421601750764797;
P(idx(0, 1, 0), 5, p) = 6.961348543832062;
P(idx(0, 1, 0), 6, p) = 3.5776874809726587;
P(idx(0, 1, 0), 7, p) = -2.77507906596416;
P(idx(0, 1, 0), 8, p) = 5.172330290276515;
P(idx(0, 1, 0), 9, p) = 29.398736610366683;
P(idx(1, 0, 0), 5, p) = -19.491775922729772;
P(idx(1, 0, 0), 6, p) = 4.79933686471942;
P(idx(1, 0, 0), 7, p) = 5.368871559779907;
P(idx(1, 0, 0), 8, p) = 4.527468332008274;
P(idx(1, 0, 0), 9, p) = 29.398736610366683;
}
}
else if (x0[p] + x1[p] > 0.5)
{
P(idx(0, 0), 5, p) = 19.491775922729772 - 19.491775922729772 * x2[p]
- 19.491775922729772 * x1[p]
- 19.491775922729772 * x0[p];
P(idx(0, 0), 6, p) = -4.79933686471942 + 4.79933686471942 * x2[p]
+ 4.79933686471942 * x1[p]
+ 4.79933686471942 * x0[p];
P(idx(0, 0), 7, p) = -17.793974312413408 + 30.219077065046907 * x2[p]
+ 30.219077065046907 * x1[p]
+ 5.368871559779907 * x0[p];
P(idx(0, 0), 8, p) = 8.692201812490664 - 0.6448619582682409 * x2[p]
- 21.9118719569896 * x1[p]
+ 4.527468332008274 * x0[p];
P(idx(0, 0), 9, p) = -16.57019699857031 + 29.398736610366683 * x1[p]
+ 29.398736610366683 * x0[p];
if (nderiv >= 1)
{
P(idx(0, 0, 1), 5, p) = -19.491775922729772;
P(idx(0, 0, 1), 6, p) = 4.79933686471942;
P(idx(0, 0, 1), 7, p) = 30.219077065046907;
P(idx(0, 0, 1), 8, p) = -0.6448619582682409;
P(idx(0, 1, 0), 5, p) = -19.491775922729772;
P(idx(0, 1, 0), 6, p) = 4.79933686471942;
P(idx(0, 1, 0), 7, p) = 30.219077065046907;
P(idx(0, 1, 0), 8, p) = -21.9118719569896;
P(idx(0, 1, 0), 9, p) = 29.398736610366683;
P(idx(1, 0, 0), 5, p) = -19.491775922729772;
P(idx(1, 0, 0), 6, p) = 4.79933686471942;
P(idx(1, 0, 0), 7, p) = 5.368871559779907;
P(idx(1, 0, 0), 8, p) = 4.527468332008274;
P(idx(1, 0, 0), 9, p) = 29.398736610366683;
}
}
else
{
P(idx(0, 0), 5, p) = 9.745887961364886 - 19.491775922729772 * x2[p];
P(idx(0, 0), 6, p) = 9.947716410509344 + 4.79933686471942 * x2[p]
- 24.69476968573811 * x1[p]
- 24.69476968573811 * x0[p];
P(idx(0, 0), 7, p) = -17.110663386623237 + 30.219077065046907 * x2[p]
+ 28.85245521346657 * x1[p]
+ 4.002249708199567 * x0[p];
P(idx(0, 0), 8, p) = -1.5584163991482487 - 0.6448619582682409 * x2[p]
- 1.4106355337117769 * x1[p]
+ 25.0287047552861 * x0[p];
P(idx(0, 0), 9, p) = 2.138089935299395 - 8.017837257372731 * x1[p]
- 8.017837257372731 * x0[p];
if (nderiv >= 1)
{
P(idx(0, 0, 1), 5, p) = -19.491775922729772;
P(idx(0, 0, 1), 6, p) = 4.79933686471942;
P(idx(0, 0, 1), 7, p) = 30.219077065046907;
P(idx(0, 0, 1), 8, p) = -0.6448619582682409;
P(idx(0, 1, 0), 6, p) = -24.69476968573811;
P(idx(0, 1, 0), 7, p) = 28.85245521346657;
P(idx(0, 1, 0), 8, p) = -1.4106355337117769;
P(idx(0, 1, 0), 9, p) = -8.017837257372731;
P(idx(1, 0, 0), 6, p) = -24.69476968573811;
P(idx(1, 0, 0), 7, p) = 4.002249708199567;
P(idx(1, 0, 0), 8, p) = 25.0287047552861;
P(idx(1, 0, 0), 9, p) = -8.017837257372731;
}
}
}
}
else
{
throw std::runtime_error("Only degree 0 and 1 macro polysets are currently "
"implemented on a tetrahedron.");
}
}
//-----------------------------------------------------------------------------
/// Compute the complete set of derivatives from 0 to nderiv, for all
/// the piecewise polynomials up to order n on a hexahedron split into 4 by
/// splitting each edge into two parts
template <typename T>
Expand Down Expand Up @@ -2682,6 +3016,9 @@ void polyset::tabulate(
case cell::type::triangle:
tabulate_polyset_triangle_macroedge_derivs(P, d, n, x);
return;
case cell::type::tetrahedron:
tabulate_polyset_tetrahedron_macroedge_derivs(P, d, n, x);
return;
case cell::type::quadrilateral:
tabulate_polyset_quadrilateral_macroedge_derivs(P, d, n, x);
return;
Expand Down Expand Up @@ -2760,6 +3097,8 @@ int polyset::dim(cell::type celltype, polyset::type ptype, int d)
return 2 * d + 1;
case cell::type::triangle:
return (d + 1) * (2 * d + 1);
case cell::type::tetrahedron:
return (d + 1) * (2 * d + 1) * (2 * d + 3) / 3;
case cell::type::quadrilateral:
return (2 * d + 1) * (2 * d + 1);
case cell::type::hexahedron:
Expand Down
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