void
TestInterpolationHDiv<Dim>::testInterpolation()
{
// expr to interpolate
int is3D = 0;
if( Dim == 3 )
is3D = 1;
auto myexpr = unitX() + unitY() + is3D*unitZ() ; //(1,1)
auto mesh = loadMesh( _mesh=new Mesh<Simplex<Dim>> );
space_ptrtype Xh = space_type::New( mesh ); // RT function space
auto u_on = Xh->element();
auto u_proj = Xh->element();
//test on keyword
u_on.on(_range=elements(mesh), _expr=myexpr);
//test project keyword
u_proj = vf::project(_space=Xh, _range=elements(mesh), _expr=myexpr);
//L2 norm of error
auto error_on = vf::project(_space=Xh, _range=elements(mesh), _expr=myexpr - idv(u_on) );
double L2error_on = error_on.l2Norm();
std::cout << "[on] L2 error = " << L2error_on << std::endl;
auto error_proj = vf::project(_space=Xh, _range=elements(mesh), _expr=myexpr - idv(u_proj) );
double L2error_proj = error_proj.l2Norm();
std::cout << "[proj] L2 error = " << L2error_proj << std::endl;
}
void
TestInterpolationHDiv<Dim>::testInterpolationOneElt( std::string one_element_mesh )
{
// expr to interpolate
int is3D = 0;
if( Dim == 3 )
is3D = 1;
auto myexpr = unitX() + unitY() + is3D*unitZ() ; //(1,1)
// one element mesh
auto mesh_name = one_element_mesh + ".msh"; //create the mesh and load it
fs::path mesh_path( mesh_name );
mesh_ptrtype oneelement_mesh = loadMesh( _mesh=new mesh_type,
_filename=mesh_name);
// refined mesh (export)
auto refine_level = std::floor(1 - math::log( 0.1 )); //Deduce refine level from meshSize (option)
mesh_ptrtype mesh = loadMesh( _mesh=new mesh_type,
_filename=mesh_name,
_refine=( int )refine_level);
space_ptrtype Xh = space_type::New( oneelement_mesh );
//std::cout << "nb dof = " << Xh->nDof() << std::endl;
std::vector<std::string> faces;
if(Dim == 2)
faces = { "hypo","vert","hor"};
else if (Dim == 3)
faces = {"xzFace","xyFace","xyzFace","yzFace"};
element_type U_h_int = Xh->element();
element_type U_h_on = Xh->element();
// handly computed interpolant coeff (in hdiv basis)
for ( int i = 0; i < Xh->nLocalDof(); ++i )
{
CHECK( mesh->hasMarkers( {faces[i]} ) );
U_h_int(i) = integrate( markedfaces( oneelement_mesh, faces[i] ), trans( N() )*myexpr ).evaluate()(0,0);
}
// raviart-thomas interpolant using on
U_h_on.zero();
U_h_on.on(_range=elements(oneelement_mesh), _expr=myexpr);
auto exporter_proj = exporter( _mesh=mesh, _name=( boost::format( "%1%-%2%" ) % this->about().appName() %mesh_path.stem().string() ).str() );
exporter_proj->step( 0 )->add( "U_interpolation_handly-" + mesh_path.stem().string(), U_h_int );
exporter_proj->step( 0 )->add( "U_interpolation_on-" + mesh_path.stem().string(), U_h_on );
exporter_proj->save();
U_h_int.printMatlab( "U_h_int_" + mesh_path.stem().string() + ".m" );
U_h_on.printMatlab( "U_h_on_" + mesh_path.stem().string() + ".m" );
//L2 norm of error
auto error = vf::project(_space=Xh, _range=elements(oneelement_mesh), _expr=idv(U_h_int) - idv(U_h_on) );
double L2error = error.l2Norm();
std::cout << "L2 error = " << L2error << std::endl;
}
RotationMatrices::RotationMatrices()
{
matrices[0] = math::mat3(1.0f);
math::mat3 rotateZ90 = math::mat3(0, 1, 0, -1, 0, 0, 0, 0, 1);
for (int i = 1; i < 4; ++i)
matrices[i] = matrices[i - 1] * rotateZ90;
math::mat3 rotateXP90 = math::mat3(1, 0, 0, 0, 0, 1, 0, -1, 0);
for (int i = 0; i < 4; ++i)
{
matrices[4 + i] = rotateXP90 * matrices[i];
}
math::mat3 rotateYP90 = math::mat3(0, 0, -1, 0, 1, 0, 1, 0, 0);
for (int i = 0; i < 4; ++i)
{
matrices[8 + i] = rotateYP90 * matrices[i];
}
math::mat3 rotateXN90 = math::mat3(1, 0, 0, 0, 0, -1, 0, 1, 0);
for (int i = 0; i < 4; ++i)
{
matrices[12 + i] = rotateXN90 * matrices[i];
}
math::mat3 rotateYN90 = math::mat3(0, 0, 1, 0, 1, 0, -1, 0, 0);
for (int i = 0; i < 4; ++i)
{
matrices[16 + i] = rotateYN90 * matrices[i];
}
math::mat3 rotateXP180 = rotateXP90 * rotateXP90;
for (int i = 0; i < 4; ++i)
{
matrices[20 + i] = rotateXP180 * matrices[i];
}
math::mat3 neg = math::mat3(1.0) * (-1.0f);
for (int i = 0; i < 24; ++i)
{
matrices[24 + i] = neg * matrices[i];
}
for (int i = 0; i < 48; ++i)
{
invMatrices[i] = math::inverse(matrices[i]);
for (int dir = 0; dir < 6; ++dir)
{
math::vec3 v = dirToVec((Dir) dir);
v = invMatrices[i] * v;
invDirs[i * 6 + dir] = vecToDir(v);
}
}
quadRotations[(int) Dir::XN] = 4;
quadRotations[(int) Dir::XP] = 0;
quadRotations[(int) Dir::YN] = 0;
quadRotations[(int) Dir::YP] = 4;
quadRotations[(int) Dir::ZN] = 4;
quadRotations[(int) Dir::ZP] = 0;
const math::mat2 texMat[8] = {math::mat2(1, 0, 0, 1), math::mat2(0, -1, 1, 0), math::mat2(-1, 0, 0, -1), math::mat2(0, 1, -1, 0), math::mat2(-1, 0, 0, 1), math::mat2(0, -1, -1, 0), math::mat2(1, 0, 0, -1), math::mat2(0, 1, 1, 0)};
math::vec3 unitX(1.0f, 0.0f, 0.0f);
math::vec3 unitY(0.0f, 1.0f, 0.0f);
math::vec3 unitZ(0.0f, 0.0f, 1.0f);
for (int i = 1; i < 48; ++i)
{
for (int dir = 0; dir < 6; ++dir)
{
quadRotations[i * 6 + dir] = 0;
Dir origDir = invDirs[i * 6 + dir];
math::mat3 origMat = textureMatrixToMat3(math::inverse(texMat[quadRotations[(int) origDir]]), origDir);
math::vec3 destUnitX = matrices[i] * origMat * unitX;
math::vec3 destUnitY = matrices[i] * origMat * unitY;
math::vec3 destUnitZ = matrices[i] * origMat * unitZ;
math::vec3 destUnit[2];
int j = 0;
if (math::length(destUnitX) > 0.9)
destUnit[j++] = destUnitX;
if (math::length(destUnitY) > 0.9)
destUnit[j++] = destUnitY;
if (math::length(destUnitZ) > 0.9)
destUnit[j++] = destUnitZ;
assert(j == 2);
int k = 0;
for (; k < 8; ++k)
{
math::vec3 testUnitX = textureMatrixToMat3(math::inverse(texMat[k]), (Dir) dir) * unitX;
math::vec3 testUnitY = textureMatrixToMat3(math::inverse(texMat[k]), (Dir) dir) * unitY;
math::vec3 testUnitZ = textureMatrixToMat3(math::inverse(texMat[k]), (Dir) dir) * unitZ;
math::vec3 testUnit[2];
j = 0;
if (math::length(testUnitX) > 0.9)
testUnit[j++] = testUnitX;
if (math::length(testUnitY) > 0.9)
testUnit[j++] = testUnitY;
if (math::length(testUnitZ) > 0.9)
testUnit[j++] = testUnitZ;
assert(j == 2);
if (testUnit[0] == destUnit[0] && testUnit[1] == destUnit[1])
{
quadRotations[i * 6 + dir] = k;
break;
}
}
assert(k < 8);
}
}
}