/**
* @param x coordinates of point to be tested
* @param t coordinates of apex point of cone
* @param b coordinates of center of basement circle
* @param aperture in radians
Code copied from http://stackoverflow.com/questions/10768142/verify-if-point-is-inside-a-cone-in-3d-space
credit to: furikuretsu
altered to suit this purpose
*/
static bool isLyingInCone(float x[], float t[], float b[], float radius, float height)
{
float aperture = 2.f * atan(radius/height);
// This is for our convenience
float halfAperture = aperture/2.f;
// Vector pointing to X point from apex
float apexToXVect[] = {t[0]-x[0],t[1]-x[1],t[2]-x[2]};
// Vector pointing from apex to circle-center point.
float axisVect[] = {t[0]-b[0],t[1]-b[1],t[2]-b[2]};
// X is lying in cone only if it's lying in
// infinite version of its cone -- that is,
// not limited by "round basement".
// We'll use dotProd() to
// determine angle between apexToXVect and axis.
bool isInInfiniteCone = dotProd(apexToXVect,axisVect)/magn(apexToXVect)/magn(axisVect) > cos(halfAperture);
// We can safely compare cos() of angles
// between vectors instead of bare angles.
return isInInfiniteCone;
}
void NonlinSystem::assemble(bool rhsonly)
{
// sanity checks
int ndof = this->get_num_dofs();
if (rhsonly) error("Parameter rhsonly = true has no meaning in NonlinSystem.");
if (this->have_spaces == false)
error("Before assemble(), you need to initialize spaces.");
if (this->spaces == NULL) error("spaces = NULL in LinSystem::assemble().");
// assemble J(Y_n) and store in A, assemble F(Y_n) and store in RHS
LinSystem::assemble();
// calculate norms of the residual F(Y_n)
res_l2 = res_l1 = res_max = 0.0;
for (int i = 0; i < ndof; i++)
{
res_l2 += sqr(this->RHS[i]);
res_l1 += magn(this->RHS[i]);
if (magn(this->RHS[i]) > res_max) res_max = magn(this->RHS[i]);
}
res_l2 = sqrt(res_l2);
// multiply RHS by -alpha
for (int i = 0; i < ndof; i++)
this->RHS[i] *= -this->alpha;
}
const BigInt operator /(const BigInt& amount1, const BigInt& amount2)
{
// magn = magnificent;
BigInt quotient, magn(amount2), dividend(amount1), divisor(amount2);
dividend.sign = divisor.sign = 0;
if(dividend < divisor)
return BigInt(0);
if(dividend > divisor)
magn = magn.leftShift(dividend.length - divisor.length);
//if(dividend < magn)
// magn = magn.rightShift(); // magn = magn/10;
if(dividend >= magn)
quotient.length = amount1.length - amount2.length + 1;
else{
quotient.length = amount1.length - amount2.length;
magn = magn.rightShift(); // magn = magn/10;
}
quotient.digit = new int[quotient.length];
for(int i = 0 ; i < quotient.length ; i++)
quotient.digit[i] = 0;
int index(0);
while(dividend >= divisor){
while(dividend >= magn)
{
quotient.digit[index]++;
dividend = dividend - magn;
}
magn = magn.rightShift();
index++;
}
if(amount1.getSign() == amount2.getSign())
return BigInt( quotient.digit , quotient.length, quotient.sign);
else
return BigInt( quotient.digit , quotient.length, !quotient.sign);
}
//"рисует" одну линию поля из начальной точки PointB
//с помощью функций работающих с Z-буфером
void LineField(HDC hdc,POINT3 PointB,COLORREF rgb, double force)
{
VECTORS vect;
vect.x = PointB.x;
vect.y = PointB.y;
vect.z = PointB.z;
//видовые координаты проецируемой точки
double xe, ye, ze1, ze2;
//координаты пикселов
int x1,y1,x2,y2;
double dt = force > 0 ? 0.1 : -0.1; //длина шага на линии поля
double x, y, z, Hx, Hy, Hz, Ha;
int k = 0;
VECMAG mag;
int step = 0;
double xt1,yt1,zt1,xt2,yt2,zt2;
do
{
step++;
x = vect.x;
y = vect.y;
z = vect.z;
mag = magn(x,y,z);
Hx = mag.hx;
Hy = mag.hy;
Hz = mag.hz;
Ha = sqrt(Hx*Hx + Hy*Hy + Hz*Hz);
vect.dx = Hx/Ha;
vect.dy = Hy/Ha;
vect.dz = Hz/Ha;
xt1 = vect.x; yt1 = vect.y; zt1 = vect.z;
xt2 = xt1 + vect.dx*dt;
yt2 = yt1 + vect.dy*dt;
zt2 = zt1 + vect.dz*dt;
xe = Xe(xt1, yt1, zt1);
ye=Ye(xt1,yt1,zt1);
ze1=Ze(xt1,yt1,zt1);
x1=xn(xe);
y1=ym(ye);
xe = Xe(xt2, yt2, zt1);
ye=Ye(xt2,yt2,zt2);
ze2=Ze(xt2,yt2,zt2);
x2=xn(xe);
y2=ym(ye);
//"рисуем" отрезок линии поля
ZbufLineWidth(hdc,x1,y1,x2,y2,ze1,ze2,3,rgb);
vect.x = xt2;
vect.y = yt2;
vect.z = zt2;
//после 10-и шагов на лини поля "рисуем" стрелку
k++;
if(k == 10)
{
arrowVector(hdc,x1,y1,x2,y2,ze2,RGB(0,0,255));
k = 0;
}
//прекращаем рисовать линию поля на границе куба
} while (step < 1000 && (x>-xmax) && (x<xmax) && (y>-ymax) && (y<ymax) && (z>-zmax) && (z<zmax));
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
MeshReaderH2D mloader;
if (ALIGN_MESH)
mloader.load("oven_load_circle.mesh", &mesh);
else
mloader.load("oven_load_square.mesh", &mesh);
// Perform initial mesh refinemets.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Initialize boundary conditions
DefaultEssentialBCConst<std::complex<double> > bc_essential(BDY_PERFECT_CONDUCTOR, std::complex<double>(0.0, 0.0));
EssentialBCs<std::complex<double> > bcs(&bc_essential);
// Create an Hcurl space with default shapeset.
HcurlSpace<std::complex<double> > space(&mesh, &bcs, P_INIT);
int ndof = space.get_num_dofs();
Hermes::Mixins::Loggable::Static::info("ndof = %d", ndof);
// Initialize the weak formulation.
CustomWeakForm wf(e_0, mu_0, mu_r, kappa, omega, J, ALIGN_MESH, &mesh, BDY_CURRENT);
// Initialize coarse and reference mesh solution.
Solution<std::complex<double> > sln, ref_sln;
// Initialize refinements selector.
HcurlProjBasedSelector<std::complex<double> > selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Initialize views.
ScalarView eview("Electric field", new WinGeom(0, 0, 580, 400));
OrderView oview("Polynomial orders", new WinGeom(590, 0, 550, 400));
// DOF and CPU convergence graphs initialization.
SimpleGraph graph_dof, graph_cpu;
// Time measurement.
Hermes::Mixins::TimeMeasurable cpu_time;
cpu_time.tick();
// Adaptivity loop:
int as = 1; bool done = false;
do
{
Hermes::Mixins::Loggable::Static::info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
Mesh::ReferenceMeshCreator refMeshCreator(&mesh);
Mesh* ref_mesh = refMeshCreator.create_ref_mesh();
Space<std::complex<double> >::ReferenceSpaceCreator refSpaceCreator(&space, ref_mesh);
Space<std::complex<double> >* ref_space = refSpaceCreator.create_ref_space();
int ndof_ref = Space<std::complex<double> >::get_num_dofs(ref_space);
// Initialize reference problem.
Hermes::Mixins::Loggable::Static::info("Solving on reference mesh.");
DiscreteProblem<std::complex<double> > dp(&wf, ref_space);
// Time measurement.
cpu_time.tick();
// Perform Newton's iteration.
Hermes::Hermes2D::NewtonSolver<std::complex<double> > newton(&dp);
try
{
newton.set_newton_max_iter(NEWTON_MAX_ITER);
newton.set_newton_tol(NEWTON_TOL);
newton.solve();
}
catch(Hermes::Exceptions::Exception e)
{
e.print_msg();
throw Hermes::Exceptions::Exception("Newton's iteration failed.");
};
// Translate the resulting coefficient vector into the Solution<std::complex<double> > sln.
Hermes::Hermes2D::Solution<std::complex<double> >::vector_to_solution(newton.get_sln_vector(), ref_space, &ref_sln);
// Project the fine mesh solution onto the coarse mesh.
Hermes::Mixins::Loggable::Static::info("Projecting reference solution on coarse mesh.");
OGProjection<std::complex<double> > ogProjection; ogProjection.project_global(&space, &ref_sln, &sln);
// View the coarse mesh solution and polynomial orders.
RealFilter real(&sln);
MagFilter<double> magn(&real);
ValFilter limited_magn(&magn, 0.0, 4e3);
char title[100];
sprintf(title, "Electric field, adaptivity step %d", as);
eview.set_title(title);
//eview.set_min_max_range(0.0, 4e3);
eview.show(&limited_magn);
sprintf(title, "Polynomial orders, adaptivity step %d", as);
oview.set_title(title);
oview.show(&space);
// Calculate element errors and total error estimate.
Hermes::Mixins::Loggable::Static::info("Calculating error estimate.");
Adapt<std::complex<double> >* adaptivity = new Adapt<std::complex<double> >(&space);
// Set custom error form and calculate error estimate.
CustomErrorForm cef(kappa);
adaptivity->set_error_form(0, 0, &cef);
double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln) * 100;
// Report results.
Hermes::Mixins::Loggable::Static::info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%",
Space<std::complex<double> >::get_num_dofs(&space),
Space<std::complex<double> >::get_num_dofs(ref_space), err_est_rel);
// Time measurement.
cpu_time.tick();
// Add entry to DOF and CPU convergence graphs.
graph_dof.add_values(Space<std::complex<double> >::get_num_dofs(&space), err_est_rel);
graph_dof.save("conv_dof_est.dat");
graph_cpu.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu.save("conv_cpu_est.dat");
// If err_est too large, adapt the mesh.
if (err_est_rel < ERR_STOP) done = true;
else
{
Hermes::Mixins::Loggable::Static::info("Adapting coarse mesh.");
done = adaptivity->adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);
}
if (space.get_num_dofs() >= NDOF_STOP) done = true;
delete adaptivity;
if(!done)
{
delete ref_space->get_mesh();
delete ref_space;
}
// Increase counter.
as++;
}
while (done == false);
Hermes::Mixins::Loggable::Static::info("Total running time: %g s", cpu_time.accumulated());
RealFilter ref_real(&sln);
MagFilter<double> ref_magn(&ref_real);
ValFilter ref_limited_magn(&ref_magn, 0.0, 4e3);
eview.set_title("Fine mesh solution - magnitude");
eview.show(&ref_limited_magn);
// Output solution in VTK format.
Linearizer lin;
bool mode_3D = true;
lin.save_solution_vtk(&ref_limited_magn, "sln.vtk", "Magnitude of E", mode_3D);
Hermes::Mixins::Loggable::Static::info("Solution in VTK format saved to file %s.", "sln.vtk");
// Wait for all views to be closed.
View::wait();
return 0;
}
