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SyFi
0.3
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SyFi
0.3
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#include <RaviartThomas.h>
Public Member Functions | |
| RaviartThomas () | |
| RaviartThomas (Polygon &p, int order=1, bool pointwise=true) | |
| virtual | ~RaviartThomas () |
| virtual void | compute_basis_functions () |
Public Attributes | |
| bool | pointwise |
| GiNaC::lst | dof_repr |
Definition at line 26 of file RaviartThomas.h.
Definition at line 30 of file RaviartThomas.cpp.
References SyFi::StandardFE::description.
: StandardFE() { description = "RaviartThomas"; }
| SyFi::RaviartThomas::RaviartThomas | ( | Polygon & | p, |
| int | order = 1, |
||
| bool | pointwise = true |
||
| ) |
Definition at line 35 of file RaviartThomas.cpp.
References compute_basis_functions(), and pointwise.
: StandardFE(p, order) { pointwise = pointwise_; compute_basis_functions(); }
| virtual SyFi::RaviartThomas::~RaviartThomas | ( | ) | [inline, virtual] |
Definition at line 33 of file RaviartThomas.h.
{}
| void SyFi::RaviartThomas::compute_basis_functions | ( | ) | [virtual] |
Reimplemented from SyFi::StandardFE.
Definition at line 41 of file RaviartThomas.cpp.
References SyFi::bernstein(), SyFi::bernsteinv(), test_syfi::debug::c, SyFi::collapse(), SyFi::StandardFE::description, dof_repr, SyFi::StandardFE::dofs, SyFi::inner(), SyFi::Line::integrate(), SyFi::Triangle::integrate(), SyFi::Tetrahedron::integrate(), SyFi::interior_coordinates(), SyFi::istr(), SyFi::Triangle::line(), SyFi::matrix_from_equations(), SyFi::normal(), SyFi::StandardFE::Ns, SyFi::StandardFE::order, SyFi::StandardFE::p, pointwise, SyFi::Polygon::str(), SyFi::t, SyFi::Tetrahedron::triangle(), SyFi::Polygon::vertex(), SyFi::x, SyFi::y, and SyFi::z.
Referenced by check_RaviartThomas(), main(), and RaviartThomas().
{
if ( order < 1 )
{
throw(std::logic_error("Raviart-Thomas elements must be of order 1 or higher."));
}
if ( p == NULL )
{
throw(std::logic_error("You need to set a polygon before the basisfunctions can be computed"));
}
// see e.g. Brezzi and Fortin book page 116 for the definition
GiNaC::ex nsymb = GiNaC::symbol("n");
if (pointwise)
{
if ( p->str().find("ReferenceLine") != string::npos )
{
cout <<"Can not define the Raviart-Thomas element on a line"<<endl;
}
else if ( p->str().find("Triangle") != string::npos )
{
description = istr("RaviartThomas_", order) + "_2D";
Triangle& triangle = (Triangle&)(*p);
GiNaC::lst equations;
GiNaC::lst variables;
GiNaC::ex polynom_space1 = bernstein(order-1, triangle, "a");
GiNaC::ex polynom1 = polynom_space1.op(0);
GiNaC::ex polynom1_vars = polynom_space1.op(1);
GiNaC::ex polynom1_basis = polynom_space1.op(2);
GiNaC::lst polynom_space2 = bernsteinv(2,order-1, triangle, "b");
GiNaC::ex polynom2 = polynom_space2.op(0).op(0);
GiNaC::ex polynom3 = polynom_space2.op(0).op(1);
GiNaC::lst pspace = GiNaC::lst( polynom2 + polynom1*x,
polynom3 + polynom1*y);
GiNaC::lst v2 = collapse(GiNaC::ex_to<GiNaC::lst>(polynom_space2.op(1)));
variables = collapse(GiNaC::lst(polynom_space1.op(1), v2));
// remove multiple dofs
if ( order >= 2)
{
GiNaC::ex expanded_pol = GiNaC::expand(polynom1);
for (unsigned int c1=0; c1<= order-2;c1++)
{
for (unsigned int c2=0; c2<= order-2;c2++)
{
for (unsigned int c3=0; c3<= order-2;c3++)
{
if ( c1 + c2 + c3 <= order -2 )
{
GiNaC::ex eq = expanded_pol.coeff(x,c1).coeff(y,c2).coeff(z,c3);
if ( eq != GiNaC::numeric(0) )
{
equations.append(eq == 0);
}
}
}
}
}
}
int removed_dofs = equations.nops();
GiNaC::ex bernstein_pol;
int counter = 0;
GiNaC::symbol t("t");
GiNaC::ex dofi;
// dofs related to edges
for (int i=0; i< 3; i++)
{
Line line = triangle.line(i);
GiNaC::lst normal_vec = normal(triangle, i);
GiNaC::ex Vn = inner(pspace, normal_vec);
GiNaC::lst points = interior_coordinates(line, order-1);
GiNaC::ex edge_length = line.integrate(GiNaC::numeric(1));
GiNaC::ex point;
for (unsigned int j=0; j< points.nops(); j++)
{
point = points.op(j);
dofi = Vn.subs(x == point.op(0)).subs(y == point.op(1))*edge_length;
GiNaC::ex eq = dofi == GiNaC::numeric(0);
equations.append(eq);
dofs.insert(dofs.end(), GiNaC::lst(point,nsymb));
}
}
// dofs related to the whole triangle
if ( order > 1)
{
counter++;
GiNaC::lst points = interior_coordinates(triangle, order-2);
GiNaC::ex point;
for (unsigned int j=0; j< points.nops(); j++)
{
point = points.op(j);
// x -component
dofi = pspace.op(0).subs(x == point.op(0)).subs(y == point.op(1));
GiNaC::ex eq = dofi == GiNaC::numeric(0);
equations.append(eq);
dofs.insert(dofs.end(), GiNaC::lst(point,0));
// y -component
dofi = pspace.op(1).subs(x == point.op(0)).subs(y == point.op(1));
eq = dofi == GiNaC::numeric(0);
equations.append(eq);
dofs.insert(dofs.end(), GiNaC::lst(point,1));
}
}
// std::cout <<"no variables "<<variables.nops()<<std::endl;
// std::cout <<"no equations "<<equations.nops()<<std::endl;
// invert the matrix:
// GiNaC has a bit strange way to invert a matrix.
// It solves the system AA^{-1} = Id.
// It seems that this way is the only way to do
// properly with the solve_algo::gauss flag.
//
GiNaC::matrix b; GiNaC::matrix A;
matrix_from_equations(equations, variables, A, b);
unsigned int ncols = A.cols();
GiNaC::matrix vars_sq(ncols, ncols);
// matrix of symbols
for (unsigned r=0; r<ncols; ++r)
for (unsigned c=0; c<ncols; ++c)
vars_sq(r, c) = GiNaC::symbol();
GiNaC::matrix id(ncols, ncols);
// identity
const GiNaC::ex _ex1(1);
for (unsigned i=0; i<ncols; ++i)
id(i, i) = _ex1;
// invert the matrix
GiNaC::matrix m_inv(ncols, ncols);
m_inv = A.solve(vars_sq, id, GiNaC::solve_algo::gauss);
for (unsigned int i=0; i<dofs.size(); i++)
{
b.let_op(removed_dofs + i) = GiNaC::numeric(1);
GiNaC::ex xx = m_inv.mul(GiNaC::ex_to<GiNaC::matrix>(b));
GiNaC::lst subs;
for (unsigned int ii=0; ii<xx.nops(); ii++)
{
subs.append(variables.op(ii) == xx.op(ii));
}
GiNaC::ex Nj1 = pspace.op(0).subs(subs);
GiNaC::ex Nj2 = pspace.op(1).subs(subs);
Ns.insert(Ns.end(), GiNaC::matrix(2,1,GiNaC::lst(Nj1,Nj2)));
b.let_op(removed_dofs + i) = GiNaC::numeric(0);
}
}
else if ( p->str().find("Tetrahedron") != string::npos )
{
description = istr("RaviartThomas_", order) + "_3D";
Tetrahedron& tetrahedron = (Tetrahedron&)(*p);
GiNaC::lst equations;
GiNaC::lst variables;
GiNaC::ex polynom_space1 = bernstein(order-1, tetrahedron, "a");
GiNaC::ex polynom1 = polynom_space1.op(0);
GiNaC::ex polynom1_vars = polynom_space1.op(1);
GiNaC::ex polynom1_basis = polynom_space1.op(2);
GiNaC::lst polynom_space2 = bernsteinv(3,order-1, tetrahedron, "b");
GiNaC::ex polynom2 = polynom_space2.op(0).op(0);
GiNaC::ex polynom3 = polynom_space2.op(0).op(1);
GiNaC::ex polynom4 = polynom_space2.op(0).op(2);
GiNaC::lst pspace = GiNaC::lst( polynom2 + polynom1*x,
polynom3 + polynom1*y,
polynom4 + polynom1*z);
GiNaC::lst v2 = collapse(GiNaC::ex_to<GiNaC::lst>(polynom_space2.op(1)));
variables = collapse(GiNaC::lst(polynom_space1.op(1), v2));
GiNaC::ex bernstein_pol;
// remove multiple dofs
if ( order >= 2)
{
GiNaC::ex expanded_pol = GiNaC::expand(polynom1);
for (unsigned int c1=0; c1<= order-2;c1++)
{
for (unsigned int c2=0; c2<= order-2;c2++)
{
for (unsigned int c3=0; c3<= order-2;c3++)
{
if ( c1 + c2 + c3 <= order -2 )
{
GiNaC::ex eq = expanded_pol.coeff(x,c1).coeff(y,c2).coeff(z,c3);
if ( eq != GiNaC::numeric(0) )
{
equations.append(eq == 0);
}
}
}
}
}
}
int removed_dofs = equations.nops();
GiNaC::symbol t("t");
GiNaC::ex dofi;
// dofs related to edges
for (int i=0; i< 4; i++)
{
Triangle triangle = tetrahedron.triangle(i);
GiNaC::lst normal_vec = normal(tetrahedron, i);
GiNaC::ex Vn = inner(pspace, normal_vec);
GiNaC::lst points = interior_coordinates(triangle, order-1);
GiNaC::ex triangle_size = triangle.integrate(GiNaC::numeric(1));
GiNaC::ex point;
for (unsigned int j=0; j< points.nops(); j++)
{
point = points.op(j);
dofi = Vn.subs(x == point.op(0)).subs(y == point.op(1)).subs(z == point.op(2))*triangle_size;
GiNaC::ex eq = dofi == GiNaC::numeric(0);
equations.append(eq);
dofs.insert(dofs.end(), GiNaC::lst(point,nsymb));
}
}
// dofs related to the whole tetrahedron
if ( order > 1)
{
GiNaC::lst points = interior_coordinates(tetrahedron, order-2);
GiNaC::ex point;
for (unsigned int j=0; j< points.nops(); j++)
{
point = points.op(j);
// x -component
dofi = pspace.op(0).subs(x == point.op(0)).subs(y == point.op(1)).subs(z == point.op(2));
GiNaC::ex eq = dofi == GiNaC::numeric(0);
equations.append(eq);
dofs.insert(dofs.end(), GiNaC::lst(point,0));
// y -component
dofi = pspace.op(1).subs(x == point.op(0)).subs(y == point.op(1)).subs(z == point.op(2));
eq = dofi == GiNaC::numeric(0);
equations.append(eq);
dofs.insert(dofs.end(), GiNaC::lst(point,1));
// z -component
dofi = pspace.op(2).subs(x == point.op(0)).subs(y == point.op(1)).subs(z == point.op(2));
eq = dofi == GiNaC::numeric(0);
equations.append(eq);
dofs.insert(dofs.end(), GiNaC::lst(point,1));
}
}
// std::cout <<"no variables "<<variables.nops()<<std::endl;
// std::cout <<"no equations "<<equations.nops()<<std::endl;
// invert the matrix:
// GiNaC has a bit strange way to invert a matrix.
// It solves the system AA^{-1} = Id.
// It seems that this way is the only way to do
// properly with the solve_algo::gauss flag.
//
GiNaC::matrix b; GiNaC::matrix A;
matrix_from_equations(equations, variables, A, b);
unsigned int ncols = A.cols();
GiNaC::matrix vars_sq(ncols, ncols);
// matrix of symbols
for (unsigned r=0; r<ncols; ++r)
for (unsigned c=0; c<ncols; ++c)
vars_sq(r, c) = GiNaC::symbol();
GiNaC::matrix id(ncols, ncols);
// identity
const GiNaC::ex _ex1(1);
for (unsigned i=0; i<ncols; ++i)
id(i, i) = _ex1;
// invert the matrix
GiNaC::matrix m_inv(ncols, ncols);
m_inv = A.solve(vars_sq, id, GiNaC::solve_algo::gauss);
for (unsigned int i=0; i<dofs.size(); i++)
{
b.let_op(removed_dofs + i) = GiNaC::numeric(1);
GiNaC::ex xx = m_inv.mul(GiNaC::ex_to<GiNaC::matrix>(b));
GiNaC::lst subs;
for (unsigned int ii=0; ii<xx.nops(); ii++)
{
subs.append(variables.op(ii) == xx.op(ii));
}
GiNaC::ex Nj1 = pspace.op(0).subs(subs);
GiNaC::ex Nj2 = pspace.op(1).subs(subs);
GiNaC::ex Nj3 = pspace.op(2).subs(subs);
Ns.insert(Ns.end(), GiNaC::matrix(3,1,GiNaC::lst(Nj1,Nj2,Nj3)));
b.let_op(removed_dofs + i) = GiNaC::numeric(0);
}
}
}
else
{
if ( p->str().find("ReferenceLine") != string::npos )
{
cout <<"Can not define the Raviart-Thomas element on a line"<<endl;
}
else if ( p->str().find("Triangle") != string::npos )
{
description = istr("RaviartThomas_", order) + "_2D";
Triangle& triangle = (Triangle&)(*p);
GiNaC::lst equations;
GiNaC::lst variables;
GiNaC::ex polynom_space1 = bernstein(order-1, triangle, "a");
GiNaC::ex polynom1 = polynom_space1.op(0);
GiNaC::ex polynom1_vars = polynom_space1.op(1);
GiNaC::ex polynom1_basis = polynom_space1.op(2);
GiNaC::lst polynom_space2 = bernsteinv(2,order-1, triangle, "b");
GiNaC::ex polynom2 = polynom_space2.op(0).op(0);
GiNaC::ex polynom3 = polynom_space2.op(0).op(1);
GiNaC::lst pspace = GiNaC::lst( polynom2 + polynom1*x,
polynom3 + polynom1*y);
GiNaC::lst v2 = collapse(GiNaC::ex_to<GiNaC::lst>(polynom_space2.op(1)));
variables = collapse(GiNaC::lst(polynom_space1.op(1), v2));
// remove multiple dofs
if ( order >= 2)
{
GiNaC::ex expanded_pol = GiNaC::expand(polynom1);
for (unsigned int c1=0; c1<= order-2;c1++)
{
for (unsigned int c2=0; c2<= order-2;c2++)
{
for (unsigned int c3=0; c3<= order-2;c3++)
{
if ( c1 + c2 + c3 <= order -2 )
{
GiNaC::ex eq = expanded_pol.coeff(x,c1).coeff(y,c2).coeff(z,c3);
if ( eq != GiNaC::numeric(0) )
{
equations.append(eq == 0);
}
}
}
}
}
}
int removed_dofs = equations.nops();
GiNaC::ex bernstein_pol;
int counter = 0;
GiNaC::symbol t("t");
GiNaC::ex dofi;
// dofs related to edges
for (int i=0; i< 3; i++)
{
Line line = triangle.line(i);
GiNaC::lst normal_vec = normal(triangle, i);
bernstein_pol = bernstein(order-1, line, istr("a",i));
GiNaC::ex basis_space = bernstein_pol.op(2);
GiNaC::ex pspace_n = inner(pspace, normal_vec);
GiNaC::ex basis;
for (unsigned int j=0; j< basis_space.nops(); j++)
{
counter++;
basis = basis_space.op(j);
GiNaC::ex integrand = pspace_n*basis;
dofi = line.integrate(integrand);
GiNaC::ex eq = dofi == GiNaC::numeric(0);
equations.append(eq);
GiNaC::lst d = GiNaC::lst(GiNaC::lst(line.vertex(0), line.vertex(1)),j);
dofs.insert(dofs.end(), d);
GiNaC::ex u = GiNaC::matrix(2,1,GiNaC::lst(GiNaC::symbol("v[0]"), GiNaC::symbol("v[1]")));
GiNaC::ex n = GiNaC::matrix(2,1,GiNaC::lst(GiNaC::symbol("normal_vec[0]"), GiNaC::symbol("normal_vec[1]")));
dof_repr.append(GiNaC::lst(inner(u,n)*basis.subs( x == GiNaC::symbol("xi[0]"))
.subs( y == GiNaC::symbol("xi[1]")), d));
}
}
// dofs related to the whole triangle
GiNaC::lst bernstein_polv;
if ( order > 1)
{
counter++;
bernstein_polv = bernsteinv(2,order-2, triangle, "a");
GiNaC::ex basis_space = bernstein_polv.op(2);
for (unsigned int i=0; i< basis_space.nops(); i++)
{
GiNaC::lst basis = GiNaC::ex_to<GiNaC::lst>(basis_space.op(i));
GiNaC::ex integrand = inner(pspace, basis);
dofi = triangle.integrate(integrand);
GiNaC::ex eq = dofi == GiNaC::numeric(0);
equations.append(eq);
GiNaC::lst d = GiNaC::lst(GiNaC::lst(triangle.vertex(0), triangle.vertex(1), triangle.vertex(2)), i);
dofs.insert(dofs.end(), d);
}
}
// invert the matrix:
// GiNaC has a bit strange way to invert a matrix.
// It solves the system AA^{-1} = Id.
// It seems that this way is the only way to do
// properly with the solve_algo::gauss flag.
//
GiNaC::matrix b; GiNaC::matrix A;
matrix_from_equations(equations, variables, A, b);
unsigned int ncols = A.cols();
GiNaC::matrix vars_sq(ncols, ncols);
// matrix of symbols
for (unsigned r=0; r<ncols; ++r)
for (unsigned c=0; c<ncols; ++c)
vars_sq(r, c) = GiNaC::symbol();
GiNaC::matrix id(ncols, ncols);
// identity
const GiNaC::ex _ex1(1);
for (unsigned i=0; i<ncols; ++i)
id(i, i) = _ex1;
// invert the matrix
GiNaC::matrix m_inv(ncols, ncols);
m_inv = A.solve(vars_sq, id, GiNaC::solve_algo::gauss);
for (unsigned int i=0; i<dofs.size(); i++)
{
b.let_op(removed_dofs + i) = GiNaC::numeric(1);
GiNaC::ex xx = m_inv.mul(GiNaC::ex_to<GiNaC::matrix>(b));
GiNaC::lst subs;
for (unsigned int ii=0; ii<xx.nops(); ii++)
{
subs.append(variables.op(ii) == xx.op(ii));
}
GiNaC::ex Nj1 = pspace.op(0).subs(subs);
GiNaC::ex Nj2 = pspace.op(1).subs(subs);
Ns.insert(Ns.end(), GiNaC::matrix(2,1,GiNaC::lst(Nj1,Nj2)));
b.let_op(removed_dofs + i) = GiNaC::numeric(0);
}
}
else if ( p->str().find("Tetrahedron") != string::npos )
{
description = istr("RaviartThomas_", order) + "_3D";
Tetrahedron& tetrahedron = (Tetrahedron&)(*p);
GiNaC::lst equations;
GiNaC::lst variables;
GiNaC::ex polynom_space1 = bernstein(order-1, tetrahedron, "a");
GiNaC::ex polynom1 = polynom_space1.op(0);
GiNaC::ex polynom1_vars = polynom_space1.op(1);
GiNaC::ex polynom1_basis = polynom_space1.op(2);
GiNaC::lst polynom_space2 = bernsteinv(3,order-1, tetrahedron, "b");
GiNaC::ex polynom2 = polynom_space2.op(0).op(0);
GiNaC::ex polynom3 = polynom_space2.op(0).op(1);
GiNaC::ex polynom4 = polynom_space2.op(0).op(2);
GiNaC::lst pspace = GiNaC::lst( polynom2 + polynom1*x,
polynom3 + polynom1*y,
polynom4 + polynom1*z);
GiNaC::lst v2 = collapse(GiNaC::ex_to<GiNaC::lst>(polynom_space2.op(1)));
variables = collapse(GiNaC::lst(polynom_space1.op(1), v2));
GiNaC::ex bernstein_pol;
// remove multiple dofs
if ( order >= 2)
{
GiNaC::ex expanded_pol = GiNaC::expand(polynom1);
for (unsigned int c1=0; c1<= order-2;c1++)
{
for (unsigned int c2=0; c2<= order-2;c2++)
{
for (unsigned int c3=0; c3<= order-2;c3++)
{
if ( c1 + c2 + c3 <= order -2 )
{
GiNaC::ex eq = expanded_pol.coeff(x,c1).coeff(y,c2).coeff(z,c3);
if ( eq != GiNaC::numeric(0) )
{
equations.append(eq == 0);
}
}
}
}
}
}
int removed_dofs = equations.nops();
int counter = 0;
GiNaC::symbol t("t");
GiNaC::ex dofi;
// dofs related to edges
for (int i=0; i< 4; i++)
{
Triangle triangle = tetrahedron.triangle(i);
GiNaC::lst normal_vec = normal(tetrahedron, i);
bernstein_pol = bernstein(order-1, triangle, istr("a",i));
GiNaC::ex basis_space = bernstein_pol.op(2);
GiNaC::ex pspace_n = inner(pspace, normal_vec);
GiNaC::ex basis;
for (unsigned int j=0; j< basis_space.nops(); j++)
{
counter++;
basis = basis_space.op(j);
GiNaC::ex integrand = pspace_n*basis;
dofi = triangle.integrate(integrand);
GiNaC::ex eq = dofi == GiNaC::numeric(0);
equations.append(eq);
GiNaC::lst d = GiNaC::lst(GiNaC::lst(triangle.vertex(0), triangle.vertex(1), triangle.vertex(2)), j);
dofs.insert(dofs.end(), d);
GiNaC::ex u = GiNaC::matrix(3,1,GiNaC::lst(GiNaC::symbol("v[0]"), GiNaC::symbol("v[1]"), GiNaC::symbol("v[2]")));
GiNaC::ex n = GiNaC::matrix(3,1,GiNaC::lst(GiNaC::symbol("normal_vec[0]"), GiNaC::symbol("normal_vec[1]"), GiNaC::symbol("normal_vec[2]")));
dof_repr.append(GiNaC::lst(inner(u,n)*basis.subs( x == GiNaC::symbol("xi[0]"))
.subs( y == GiNaC::symbol("xi[1]"))
.subs( z == GiNaC::symbol("xi[2]")), d));
}
}
// dofs related to the whole tetrahedron
GiNaC::lst bernstein_polv;
if ( order > 1)
{
counter++;
bernstein_polv = bernsteinv(3,order-2, tetrahedron, "a");
GiNaC::ex basis_space = bernstein_polv.op(2);
for (unsigned int i=0; i< basis_space.nops(); i++)
{
GiNaC::lst basis = GiNaC::ex_to<GiNaC::lst>(basis_space.op(i));
GiNaC::ex integrand = inner(pspace, basis);
dofi = tetrahedron.integrate(integrand);
GiNaC::ex eq = dofi == GiNaC::numeric(0);
equations.append(eq);
GiNaC::lst d = GiNaC::lst(GiNaC::lst(tetrahedron.vertex(0), tetrahedron.vertex(1), tetrahedron.vertex(2), tetrahedron.vertex(3)), i);
dofs.insert(dofs.end(), d);
}
}
// invert the matrix:
// GiNaC has a bit strange way to invert a matrix.
// It solves the system AA^{-1} = Id.
// It seems that this way is the only way to do
// properly with the solve_algo::gauss flag.
//
GiNaC::matrix b; GiNaC::matrix A;
matrix_from_equations(equations, variables, A, b);
unsigned int ncols = A.cols();
GiNaC::matrix vars_sq(ncols, ncols);
// matrix of symbols
for (unsigned r=0; r<ncols; ++r)
for (unsigned c=0; c<ncols; ++c)
vars_sq(r, c) = GiNaC::symbol();
GiNaC::matrix id(ncols, ncols);
// identity
const GiNaC::ex _ex1(1);
for (unsigned i=0; i<ncols; ++i)
id(i, i) = _ex1;
// invert the matrix
GiNaC::matrix m_inv(ncols, ncols);
m_inv = A.solve(vars_sq, id, GiNaC::solve_algo::gauss);
for (unsigned int i=0; i<dofs.size(); i++)
{
b.let_op(removed_dofs + i) = GiNaC::numeric(1);
GiNaC::ex xx = m_inv.mul(GiNaC::ex_to<GiNaC::matrix>(b));
GiNaC::lst subs;
for (unsigned int ii=0; ii<xx.nops(); ii++)
{
subs.append(variables.op(ii) == xx.op(ii));
}
GiNaC::ex Nj1 = pspace.op(0).subs(subs);
GiNaC::ex Nj2 = pspace.op(1).subs(subs);
GiNaC::ex Nj3 = pspace.op(2).subs(subs);
Ns.insert(Ns.end(), GiNaC::matrix(3,1,GiNaC::lst(Nj1,Nj2,Nj3)));
b.let_op(removed_dofs + i) = GiNaC::numeric(0);
}
}
}
}
| GiNaC::lst SyFi::RaviartThomas::dof_repr |
Definition at line 30 of file RaviartThomas.h.
Referenced by compute_basis_functions().
Definition at line 29 of file RaviartThomas.h.
Referenced by compute_basis_functions(), and RaviartThomas().
1.7.6.1