void
prepare_surface3d(psurface3d gr)
{
const real(*x)[3] = (const real(*)[3]) gr->x;
const uint(*t)[3] = (const uint(*)[3]) gr->t;
real(*n)[3] = gr->n;
real *g = gr->g;
real dx[3], dy[3], dz[3];
real norm, height, hmin, hmax, a, b, c;
uint triangles = gr->triangles;
uint i;
hmin = 1e30;
hmax = 0.0;
for (i = 0; i < triangles; i++) {
dx[0] = x[t[i][1]][0] - x[t[i][0]][0];
dx[1] = x[t[i][1]][1] - x[t[i][0]][1];
dx[2] = x[t[i][1]][2] - x[t[i][0]][2];
dy[0] = x[t[i][2]][0] - x[t[i][0]][0];
dy[1] = x[t[i][2]][1] - x[t[i][0]][1];
dy[2] = x[t[i][2]][2] - x[t[i][0]][2];
dz[0] = x[t[i][2]][0] - x[t[i][1]][0];
dz[1] = x[t[i][2]][1] - x[t[i][1]][1];
dz[2] = x[t[i][2]][2] - x[t[i][1]][2];
n[i][0] = dx[1] * dy[2] - dx[2] * dy[1];
n[i][1] = dx[2] * dy[0] - dx[0] * dy[2];
n[i][2] = dx[0] * dy[1] - dx[1] * dy[0];
norm =
REAL_SQRT(REAL_SQR(n[i][0]) + REAL_SQR(n[i][1]) + REAL_SQR(n[i][2]));
g[i] = norm;
n[i][0] /= norm;
n[i][1] /= norm;
n[i][2] /= norm;
a = REAL_SQRT(REAL_SQR(dx[0]) + REAL_SQR(dx[1]) + REAL_SQR(dx[2]));
b = REAL_SQRT(REAL_SQR(dy[0]) + REAL_SQR(dy[1]) + REAL_SQR(dy[2]));
c = REAL_SQRT(REAL_SQR(dz[0]) + REAL_SQR(dz[1]) + REAL_SQR(dz[2]));
height = 2.0 * REAL_MIN3(a, b, c);
a *= a;
b *= b;
c *= c;
height =
REAL_SQRT(2 * (a * b + b * c + a * c) -
(a * a + b * b + c * c)) / height;
hmin = REAL_MIN(hmin, height);
hmax = REAL_MAX(hmax, height);
}
gr->hmin = hmin;
gr->hmax = hmax;
}
field
rhs_dirichlet_point_helmholtzbem3d(const real * x, const real * n,
const void *data)
{
helmholtz_data *hdata = (helmholtz_data *) data;
field *kvec = hdata->kvec;
field k =
REAL_SQRT(ABSSQR(kvec[0]) + ABSSQR(kvec[1]) + ABSSQR(kvec[2]));
real *s = hdata->source;
real r =
REAL_SQRT(REAL_SQR(x[0] - s[0]) + REAL_SQR(x[1] - s[1]) +
REAL_SQR(x[2] - s[2]));
(void) n;
return cexp(I * k * r) / r;
}
real
max_rel_inner_error(pcbem3d bem, helmholtz_data * hdata, pcavector x,
boundary_func3d rhs)
{
uint nx, nz, npoints;
real(*xdata)[3];
field *ydata;
uint i, j;
real error, maxerror;
real eta_bw =
REAL_SQRT(ABSSQR(bem->kvec[0]) + ABSSQR(bem->kvec[1]) +
ABSSQR(bem->kvec[2]));
nx = 20;
nz = 20;
npoints = nx * nz;
xdata = (real(*)[3]) allocreal(3 * npoints);
npoints = 0;
for (j = 0; j < nz; ++j) {
for (i = 0; i < nx; ++i) {
xdata[npoints][0] = -1.0 + (2.0 / (nx - 1)) * i;
xdata[npoints][1] = 0.0;
xdata[npoints][2] = -1.0 + (2.0 / (nz - 1)) * j;
if (REAL_SQR(xdata[npoints][0]) + REAL_SQR(xdata[npoints][2]) < 1) {
npoints++;
}
}
}
ydata = allocfield(npoints);
#pragma omp parallel for
for (j = 0; j < npoints; ++j) {
ydata[j] = eval_brakhage_werner_c(bem, x, eta_bw, xdata[j]);
}
j = 0;
maxerror =
ABS(ydata[j] -
rhs(xdata[j], NULL, hdata)) / ABS(rhs(xdata[j], NULL, hdata));
for (j = 1; j < npoints; ++j) {
error =
ABS(ydata[j] -
rhs(xdata[j], NULL, hdata)) / ABS(rhs(xdata[j], NULL, hdata));
maxerror = error > maxerror ? error : maxerror;
}
freemem(ydata);
freemem(xdata);
return maxerror;
}
real
getdiam_2_cluster(pccluster t)
{
real diam2;
uint i;
diam2 = 0.0;
for (i = 0; i < t->dim; i++)
diam2 += REAL_SQR(t->bmax[i] - t->bmin[i]);
return REAL_SQRT(diam2);
}
bool
parabolic_admissibility(pdcluster rc, pdcluster cc, uint l,
uint * rd, uint * cd, void *data)
{
pcdiradmdata dad = (pcdiradmdata) data;
real eta2 = dad->eta2;
real wave_k = dad->wave_k;
preal xy = dad->xy;
real rdiam, cdiam, dist, dist2, invdist;
uint dim;
uint i, iota;
dim = rc->dim;
assert(cc->dim == dim);
/* Compute cluster diameters */
rdiam = diam_dcluster(rc);
cdiam = diam_dcluster(cc);
/* Compute distance */
dist = dist_dcluster(rc, cc);
/* Check parabolic admissibility condition */
if (wave_k * rdiam * rdiam <= eta2 * dist &&
wave_k * cdiam * cdiam <= eta2 * dist &&
rdiam <= eta2 * dist && cdiam <= eta2 * dist) {
/* Compute distance of midpoints */
dist2 = 0.0;
for (i = 0; i < dim; i++) {
xy[i] = 0.5 * (rc->bmax[i] + rc->bmin[i]
- cc->bmax[i] - cc->bmin[i]);
dist2 += REAL_SQR(xy[i]);
}
invdist = 1.0 / REAL_SQRT(dist2);
/* Scale distance vector... */
for (i = 0; i < dim; i++)
xy[i] *= invdist;
/* ... and choose a direction that is sufficiently close */
iota = finddirection_leveldir(dad->ld, l, 1.0, xy);
*rd = iota;
*cd = iota;
return true;
}
*rd = 0;
*cd = 0;
return false;
}
field
rhs_neumann_point_helmholtzbem3d(const real * x, const real * n,
const void *data)
{
helmholtz_data *hdata = (helmholtz_data *) data;
field *kvec = hdata->kvec;
field k =
REAL_SQRT(ABSSQR(kvec[0]) + ABSSQR(kvec[1]) + ABSSQR(kvec[2]));
real *s = hdata->source;
real r =
REAL_SQRT(REAL_SQR(x[0] - s[0]) + REAL_SQR(x[1] - s[1]) +
REAL_SQR(x[2] - s[2]));
field res;
res = cexp(I * k * r) / (r * r * r) * (I * k * r - 1.0);
res = res
* (n[0] * (x[0] - s[0]) + n[1] * (x[1] - s[1]) + n[2] * (x[2] - s[2]));
return res;
}
void
smooth_unitcircle_tri2d(ptri2d t2)
{
uint i;
real normL2, normL1;
/* Scaling vertices */
for (i = 0; i < t2->vertices; i++) {
normL1 = REAL_ABS(t2->x[i][0]) + REAL_ABS(t2->x[i][1]);
normL2 = REAL_SQRT(t2->x[i][0] * t2->x[i][0] + t2->x[i][1] * t2->x[i][1]);
if (normL1 != 0.0) {
t2->x[i][0] = t2->x[i][0] * normL1 / normL2;
t2->x[i][1] = t2->x[i][1] * normL1 / normL2;
}
}
}
real
getdist_2_cluster(pccluster t, pccluster s)
{
real dist2;
uint i;
assert(t->dim == s->dim);
dist2 = 0.0;
for (i = 0; i < t->dim; i++)
if (t->bmax[i] < s->bmin[i]) /* t to the "left" of s */
dist2 += REAL_SQR(s->bmin[i] - t->bmax[i]);
else if (s->bmax[i] < t->bmin[i]) /* t to the "right" of s */
dist2 += REAL_SQR(t->bmin[i] - s->bmax[i]);
return REAL_SQRT(dist2);
}
/* Compute the L_2-error for constant basis functions */
static real
L2gamma_c_diff_norm2(pbem2d bem, pavector x, boundary_func2d rhs)
{
pccurve2d gr = bem->gr;
const real(*gr_x)[2] = (const real(*)[2]) gr->x;
const uint(*gr_e)[2] = (const uint(*)[2]) gr->e;
const real(*gr_n)[2] = (const real(*)[2]) gr->n;
const preal gr_g = (const preal) gr->g;
uint n = x->dim;
uint nq = bem->sq->n_single;
real *xx = bem->sq->x_single;
real *ww = bem->sq->w_single;
const real *A, *B, *N;
uint e, q;
real norm, sum, X[2], tx, Ax, Bx;
assert(n == gr->edges);
norm = 0.0;
for (e = 0; e < n; ++e) {
A = gr_x[gr_e[e][0]];
B = gr_x[gr_e[e][1]];
N = gr_n[e];
sum = 0.0;
for (q = 0; q < nq; ++q) {
tx = xx[q];
Ax = 1.0 - tx;
Bx = tx;
X[0] = A[0] * Ax + B[0] * Bx;
X[1] = A[1] * Ax + B[1] * Bx;
sum += ww[q] * ABSSQR(rhs(X, N) - x->v[e]);
}
norm += sum * gr_g[e];
}
norm = REAL_SQRT(norm);
return norm;
}
void
prepare_curve2d(pcurve2d gr)
{
const real(*x)[2] = (const real(*)[2]) gr->x;
const uint(*e)[2] = (const uint(*)[2]) gr->e;
real(*n)[2] = gr->n;
real *g = gr->g;
real norm;
uint edges = gr->edges;
uint i;
for (i = 0; i < edges; i++) {
n[i][0] = x[e[i][1]][1] - x[e[i][0]][1];
n[i][1] = x[e[i][0]][0] - x[e[i][1]][0];
norm = REAL_SQRT(REAL_SQR(n[i][0]) + REAL_SQR(n[i][1]));
g[i] = norm;
n[i][0] /= norm;
n[i][1] /= norm;
}
}
real
norm2chol_sparsematrix(pchmatrix LU, pcsparsematrix sp)
{
avector tmp1, tmp2;
uint rows = LU->rc->size;
uint cols = LU->cc->size;
pavector x, y;
real norm;
uint j;
assert(sp->rows == rows);
assert(sp->cols == cols);
x = init_avector(&tmp1, cols);
y = init_avector(&tmp2, rows);
random_avector(x);
norm = norm2_avector(x);
scale_avector(1.0 / norm, x);
for (j = 0; j < NORM_STEPS; j++) {
// printf("norm = %g \n", sqrt( norm));
clear_avector(y);
mvm_sparsematrix_avector(1.0, false, sp, x, y);
triangularsolve_hmatrix_avector(true, false, false, LU, y);
triangularsolve_hmatrix_avector(true, false, true, LU, y);
add_avector(-1.0, y, x);
copy_avector(x, y);
triangularsolve_hmatrix_avector(true, false, false, LU, y);
triangularsolve_hmatrix_avector(true, false, true, LU, y);
mvm_sparsematrix_avector(-1.0, true, sp, y, x);
norm = norm2_avector(x);
scale_avector(1.0 / norm, x);
}
uninit_avector(y);
uninit_avector(x);
return REAL_SQRT(norm);
}
void
statistics_tet3d(pctet3d t3, preal hmin, preal hmax, preal volmin,
preal volmax, preal relvolmin, preal relvolmax)
{
const real(*x)[3] = (const real(*)[3]) t3->x;
uint tetrahedra = t3->tetrahedra;
real xl[4][3];
real xd[6][3];
real h, norm, vol;
uint v[4];
uint i, j;
for (i = 0; i < tetrahedra; i++) {
getvertices_tet3d(t3, i, v);
/* Get coordinates of vertices */
for (j = 0; j < 4; j++) {
xl[j][0] = x[v[j]][0];
xl[j][1] = x[v[j]][1];
xl[j][2] = x[v[j]][2];
}
/* Compute edge vectors */
xd[0][0] = xl[1][0] - xl[0][0];
xd[0][1] = xl[1][1] - xl[0][1];
xd[0][2] = xl[1][2] - xl[0][2];
xd[1][0] = xl[2][0] - xl[0][0];
xd[1][1] = xl[2][1] - xl[0][1];
xd[1][2] = xl[2][2] - xl[0][2];
xd[2][0] = xl[3][0] - xl[0][0];
xd[2][1] = xl[3][1] - xl[0][1];
xd[2][2] = xl[3][2] - xl[0][2];
xd[3][0] = xl[2][0] - xl[1][0];
xd[3][1] = xl[2][1] - xl[1][1];
xd[3][2] = xl[2][2] - xl[1][2];
xd[4][0] = xl[3][0] - xl[1][0];
xd[4][1] = xl[3][1] - xl[1][1];
xd[4][2] = xl[3][2] - xl[1][2];
xd[5][0] = xl[3][0] - xl[2][0];
xd[5][1] = xl[3][1] - xl[2][1];
xd[5][2] = xl[3][2] - xl[2][2];
/* Update h, hmin and hmax */
h = 0.0;
for (j = 0; j < 6; j++) {
norm =
REAL_SQRT(REAL_SQR(xd[j][0]) + REAL_SQR(xd[j][1]) +
REAL_SQR(xd[j][2]));
if (i == 0 || norm < *hmin)
*hmin = norm;
if (i == 0 || norm > *hmax)
*hmax = norm;
if (norm > h)
h = norm;
}
/* Compute volume */
vol = fabs(xd[0][0] * xd[1][1] * xd[2][2] + xd[1][0] * xd[2][1] * xd[0][2]
+ xd[2][0] * xd[0][1] * xd[1][2]
- xd[0][0] * xd[2][1] * xd[1][2]
- xd[1][0] * xd[0][1] * xd[2][2]
- xd[2][0] * xd[1][1] * xd[0][2])
/ 6.0;
if (i == 0 || vol < *volmin)
*volmin = vol;
if (i == 0 || vol > *volmax)
*volmax = vol;
/* Compute relative volume */
vol /= h * h * h;
if (i == 0 || vol < *relvolmin)
*relvolmin = vol;
if (i == 0 || vol > *relvolmax)
*relvolmax = vol;
}
}
ptet3d
new_regular_tet3d()
{
ptet3d t3;
real r, h, c, y;
r = 1.0;
h = REAL_SQRT(2.0) - 1.0;
c = REAL_SQRT(0.75);
y = 1.0 - REAL_SQRT(0.5);
t3 = new_tet3d(4, 6, 4, 1);
t3->x[0][0] = 0.0;
t3->x[0][1] = -h - y;
t3->x[0][2] = -r;
t3->x[1][0] = -c * r;
t3->x[1][1] = -h - y;
t3->x[1][2] = 0.5 * r;
t3->x[2][0] = c * r;
t3->x[2][1] = -h - y;
t3->x[2][2] = 0.5 * r;
t3->x[3][0] = 0.0;
t3->x[3][1] = 1.0 - y;
t3->x[3][2] = 0.0;
t3->e[0][0] = 1;
t3->e[0][1] = 2;
t3->e[1][0] = 2;
t3->e[1][1] = 3;
t3->e[2][0] = 3;
t3->e[2][1] = 1;
t3->e[3][0] = 0;
t3->e[3][1] = 1;
t3->e[4][0] = 0;
t3->e[4][1] = 2;
t3->e[5][0] = 0;
t3->e[5][1] = 3;
t3->f[0][0] = 1;
t3->f[0][1] = 2;
t3->f[0][2] = 0;
t3->f[1][0] = 1;
t3->f[1][1] = 4;
t3->f[1][2] = 5;
t3->f[2][0] = 2;
t3->f[2][1] = 5;
t3->f[2][2] = 3;
t3->f[3][0] = 0;
t3->f[3][1] = 3;
t3->f[3][2] = 4;
t3->t[0][0] = 0;
t3->t[0][1] = 1;
t3->t[0][2] = 2;
t3->t[0][3] = 3;
t3->xb[0] = t3->xb[1] = t3->xb[2] = t3->xb[3] = 1;
t3->eb[0] = t3->eb[1] = t3->eb[2] = t3->eb[3] = t3->eb[4] = t3->eb[5] = 1;
t3->fb[0] = t3->fb[1] = t3->fb[2] = t3->fb[3] = 1;
t3->vertices = 4;
t3->edges = 6;
t3->faces = 4;
t3->tetrahedra = 1;
return t3;
}
int
main(int argc, char **argv)
{
pmacrosurface3d mg;
psurface3d gr;
pamatrix Vfull, KMfull;
pbem3d bem_slp, bem_dlp;
pcluster root;
pblock block;
phmatrix V, KM;
pclusterbasis Vrb, Vcb, KMrb, KMcb;
ph2matrix V2, KM2;
uint n, q, clf, m, l;
real eta, delta, eps_aca;
field kvec[3];
cl_device_id *devices;
cl_uint ndevices;
uint *idx;
uint i;
init_h2lib(&argc, &argv);
get_opencl_devices(&devices, &ndevices);
ndevices = 1;
set_opencl_devices(devices, ndevices, 2);
kvec[0] = 2.0, kvec[1] = 0.0, kvec[2] = 0.0;
n = 512;
q = 2;
clf = 16;
eta = 1.0;
mg = new_sphere_macrosurface3d();
gr = build_from_macrosurface3d_surface3d(mg, REAL_SQRT(n * 0.125));
n = gr->triangles;
printf("Testing unit sphere with %d triangles\n", n);
bem_slp = new_slp_helmholtz_ocl_bem3d(kvec, gr, q, q + 2,
BASIS_CONSTANT_BEM3D);
bem_dlp = new_dlp_helmholtz_ocl_bem3d(kvec, gr, q, q + 2,
BASIS_CONSTANT_BEM3D,
BASIS_CONSTANT_BEM3D, 0.5);
root = build_bem3d_cluster(bem_slp, clf, BASIS_CONSTANT_BEM3D);
block = build_nonstrict_block(root, root, &eta, admissible_max_cluster);
max_pardepth = 0;
Vfull = new_amatrix(n, n);
KMfull = new_amatrix(n, n);
idx = allocuint(n);
for (i = 0; i < n; ++i) {
idx[i] = i;
}
SCHEDULE_OPENCL(0, 1, bem_slp->nearfield, idx, idx, bem_slp, false, Vfull);
SCHEDULE_OPENCL(0, 1, bem_dlp->nearfield, idx, idx, bem_dlp, false, KMfull);
V = build_from_block_hmatrix(block, 0);
KM = build_from_block_hmatrix(block, 0);
printf("----------------------------------------\n");
printf("Testing outer Boundary integral equations:\n");
printf("----------------------------------------\n\n");
/*
* Test Interpolation
*/
m = 4;
setup_hmatrix_aprx_inter_row_bem3d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_row_bem3d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation row", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_inter_col_bem3d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_col_bem3d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation column", Vfull, KMfull, block, bem_slp,
V, bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_inter_mixed_bem3d(bem_slp, root, root, block, m);
setup_hmatrix_aprx_inter_mixed_bem3d(bem_dlp, root, root, block, m);
test_hmatrix_system("Interpolation mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
/*
* Test Green
*/
m = 5;
l = 1;
delta = 0.5;
setup_hmatrix_aprx_green_row_bem3d(bem_slp, root, root, block, m, l, delta,
build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_green_row_bem3d(bem_dlp, root, root, block, m, l, delta,
build_bem3d_cube_quadpoints);
test_hmatrix_system("Green row", Vfull, KMfull, block, bem_slp, V, bem_dlp,
KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_green_col_bem3d(bem_slp, root, root, block, m, l, delta,
build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_green_col_bem3d(bem_dlp, root, root, block, m, l, delta,
build_bem3d_cube_quadpoints);
test_hmatrix_system("Green column", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_green_mixed_bem3d(bem_slp, root, root, block, m, l,
delta, build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_green_mixed_bem3d(bem_dlp, root, root, block, m, l,
delta, build_bem3d_cube_quadpoints);
test_hmatrix_system("Green mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
/*
* Test Greenhybrid
*/
m = 2;
l = 1;
delta = 1.0;
eps_aca = 2.0e-2;
setup_hmatrix_aprx_greenhybrid_row_bem3d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_greenhybrid_row_bem3d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
test_hmatrix_system("Greenhybrid row", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_greenhybrid_col_bem3d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_greenhybrid_col_bem3d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
test_hmatrix_system("Greenhybrid column", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_greenhybrid_mixed_bem3d(bem_slp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
setup_hmatrix_aprx_greenhybrid_mixed_bem3d(bem_dlp, root, root, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
test_hmatrix_system("Greenhybrid mixed", Vfull, KMfull, block, bem_slp, V,
bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
/*
* Test ACA / PACA / HCA
*/
m = 2;
eps_aca = 1.0e-2;
/* Nearfield computation on GPU not applicable here yet! */
// setup_hmatrix_aprx_aca_bem3d(bem_slp, root, root, block, eps_aca);
// setup_hmatrix_aprx_aca_bem3d(bem_dlp, root, root, block, eps_aca);
// test_hmatrix_system("ACA full pivoting", Vfull, KMfull, block, bem_slp, V,
// bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
//
// setup_hmatrix_aprx_paca_bem3d(bem_slp, root, root, block, eps_aca);
// setup_hmatrix_aprx_paca_bem3d(bem_slp, root, root, block, eps_aca);
// test_hmatrix_system("ACA partial pivoting", Vfull, KMfull, block, bem_slp, V,
// bem_dlp, KM, false, true, 1.0e-3, 2.0e-3);
setup_hmatrix_aprx_hca_bem3d(bem_slp, root, root, block, m, eps_aca);
setup_hmatrix_aprx_hca_bem3d(bem_slp, root, root, block, m, eps_aca);
test_hmatrix_system("HCA2", Vfull, KMfull, block, bem_slp, V, bem_dlp, KM,
false, true, 1.0e-3, 2.0e-3);
del_hmatrix(V);
del_hmatrix(KM);
del_block(block);
/*
* H2-matrix
*/
block = build_strict_block(root, root, &eta, admissible_max_cluster);
Vrb = build_from_cluster_clusterbasis(root);
Vcb = build_from_cluster_clusterbasis(root);
KMrb = build_from_cluster_clusterbasis(root);
KMcb = build_from_cluster_clusterbasis(root);
V2 = build_from_block_h2matrix(block, Vrb, Vcb);
KM2 = build_from_block_h2matrix(block, KMrb, KMcb);
/*
* Test Interpolation
*/
m = 3;
setup_h2matrix_aprx_inter_bem3d(bem_slp, Vrb, Vcb, block, m);
setup_h2matrix_aprx_inter_bem3d(bem_dlp, KMrb, KMcb, block, m);
test_h2matrix_system("Interpolation", Vfull, KMfull, block, bem_slp, V2,
bem_dlp, KM2, false, true, 1.0e-3, 2.0e-3);
/*
* Test Greenhybrid
*/
m = 2;
l = 1;
delta = 1.0;
eps_aca = 2.0e-2;
setup_h2matrix_aprx_greenhybrid_bem3d(bem_slp, Vrb, Vcb, block, m, l, delta,
eps_aca, build_bem3d_cube_quadpoints);
setup_h2matrix_aprx_greenhybrid_bem3d(bem_dlp, KMrb, KMcb, block, m, l,
delta, eps_aca,
build_bem3d_cube_quadpoints);
test_h2matrix_system("Greenhybrid", Vfull, KMfull, block, bem_slp, V2,
bem_dlp, KM2, false, true, 1.0e-3, 2.0e-3);
/* Nearfield computation on GPU not applicable here yet! */
// setup_h2matrix_aprx_greenhybrid_ortho_bem3d(bem_slp, Vrb, Vcb, block, m, l,
// delta, eps_aca, build_bem3d_cube_quadpoints);
// setup_h2matrix_aprx_greenhybrid_ortho_bem3d(bem_dlp, KMrb, KMcb, block, m, l,
// delta, eps_aca, build_bem3d_cube_quadpoints);
// test_h2matrix_system("Greenhybrid ortho", Vfull, KMfull, block, bem_slp, V2,
// bem_dlp, KM2, false, true, 1.0e-3, 2.0e-3);
del_h2matrix(V2);
del_h2matrix(KM2);
del_block(block);
freemem(root->idx);
del_cluster(root);
del_helmholtz_ocl_bem3d(bem_slp);
del_helmholtz_ocl_bem3d(bem_dlp);
del_amatrix(Vfull);
del_amatrix(KMfull);
del_surface3d(gr);
del_macrosurface3d(mg);
freemem(idx);
(void) printf("----------------------------------------\n"
" %u matrices and\n"
" %u vectors still active\n"
" %u errors found\n", getactives_amatrix(),
getactives_avector(), problems);
uninit_h2lib();
return problems;
}
static void
test_h2matrix_system(const char *apprxtype, pcamatrix Vfull,
pcamatrix KMfull, pblock block, pbem3d bem_slp,
ph2matrix V, pbem3d bem_dlp, ph2matrix KM, bool linear,
bool exterior, real low, real high)
{
struct _eval_A eval;
helmholtz_data hdata;
pavector x, b;
real errorV, errorKM, error_solve, eps_solve;
uint steps;
boundary_func3d rhs = (boundary_func3d) rhs_dirichlet_point_helmholtzbem3d;
eps_solve = 1.0e-12;
steps = 1000;
printf("Testing: %s H2matrix %s\n"
"====================================\n\n",
(exterior == true ? "exterior" : "interior"), apprxtype);
assemble_bem3d_h2matrix_row_clusterbasis(bem_slp, V->rb);
assemble_bem3d_h2matrix_col_clusterbasis(bem_slp, V->cb);
SCHEDULE_OPENCL(0, 1, assemble_bem3d_h2matrix, bem_slp, block, V);
assemble_bem3d_h2matrix_row_clusterbasis(bem_dlp, KM->rb);
assemble_bem3d_h2matrix_col_clusterbasis(bem_dlp, KM->cb);
SCHEDULE_OPENCL(0, 1, assemble_bem3d_h2matrix, bem_dlp, block, KM);
eval.V = V;
eval.Vtype = H2MATRIX;
eval.KM = KM;
eval.KMtype = H2MATRIX;
eval.eta =
REAL_SQRT(ABSSQR(bem_slp->kvec[0]) + ABSSQR(bem_slp->kvec[1]) +
ABSSQR(bem_slp->kvec[2]));
hdata.kvec = bem_slp->kvec;
hdata.source = allocreal(3);
if (exterior) {
hdata.source[0] = 0.0, hdata.source[1] = 0.0, hdata.source[2] = 0.2;
}
else {
hdata.source[0] = 0.0, hdata.source[1] = 0.0, hdata.source[2] = 5.0;
}
errorV = norm2diff_amatrix_h2matrix(V, Vfull) / norm2_amatrix(Vfull);
printf("rel. error V : %.5e\n", errorV);
errorKM = norm2diff_amatrix_h2matrix(KM, KMfull) / norm2_amatrix(KMfull);
printf("rel. error K%c0.5*M : %.5e\n", (exterior == true ? '-' : '+'),
errorKM);
x = new_avector(Vfull->rows);
b = new_avector(KMfull->cols);
printf("Solving Dirichlet problem:\n");
integrate_bem3d_const_avector(bem_dlp, rhs, b, (void *) &hdata);
solve_gmres_bem3d(HMATRIX, &eval, b, x, eps_solve, steps);
error_solve = max_rel_outer_error(bem_slp, &hdata, x, rhs);
printf("max. rel. error : %.5e %s\n", error_solve,
(IS_IN_RANGE(low, error_solve, high) ? " okay" : "NOT okay"));
if (!IS_IN_RANGE(low, error_solve, high))
problems++;
printf("\n");
del_avector(x);
del_avector(b);
freemem(hdata.source);
}
void
draw_cairo_tri2d(pctri2d t2, const char *filename, bool mark_refedges,
int mark_triangle)
{
#ifdef USE_CAIRO
cairo_surface_t *surface;
cairo_t *cr;
const real(*x)[2] = (const real(*)[2]) t2->x;
const uint(*e)[2] = (const uint(*)[2]) t2->e;
const uint(*t)[3] = (const uint(*)[3]) t2->t;
uint vertices = t2->vertices;
uint edges = t2->edges;
uint triangles = t2->triangles;
double xmin, xmax, ymin, ymax;
double hmin, hk, x0, y0, dx, dy, nx, ny;
uint k;
xmin = xmax = x[0][0];
ymin = ymax = x[0][1];
for (k = 1; k < vertices; k++) {
if (x[k][0] < xmin)
xmin = x[k][0];
else if (x[k][0] > xmax)
xmax = x[k][0];
if (x[k][1] < ymin)
ymin = x[k][1];
else if (x[k][1] > ymax)
ymax = x[k][1];
}
surface = cairo_pdf_surface_create(filename, 100.0 * (xmax - xmin),
100.0 * (ymax - ymin));
cr = cairo_create(surface);
cairo_surface_destroy(surface);
cairo_translate(cr, -100.0 * xmin, -100.0 * ymin);
cairo_scale(cr, 95.0, 95.0);
cairo_set_line_width(cr, cairo_get_line_width(cr) / 95.0);
cairo_scale(cr, 1.0, -1.0);
cairo_set_source_rgb(cr, 1.0, 0.0, 0.0);
if (mark_triangle >= 0) {
k = mark_triangle;
cairo_move_to(cr, x[e[t[k][0]][0]][0], x[e[t[k][0]][0]][1]);
cairo_line_to(cr, x[e[t[k][0]][1]][0], x[e[t[k][0]][1]][1]);
if (e[t[k][1]][0] == e[t[k][0]][0] || e[t[k][1]][0] == e[t[k][0]][1])
cairo_line_to(cr, x[e[t[k][1]][1]][0], x[e[t[k][1]][1]][1]);
else
cairo_line_to(cr, x[e[t[k][1]][0]][0], x[e[t[k][1]][0]][1]);
cairo_close_path(cr);
cairo_fill(cr);
}
if (mark_refedges) {
hmin =
REAL_SQRT(REAL_SQR(x[e[0][0]][0] - x[e[0][1]][0]) +
REAL_SQR(x[e[0][0]][1] - x[e[0][1]][1]));
for (k = 1; k < edges; k++) {
hk =
REAL_SQRT(REAL_SQR(x[e[k][0]][0] - x[e[k][1]][0]) +
REAL_SQR(x[e[k][0]][1] - x[e[k][1]][1]));
if (hk < hmin)
hmin = hk;
}
hk = xmax - xmin;
if (ymax - ymin < hk)
hk = ymax - ymin;
if (hmin > 0.05 * hk)
hmin = 0.05 * hk;
cairo_set_source_rgb(cr, 0.0, 0.0, 1.0);
for (k = 0; k < triangles; k++) {
cairo_move_to(cr, x[e[t[k][0]][0]][0], x[e[t[k][0]][0]][1]);
cairo_line_to(cr, x[e[t[k][0]][1]][0], x[e[t[k][0]][1]][1]);
nx = x[e[t[k][0]][1]][1] - x[e[t[k][0]][0]][1];
ny = x[e[t[k][0]][0]][0] - x[e[t[k][0]][1]][0];
hk = REAL_SQRT(REAL_SQR(nx) + REAL_SQR(ny));
nx /= hk;
ny /= hk;
if (e[t[k][1]][0] == e[t[k][2]][0] || e[t[k][1]][0] == e[t[k][2]][1]) {
x0 = x[e[t[k][1]][0]][0];
y0 = x[e[t[k][1]][0]][1];
}
else {
assert(e[t[k][1]][1] == e[t[k][2]][0]
|| e[t[k][1]][1] == e[t[k][2]][1]);
x0 = x[e[t[k][1]][1]][0];
y0 = x[e[t[k][1]][1]][1];
}
dx = x0 - x[e[t[k][0]][1]][0];
dy = y0 - x[e[t[k][0]][1]][1];
hk = REAL_ABS(dx * nx + dy * ny);
dx /= hk;
dy /= hk;
cairo_line_to(cr, x[e[t[k][0]][1]][0] + hmin * 0.2 * dx,
x[e[t[k][0]][1]][1] + hmin * 0.2 * dy);
dx = x0 - x[e[t[k][0]][0]][0];
dy = y0 - x[e[t[k][0]][0]][1];
hk = REAL_ABS(dx * nx + dy * ny);
dx /= hk;
dy /= hk;
cairo_line_to(cr, x[e[t[k][0]][0]][0] + hmin * 0.2 * dx,
x[e[t[k][0]][0]][1] + hmin * 0.2 * dy);
cairo_close_path(cr);
cairo_fill(cr);
}
}
cairo_set_source_rgb(cr, 0.0, 0.0, 0.0);
for (k = 0; k < edges; k++) {
cairo_move_to(cr, x[e[k][0]][0], x[e[k][0]][1]);
cairo_line_to(cr, x[e[k][1]][0], x[e[k][1]][1]);
cairo_stroke(cr);
}
cairo_destroy(cr);
#else
fprintf(stderr, "CAIRO not supported.\n");
#endif
}
field
eval_brakhage_werner_c(pcbem3d bem, pcavector w, field eta, real * x)
{
pcsurface3d gr = bem->gr;
const real(*gr_x)[3] = (const real(*)[3]) gr->x;
const uint(*gr_t)[3] = (const uint(*)[3]) gr->t;
const real(*gr_n)[3] = (const real(*)[3]) gr->n;
const preal gr_g = (const preal) gr->g;
const uint rows = gr->triangles;
const field *kvec = bem->kvec;
uint nq = bem->sq->n_single;
real *xx = bem->sq->x_single;
real *yy = bem->sq->y_single;
real *ww = bem->sq->w_single + 3 * nq;
const real *A, *B, *C, *ns;
uint s, ss, q;
real gs_fac, dx, dy, dz, tx, sx, Ax, Bx, Cx, norm, rnorm, norm2;
field k, sum;
field res;
k = REAL_SQRT(ABSSQR(kvec[0]) + ABSSQR(kvec[1]) + ABSSQR(kvec[2]));
/*
* integrate kernel function over first variable with constant basisfunctions
*/
res = 0.0;
for (s = 0; s < rows; ++s) {
ss = s;
gs_fac = gr_g[ss] * 0.0795774715459476679;
ns = gr_n[ss];
A = gr_x[gr_t[ss][0]];
B = gr_x[gr_t[ss][1]];
C = gr_x[gr_t[ss][2]];
sum = 0.0;
for (q = 0; q < nq; ++q) {
tx = xx[q];
sx = yy[q];
Ax = 1.0 - tx;
Bx = tx - sx;
Cx = sx;
dx = x[0] - (A[0] * Ax + B[0] * Bx + C[0] * Cx);
dy = x[1] - (A[1] * Ax + B[1] * Bx + C[1] * Cx);
dz = x[2] - (A[2] * Ax + B[2] * Bx + C[2] * Cx);
norm2 = dx * dx + dy * dy + dz * dz;
rnorm = REAL_RSQRT(norm2);
norm = norm2 * rnorm;
rnorm *= rnorm * rnorm;
sum += ww[q]
* cexp(I * k * norm)
* rnorm
* ((1.0 - I * k * norm) * (dx * ns[0] + dy * ns[1] + dz * ns[2]) - I
* eta * norm2);
}
res += sum * gs_fac * w->v[ss];
}
return res;
}
void
getproperties_surface3d(pcsurface3d gr, preal hmin, preal hmax,
preal anglemin, preal angleedge)
{
uint edges = gr->edges;
uint triangles = gr->triangles;
const real(*x)[3] = (const real(*)[3]) gr->x;
const uint(*t)[3] = (const uint(*)[3]) gr->t;
const uint(*s)[3] = (const uint(*)[3]) gr->s;
const real(*n)[3] = (const real(*)[3]) gr->n;
const real *g = (const real *) gr->g;
uint *neighbour;
real dt[3], ds[3], h[3], nn, angle;
real h_min, h_max, angle_min, angle_edge;
uint i, j;
/* Just to avoid warnings */
h_min = h_max = angle_min = 0.0;
for (i = 0; i < triangles; i++) {
dt[0] = x[t[i][1]][0] - x[t[i][0]][0];
dt[1] = x[t[i][1]][1] - x[t[i][0]][1];
dt[2] = x[t[i][1]][2] - x[t[i][0]][2];
ds[0] = x[t[i][2]][0] - x[t[i][0]][0];
ds[1] = x[t[i][2]][1] - x[t[i][0]][1];
ds[2] = x[t[i][2]][2] - x[t[i][0]][2];
h[0] = (REAL_SQR(dt[0]) + REAL_SQR(dt[1]) + REAL_SQR(dt[2]));
h[1] = (REAL_SQR(ds[0]) + REAL_SQR(ds[1]) + REAL_SQR(ds[2]));
h[2] = (REAL_SQR(dt[0] - ds[0]) + REAL_SQR(dt[1] - ds[1])
+ REAL_SQR(dt[2] - ds[2]));
if (i == 0 || h[0] < h_min)
h_min = h[0];
if (i == 0 || h[0] > h_max)
h_max = h[0];
if (h[1] < h_min)
h_min = h[1];
if (h[1] > h_max)
h_max = h[1];
if (h[2] < h_min)
h_min = h[2];
if (h[2] > h_max)
h_max = h[2];
angle = g[i] / REAL_SQRT(h[0] * h[1]);
if (i == 0 || angle < angle_min)
angle_min = angle;
}
if (hmin)
*hmin = REAL_SQRT(h_min);
if (hmax)
*hmax = REAL_SQRT(h_max);
if (anglemin)
*anglemin = REAL_ASIN(angle_min);
if (angleedge) {
neighbour = (uint *) allocmem(sizeof(uint) * edges);
for (i = 0; i < edges; i++)
neighbour[i] = triangles;
angle_edge = 1.0;
for (i = 0; i < triangles; i++) {
if (neighbour[s[i][0]] < triangles) {
j = neighbour[s[i][0]];
nn = (n[i][0] * n[j][0] + n[i][1] * n[j][1] + n[i][2] * n[j][2]);
if (nn < angle_edge)
angle_edge = nn;
}
else
neighbour[s[i][0]] = i;
if (neighbour[s[i][1]] < triangles) {
j = neighbour[s[i][1]];
nn = (n[i][0] * n[j][0] + n[i][1] * n[j][1] + n[i][2] * n[j][2]);
if (nn < angle_edge)
angle_edge = nn;
}
else
neighbour[s[i][1]] = i;
if (neighbour[s[i][2]] < triangles) {
j = neighbour[s[i][2]];
nn = (n[i][0] * n[j][0] + n[i][1] * n[j][1] + n[i][2] * n[j][2]);
if (nn < angle_edge)
angle_edge = nn;
}
else
neighbour[s[i][2]] = i;
}
*angleedge = REAL_ACOS(angle_edge);
freemem(neighbour);
}
}
