Re: [Getfem-users] Interpolate RT0 elements with P0

[Gerry Rizzo]

Hi,

I've written a very simple test case for the RT0 interpolation, you can find it attached to this email.

It loads a vector (example.txt) containing the velocity of the solution of Darcy equations over a 10x10x10 mesh with constant permeability; the velocity is a positive constant along x-axis and zero along y and z axes.

I still have the same error I've showed you in the previous email.

I've tested this code with getfem 4.2, ubuntu 12.10 32bit and gcc version 4.7.2.

Thank you,

Calogero B. Rizzo

2013/12/3 Gerry Rizzo <address@hidden>

I've tried to use the interpolator function without success; here what I've done:

getfem::mesh_fem mf_p0_3;

getfem::pfem pf_p0;

pf_p0 = getfem::fem_descriptor("FEM_PK(3,0)");

mf_p0_3.init_with_mesh(mesh);

mf_p0_3.set_qdim(N);

mf_p0_3.set_finite_element(mesh.convex_index(), pf_p0);

std::vector<scalar_type> U_v_int;

U_v_int.resize(mf_p0_3.nb_basic_dof());

getfem::interpolation(mf_v,mf_p0_3,U_v,U_v_int);

mf_v is the RT0 fem and the computed velocity in RT0 is stored in U_v. I have the following error:

terminate called after throwing an instance of 'gmm::gmm_error'

  what():  Error in /usr/local/include/getfem/getfem_fem.h, line 728 : 

Wrong size for coeff vector

Thank you for the availability,

Calogero B. Rizzo

2013/12/2 Gerry Rizzo <address@hidden>

Hi,

I'm trying to make a function to interpolate three dimensional RT0 elements with P0 in order to export the function in vtk; the usual base functions are:

phy_i(x) = (x - a_i) / (d * |K|)

where a_i is a vertex of the tetrahedron, d is the dimension of the space (e.g. 3) and |K| is the volume of  the tetrahedron.

Then I can find the velocity in one point inside the thedraedron:

v(x) = sum ( v_i*phy_i(x) )

This is the function declaration (below there is the full function):

template<typename VEC,typename MAT>

void InterpolatorRT0( const getfem::mesh &mesh,                //mesh

const getfem::mesh_fem &mf_v,         //RT0 fem

const getfem::mesh_fem &mf_p,         //P0 fem

scalar_type &Vx,                                // variable for the computed Vx 

scalar_type &Vy,                                // variable for the computed Vy                                 

scalar_type &Vz,                                // variable for the computed Vz 

const scalar_type &x,                          // x, y, z are the point's coordinates where I want to compute the velocity

const scalar_type &y,

const scalar_type &z,

const VEC &gdl,                                // gdl is the velocity vector with RT0 elements

const size_type &elem,                       // elem is the thetraedron where the point lies

const MAT &A,                                  // A is the mass matrix

const size_type &shift = 0);

This function interpolate the RT0 velocity in one point given by x, y, z.

In order to guess the sign I'm using the mass matrix computed with:

getfem::asm_mass_matrix(A, im_v, mf_v, mf_p);

Unluckly this function doesn't work, I've tested it on a 3D box with constant velocity, I can't figure out the problem;

The problem may be the sign, is there a better/easier way to compute it?

Thank you,

Calogero B. Rizzo

Code snippet:

template<typename VEC,typename MAT>

void InterpolatorRT0( const getfem::mesh &mesh,

const getfem::mesh_fem &mf_v,

const getfem::mesh_fem &mf_p, 

scalar_type &Vx,

scalar_type &Vy,

scalar_type &Vz,

const scalar_type &x,

const scalar_type &y,

const scalar_type &z,

const VEC &gdl,

const size_type &elem,

const MAT &A,

const size_type &shift = 0) {

Vx = 0.;

Vy = 0.;

Vz = 0.;

scalar_type volume = mesh.convex_area_estimate(elem);

int N = mesh.dim();

std::vector<base_node> vertex;

for(int i=0; i<N+1; i++) {

vertex.push_back(mesh.points_of_convex(elem)[i]);

}

// loop over the four faces

for(int i=0; i<mf_v.nb_basic_dof_of_element(elem); i++) {

size_type idof = mf_v.ind_basic_dof_of_face_of_element(elem,i)[0];

scalar_type sign = A(idof,mf_p.ind_basic_dof_of_element(elem)[0]+shift);

sign /= (gmm::abs(sign)>0) ? gmm::abs(sign) : 1;

                        scalar_type area;

if(N==2) {

base_node x1 = mesh.points_of_face_of_convex(elem,i)[0];

base_node x2 = mesh.points_of_face_of_convex(elem,i)[1];

area = pow(pow(x2[0]-x1[0],2)+pow(x2[1]-x1[1],2),0.5);

} else {

assert(N==3);

base_node x1 = mesh.points_of_face_of_convex(elem,i)[0];

base_node x2 = mesh.points_of_face_of_convex(elem,i)[1];

base_node x3 = mesh.points_of_face_of_convex(elem,i)[2];

Geometry::Point3D xx1(x1[0],x1[1],x1[2]);

Geometry::Point3D xx2(x2[0],x2[1],x2[2]);

Geometry::Point3D xx3(x3[0],x3[1],x3[2]);

area = (Geometry::Triangle(xx1,xx2,xx3)).area();

}

// for a tetrahedron the vertex i is in front of the face i

Vx += gdl[idof]*(x-vertex[i][0])/(3*volume)*sign*area;

Vy += gdl[idof]*(y-vertex[i][1])/(3*volume)*sign*area;

Vz += gdl[idof]*(z-vertex[i][2])/(3*volume)*sign*area;

}

}