def uexactfn(t,cp): th,phi,r = cart2sph(cp[:,0],cp[:,1],cp[:,2]) return np.exp(-2*t)*np.cos(phi + np.pi / 2) if __name__ == '__main__': MBlocklist = [10,20,40,80] error = [] dx = [] comm = MPI.COMM_WORLD surface = Sphere(center=np.array([0.0, 0.0, 0.0])) # exact solution rez = 30 xx, yy, zz = surface.parametric_grid(rez) th, phi, r = cart2sph(xx,yy,zz) exactu = np.cos(phi + np.pi / 2).ravel() points = np.array([xx.ravel(),yy.ravel(),zz.ravel()]).T vsize = xx.ravel().shape[0] vAssigned = vsize // comm.size + int(comm.rank < (vsize % comm.size)) vstart = comm.exscan(vAssigned) if comm.rank == 0: vstart = 0 for MBlock in MBlocklist: opt = {'M':MBlock,'m':5,'d':3} band = Band(surface,comm,opt) _,_,v,v2 = band.createGLVectors()
def uexactfn(t,cp): th,phi,r = cart2sph(cp[:,0],cp[:,1],cp[:,2]) return np.exp(-2*t)*np.cos(phi + np.pi / 2)
p=p, diff_stencil_arm=diff_stencil_arm) cp2, distance2, _, _ = s.closest_point(grid) assert np.allclose(cp, cp2) assert np.allclose(distance, distance2) # Corners of the virtual grid, superset of `grid` ll = np.array(dim * [grid.min()]) - 3 * dx ur = np.array(dim * [grid.max()]) + 3 * dx virtual_grid_shape = np.abs(ur-ll) / dx + 1 # The (i,j,...) indices of the grid points, taking `ll` as origin. int_grid = np.round((grid - ll) / dx).astype(np.int) # Initial conditions th, phi, r = cart2sph(grid[:, 0], grid[:, 1], grid[:, 2]) u = np.cos(phi + np.pi / 2) # Let's keep a copy of the initial conditions initial_u = u.copy() # Build interpolation and differential matrix. E = build_interp_matrix(int_grid, cp, dx, p, ll, virtual_grid_shape) L = build_diff_matrix(int_grid, dx, virtual_grid_shape) M = build_linear_diagonal_splitting(L, E) # Compute eigenvalues t = time() print "Computing eigenvalues..." Evals, Evecs = splinalg.eigs(-M, k=32, which="SM") sorted_indices = np.argsort(Evals) print "...took", time() -t
p=p, diff_stencil_arm=diff_stencil_arm) cp2, distance2, _, _ = s.closest_point(grid) assert np.allclose(cp, cp2) assert np.allclose(distance, distance2) # Corners of the virtual grid, superset of `grid` ll = np.array(dim * [grid.min()]) - 3 * dx ur = np.array(dim * [grid.max()]) + 3 * dx virtual_grid_shape = np.abs(ur - ll) / dx + 1 # The (i,j,...) indices of the grid points, taking `ll` as origin. int_grid = np.round((grid - ll) / dx).astype(np.int) # Initial conditions th, phi, r = cart2sph(grid[:, 0], grid[:, 1], grid[:, 2]) u = np.cos(phi + np.pi / 2) # Let's keep a copy of the initial conditions initial_u = u.copy() # Build interpolation and differential matrix. E = build_interp_matrix(int_grid, cp, dx, p, ll, virtual_grid_shape) L = build_diff_matrix(int_grid, dx, virtual_grid_shape) xp, yp, zp = s.parametric_grid(65) _, phi_plot, _ = cart2sph(xp, yp, zp) Eplot = build_interp_matrix( int_grid, np.column_stack((xp.ravel(), yp.ravel(), zp.ravel())), dx, p, ll, virtual_grid_shape) if PLOT:
def initialu(cp): th, phi, r = cart2sph(cp[:, 0], cp[:, 1], cp[:, 2]) return np.cos(phi + np.pi / 2)
def initialu(cp): th,phi,r = cart2sph(cp[:,0],cp[:,1],cp[:,2]) return np.cos(phi + np.pi / 2)
th,phi,r = cart2sph(cp[:,0],cp[:,1],cp[:,2]) return np.cos(phi + np.pi / 2) if __name__ == '__main__': MBlocklist = [10,20,40,80] Tf = 0.5 error = [] dx = [] comm = MPI.COMM_WORLD surface = Sphere(center=np.array([0.0, 0.0, 0.0])) # exact solution rez = 30 xx, yy, zz = surface.parametric_grid(rez) th, phi, r = cart2sph(xx,yy,zz) exactu = np.cos(phi + np.pi / 2).ravel() points = np.array([xx.ravel(),yy.ravel(),zz.ravel()]).T vsize = xx.ravel().shape[0] vAssigned = vsize // comm.size + int(comm.rank < (vsize % comm.size)) vstart = comm.exscan(vAssigned) if comm.rank == 0: vstart = 0 for MBlock in MBlocklist: opt = {'M':MBlock,'m':5,'d':3} band = Band(surface,comm,opt)