def sym_operator(self): d = self.ambient_dim w = sym.make_sym_array("w", d + 1) u = w[0] v = w[1:] # boundary conditions ------------------------------------------------- # dirichlet BCs ------------------------------------------------------- dir_u = sym.cse(sym.interp("vol", self.dirichlet_tag)(u)) dir_v = sym.cse(sym.interp("vol", self.dirichlet_tag)(v)) if self.dirichlet_bc_f: # FIXME from warnings import warn warn("Inhomogeneous Dirichlet conditions on the wave equation " "are still having issues.") dir_g = sym.Field("dir_bc_u") dir_bc = join_fields(2 * dir_g - dir_u, dir_v) else: dir_bc = join_fields(-dir_u, dir_v) dir_bc = sym.cse(dir_bc, "dir_bc") # neumann BCs --------------------------------------------------------- neu_u = sym.cse(sym.interp("vol", self.neumann_tag)(u)) neu_v = sym.cse(sym.interp("vol", self.neumann_tag)(v)) neu_bc = sym.cse(join_fields(neu_u, -neu_v), "neu_bc") # radiation BCs ------------------------------------------------------- rad_normal = sym.normal(self.radiation_tag, d) rad_u = sym.cse(sym.interp("vol", self.radiation_tag)(u)) rad_v = sym.cse(sym.interp("vol", self.radiation_tag)(v)) rad_bc = sym.cse( join_fields( 0.5 * (rad_u - self.sign * np.dot(rad_normal, rad_v)), 0.5 * rad_normal * (np.dot(rad_normal, rad_v) - self.sign * rad_u)), "rad_bc") # entire operator ----------------------------------------------------- def flux(pair): return sym.interp(pair.dd, "all_faces")(self.flux(pair)) result = sym.InverseMassOperator()( join_fields(-self.c * np.dot(sym.stiffness_t(self.ambient_dim), v), -self.c * (sym.stiffness_t(self.ambient_dim) * u)) - sym.FaceMassOperator() (flux(sym.int_tpair(w)) + flux(sym.bv_tpair(self.dirichlet_tag, w, dir_bc)) + flux(sym.bv_tpair(self.neumann_tag, w, neu_bc)) + flux(sym.bv_tpair(self.radiation_tag, w, rad_bc)))) result[0] += self.source_f return result
def sym_operator(self): u = sym.var("u") def flux(pair): return sym.project(pair.dd, face_dd)(self.flux(pair)) face_dd = sym.DOFDesc(sym.FACE_RESTR_ALL, self.quad_tag) boundary_dd = sym.DOFDesc(sym.BTAG_ALL, self.quad_tag) quad_dd = sym.DOFDesc(sym.DTAG_VOLUME_ALL, self.quad_tag) to_quad = sym.project(sym.DD_VOLUME, quad_dd) stiff_t_op = sym.stiffness_t(self.ambient_dim, dd_in=quad_dd, dd_out=sym.DD_VOLUME) quad_v = to_quad(self.v) quad_u = to_quad(u) return sym.InverseMassOperator()( sum(stiff_t_op[n](quad_u * quad_v[n]) for n in range(self.ambient_dim)) - sym.FaceMassOperator(face_dd, sym.DD_VOLUME)( flux(sym.int_tpair(u, self.quad_tag)) + flux(sym.bv_tpair(boundary_dd, u, self.inflow_u)) # FIXME: Add back support for inflow/outflow tags #+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in)) #+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out)) ))
def sym_operator(self): u = sym.var("u") # boundary conditions ------------------------------------------------- bc_in = self.inflow_u all_faces_dd = sym.DOFDesc(sym.FACE_RESTR_ALL, self.quad_tag) boundary_dd = sym.DOFDesc(sym.BTAG_ALL, self.quad_tag) def flux(pair): return sym.interp(pair.dd, all_faces_dd)( self.flux(pair)) quad_dd = sym.DOFDesc("vol", self.quad_tag) to_quad = sym.interp("vol", quad_dd) stiff_t = sym.stiffness_t(self.ambient_dim, quad_dd, "vol") quad_v = to_quad(self.v) quad_u = to_quad(u) return sym.InverseMassOperator()( (stiff_t[0](quad_u * quad_v[0]) + stiff_t[1](quad_u * quad_v[1])) - sym.FaceMassOperator(all_faces_dd, "vol")( flux(sym.int_tpair(u, self.quad_tag)) + flux(sym.bv_tpair(boundary_dd, u, bc_in)) # FIXME: Add back support for inflow/outflow tags #+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in)) #+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out)) ))
def sym_operator(self, w=None): """The full operator template - the high level description of the Maxwell operator. Combines the relevant operator templates for spatial derivatives, flux, boundary conditions etc. """ from grudge.tools import count_subset w = sym.make_sym_array("w", count_subset(self.get_eh_subset())) elec_components = count_subset(self.get_eh_subset()[0:3]) mag_components = count_subset(self.get_eh_subset()[3:6]) if self.fixed_material: # need to check this material_divisor = ([self.epsilon] * elec_components + [self.mu] * mag_components) tags_and_bcs = [ (self.pec_tag, self.pec_bc(w)), (self.pmc_tag, self.pmc_bc(w)), (self.absorb_tag, self.absorbing_bc(w)), (self.incident_tag, self.incident_bc(w)), ] def flux(pair): return sym.project(pair.dd, "all_faces")(self.flux(pair)) return (-self.local_derivatives(w) - sym.InverseMassOperator() (sym.FaceMassOperator()(flux(sym.int_tpair(w)) + sum( flux(sym.bv_tpair(tag, w, bc)) for tag, bc in tags_and_bcs)))) / material_divisor
def sym_operator(self): from grudge.dof_desc import DOFDesc, DD_VOLUME, DTAG_VOLUME_ALL from meshmode.mesh import BTAG_ALL from meshmode.discretization.connection import FACE_RESTR_ALL u = sym.var("u") def flux(pair): return sym.project(pair.dd, face_dd)(self.flux(pair)) face_dd = DOFDesc(FACE_RESTR_ALL, self.quad_tag) boundary_dd = DOFDesc(BTAG_ALL, self.quad_tag) quad_dd = DOFDesc(DTAG_VOLUME_ALL, self.quad_tag) to_quad = sym.project(DD_VOLUME, quad_dd) stiff_t_op = sym.stiffness_t(self.ambient_dim, dd_in=quad_dd, dd_out=DD_VOLUME) quad_v = to_quad(self.v) quad_u = to_quad(u) return sym.InverseMassOperator()( sum(stiff_t_op[n](quad_u * quad_v[n]) for n in range(self.ambient_dim)) - sym.FaceMassOperator(face_dd, DD_VOLUME)( flux(sym.int_tpair(u, self.quad_tag)) + flux(sym.bv_tpair(boundary_dd, u, self.inflow_u)) # FIXME: Add back support for inflow/outflow tags #+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in)) #+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out)) ))
def get_strong_wave_op_with_discr_direct(cl_ctx, dims=2, order=4): from meshmode.mesh.generation import generate_regular_rect_mesh mesh = generate_regular_rect_mesh(a=(-0.5, ) * dims, b=(0.5, ) * dims, n=(16, ) * dims) logger.debug("%d elements", mesh.nelements) discr = DGDiscretizationWithBoundaries(cl_ctx, mesh, order=order) source_center = np.array([0.1, 0.22, 0.33])[:dims] source_width = 0.05 source_omega = 3 sym_x = sym.nodes(mesh.dim) sym_source_center_dist = sym_x - source_center sym_t = sym.ScalarVariable("t") from meshmode.mesh import BTAG_ALL c = -0.1 sign = -1 w = sym.make_sym_array("w", dims + 1) u = w[0] v = w[1:] source_f = ( sym.sin(source_omega * sym_t) * sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) / source_width**2)) rad_normal = sym.normal(BTAG_ALL, dims) rad_u = sym.cse(sym.interp("vol", BTAG_ALL)(u)) rad_v = sym.cse(sym.interp("vol", BTAG_ALL)(v)) rad_bc = sym.cse( sym.join_fields( 0.5 * (rad_u - sign * np.dot(rad_normal, rad_v)), 0.5 * rad_normal * (np.dot(rad_normal, rad_v) - sign * rad_u)), "rad_bc") sym_operator = ( -sym.join_fields(-c * np.dot(sym.nabla(dims), v) - source_f, -c * (sym.nabla(dims) * u)) + sym.InverseMassOperator()( sym.FaceMassOperator() (dg_flux(c, sym.int_tpair(w)) + dg_flux(c, sym.bv_tpair(BTAG_ALL, w, rad_bc))))) return (sym_operator, discr)
def sym_operator(self): u = sym.var("u") def flux(pair): return sym.project(pair.dd, "all_faces")(self.flux(pair)) return (-self.v.dot( sym.nabla(self.ambient_dim) * u ) + sym.InverseMassOperator()( sym.FaceMassOperator()( flux(sym.int_tpair(u)) + flux(sym.bv_tpair(sym.BTAG_ALL, u, self.inflow_u)) # FIXME: Add back support for inflow/outflow tags #+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in)) #+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out)) )))
def sym_operator(self): u = sym.var("u") def flux(pair): return sym.project(pair.dd, "all_faces")(self.flux(pair)) bc_in = self.inflow_u # bc_out = sym.project(sym.DD_VOLUME, self.outflow_tag)(u) return sym.InverseMassOperator()( np.dot(self.v, sym.stiffness_t(self.ambient_dim) * u) - sym.FaceMassOperator()( flux(sym.int_tpair(u)) + flux(sym.bv_tpair(sym.BTAG_ALL, u, bc_in)) # FIXME: Add back support for inflow/outflow tags #+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in)) #+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out)) ))
def sym_operator(self): u = sym.var("u") # boundary conditions ------------------------------------------------- bc_in = self.inflow_u # bc_out = sym.interp("vol", self.outflow_tag)(u) def flux(pair): return sym.interp(pair.dd, "all_faces")( self.flux(pair)) return sym.InverseMassOperator()( np.dot( self.v, sym.stiffness_t(self.ambient_dim)*u) - sym.FaceMassOperator()( flux(sym.int_tpair(u)) + flux(sym.bv_tpair(sym.BTAG_ALL, u, bc_in)) # FIXME: Add back support for inflow/outflow tags #+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in)) #+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out)) ))