def _build_eval_matrix(V, points): """Build the sparse m-by-n matrix that maps a coefficient set for a function in V to the values of that function at m given points.""" # See <https://www.allanswered.com/post/lkbkm/#zxqgk> mesh = V.mesh() bbt = BoundingBoxTree() bbt.build(mesh) dofmap = V.dofmap() el = V.element() sdim = el.space_dimension() rows = [] cols = [] data = [] for i, x in enumerate(points): cell_id = bbt.compute_first_entity_collision(Point(*x)) cell = Cell(mesh, cell_id) coordinate_dofs = cell.get_vertex_coordinates() rows.append(np.full(sdim, i)) cols.append(dofmap.cell_dofs(cell_id)) v = el.evaluate_basis_all(x, coordinate_dofs, cell_id) data.append(v) rows = np.concatenate(rows) cols = np.concatenate(cols) data = np.concatenate(data) m = len(points) n = V.dim() matrix = sparse.csr_matrix((data, (rows, cols)), shape=(m, n)) return matrix
class FEBasisFunction(object): '''Evaluator of dof of V on functions''' def __init__(self, V): self.elm = V.element() self.mesh = V.mesh() shape = V.ufl_element().value_shape() degree = V.ufl_element().degree() # A fake instanc to talk to with the world adapter = type('MiroHack', (Expression, ), {'value_shape': lambda self_, : shape, 'eval': lambda self_, values, x: self.eval(values, x)}) self.__adapter = adapter(degree=degree) is_1d_in_3d = self.mesh.topology().dim() == 1 and self.mesh.geometry().dim() == 3 self.orient_cell = cell_orientation(is_1d_in_3d) # Allocs self.__cell = Cell(self.mesh, 0) self.__cell_vertex_x = self.__cell.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(self.__cell) self.__dof = 0 self.__values = np.zeros(V.ufl_element().value_size()) @property def dof(self): return self.__dof @dof.setter def dof(self, value): assert value < self.elm.space_dimension() self.__dof = value @property def cell(self): return self.__cell @cell.setter def cell(self, value): cell_ = Cell(self.mesh, value) self.__cell_vertex_x[:] = cell_.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(cell_) self.__cell = cell_ def eval(self, values, x): self.elm.evaluate_basis(self.dof, values[:], x, self.__cell_vertex_x, self.__cell_orientation) def __call__(self, x): self.eval(self.__values, x) return 1*self.__values def as_expression(self): return self.__adapter
class FEBasisFunction(object): '''Evaluator of dof of V on functions''' def __init__(self, V): self.elm = V.element() self.mesh = V.mesh() shape = V.ufl_element().value_shape() degree = V.ufl_element().degree() # A fake instanc to talk to with the world adapter = type( 'MiroHack', (Expression, ), { 'value_shape': lambda self_, : shape, 'eval': lambda self_, values, x: self.eval(values, x) }) self.__adapter = adapter(degree=degree) is_1d_in_3d = self.mesh.topology().dim() == 1 and self.mesh.geometry( ).dim() == 3 self.orient_cell = cell_orientation(is_1d_in_3d) # Allocs self.__cell = Cell(self.mesh, 0) self.__cell_vertex_x = self.__cell.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(self.__cell) self.__dof = 0 self.__values = np.zeros(V.ufl_element().value_size()) @property def dof(self): return self.__dof @dof.setter def dof(self, value): assert value < self.elm.space_dimension() self.__dof = value @property def cell(self): return self.__cell @cell.setter def cell(self, value): cell_ = Cell(self.mesh, value) self.__cell_vertex_x[:] = cell_.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(cell_) self.__cell = cell_ def eval(self, values, x): self.elm.evaluate_basis(self.dof, values[:], x, self.__cell_vertex_x, self.__cell_orientation) def __call__(self, x): self.eval(self.__values, x) return 1 * self.__values def as_expression(self): return self.__adapter
def __init__(self, u, locations, t0=0.0, record=''): # The idea here is that u(x) means: search for cell containing x, # evaluate the basis functions of that element at x, restrict # the coef vector of u to the cell. Of these 3 steps the first # two don't change. So we cache them # Check the scalar assumption assert u.value_rank() == 0 and u.value_size() == 1 # Locate each point mesh = u.function_space().mesh() limit = mesh.num_entities_global(mesh.topology().dim()) bbox_tree = mesh.bounding_box_tree() cells_for_x = [None] * len(locations) for i, x in enumerate(locations): cell = bbox_tree.compute_first_entity_collision(Point(*x)) if -1 < cell < limit: cells_for_x[i] = cell # Ignore the cells that are not in the mesh. Note that we don't # care if a node is found in several cells -l think CPU interface xs_cells = filter(lambda (xi, c): c is not None, zip(locations, cells_for_x)) V = u.function_space() element = V.dolfin_element() coefficients = np.zeros(element.space_dimension()) # I build a series of functions bound to right variables that # when called compute the value at x evals = [] locations = [] for x, ci in xs_cells: basis_matrix = np.zeros(element.space_dimension()) cell = Cell(mesh, ci) vertex_coords, orientation = cell.get_vertex_coordinates( ), cell.orientation() # Eval the basis once element.evaluate_basis_all(basis_matrix, x, vertex_coords, orientation) def foo(A=basis_matrix, cell=cell, vc=vertex_coords): # Restrict for each call using the bound cell, vc ... u.restrict(coefficients, element, cell, vc, cell) # A here is bound to the right basis_matri return np.dot(A, coefficients) evals.append(foo) locations.append(x) self.probes = evals self.locations = locations self.rank = MPI.rank(mesh.mpi_comm()) self.data = [] self.record = record # Make the initial record self.probe(t=t0)
class DegreeOfFreedom(object): '''Evaluator of dof of V on functions''' def __init__(self, V): self.elm = V.element() self.mesh = V.mesh() is_1d_in_3d = self.mesh.topology().dim() == 1 and self.mesh.geometry().dim() == 3 self.orient_cell = cell_orientation(is_1d_in_3d) # Allocs self.__cell = Cell(self.mesh, 0) self.__cell_vertex_x = self.__cell.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(self.__cell) self.__dof = 0 @property def dof(self): return self.__dof @dof.setter def dof(self, value): assert value < self.elm.space_dimension() self.__dof = value @property def cell(self): return self.__cell @cell.setter def cell(self, value): cell_ = Cell(self.mesh, value) self.__cell_vertex_x[:] = cell_.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(cell_) self.__cell = cell_ def eval(self, f): return self.elm.evaluate_dofs(f, self.__cell_vertex_x, self.__cell_orientation, self.__cell)[self.dof] def eval_dofs(self, f): return self.elm.evaluate_dofs(f, self.__cell_vertex_x, self.__cell_orientation, self.__cell)
class FEBasisFunction(UserExpression): '''Evaluator of dof of V on functions''' def __init__(self, V, **kwargs): super().__init__(self, element=V.ufl_element(), **kwargs) self.elm = V.element() self.mesh = V.mesh() is_1d_in_3d = self.mesh.topology().dim() == 1 and self.mesh.geometry().dim() == 3 self.orient_cell = cell_orientation(is_1d_in_3d) # Allocs self.__cell = Cell(self.mesh, 0) self.__cell_vertex_x = self.__cell.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(self.__cell) self.__dof = 0 self.__values = np.zeros(V.ufl_element().value_size()) @property def dof(self): return self.__dof @dof.setter def dof(self, value): assert value < self.elm.space_dimension() self.__dof = value @property def cell(self): return self.__cell @cell.setter def cell(self, value): cell_ = Cell(self.mesh, value) self.__cell_vertex_x[:] = cell_.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(cell_) self.__cell = cell_ def eval_cell(self, values, x, cell): values[:] = self.elm.evaluate_basis(self.dof, x, self.__cell_vertex_x, self.__cell_orientation) def __call__(self, x): self.eval(self.__values, x) return 1*self.__values
def point_trace_matrix(V, TV, x0): ''' Let u in V; u = ck phi_k then u(x0) \in TV = ck phi_k(x0). So this is a 1 by dim(V) matrix where the column values are phi_k(x0). ''' mesh = V.mesh() tree = mesh.bounding_box_tree() cell = tree.compute_first_entity_collision(Point(*x0)) assert cell < mesh.num_cells() # Cell for restriction Vcell = Cell(mesh, cell) vertex_coordinates = Vcell.get_vertex_coordinates() cell_orientation = Vcell.orientation() x0 = np.fromiter(x0, dtype=float) # Columns - get all components at once all_dofs = V.dofmap().cell_dofs(cell).tolist() Vel = V.element() value_size = V.ufl_element().value_size() basis_values = np.zeros(V.element().space_dimension() * value_size) Vel.evaluate_basis_all(basis_values, x0, vertex_coordinates, cell_orientation) with petsc_serial_matrix(TV, V) as mat: # Scalar gets all if value_size == 1: component_dofs = lambda component: V.dofmap().cell_dofs(cell) # Slices else: component_dofs = lambda component: V.sub(component).dofmap( ).cell_dofs(cell) for row in map(int, TV.dofmap().cell_dofs(cell)): # R^n components sub_dofs = component_dofs(row) sub_dofs_local = [all_dofs.index(dof) for dof in sub_dofs] print row, sub_dofs, sub_dofs_local, basis_values[sub_dofs_local] mat.setValues([row], sub_dofs, basis_values[sub_dofs_local], PETSc.InsertMode.INSERT_VALUES) return mat
class DegreeOfFreedom(object): '''Evaluator of dof of V on functions''' def __init__(self, V): self.elm = V.element() self.mesh = V.mesh() is_1d_in_3d = self.mesh.topology().dim() == 1 and self.mesh.geometry().dim() == 3 self.orient_cell = cell_orientation(is_1d_in_3d) # Allocs self.__cell = Cell(self.mesh, 0) self.__cell_vertex_x = self.__cell.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(self.__cell) self.__dof = 0 @property def dof(self): return self.__dof @dof.setter def dof(self, value): assert value < self.elm.space_dimension() self.__dof = value @property def cell(self): return self.__cell @cell.setter def cell(self, value): cell_ = Cell(self.mesh, value) self.__cell_vertex_x[:] = cell_.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(cell_) self.__cell = cell_ def eval(self, f): return self.elm.evaluate_dof(self.dof, f.as_expression() if isinstance(f, FEBasisFunction) else f, self.__cell_vertex_x, self.__cell_orientation, self.__cell)
def point_trace_matrix(V, TV, x0): ''' Let u in V; u = ck phi_k then u(x0) \in TV = ck phi_k(x0). So this is a 1 by dim(V) matrix where the column values are phi_k(x0). ''' mesh = V.mesh() tree = mesh.bounding_box_tree() cell = tree.compute_first_entity_collision(Point(*x0)) assert cell < mesh.num_cells() # Cell for restriction Vcell = Cell(mesh, cell) vertex_coordinates = Vcell.get_vertex_coordinates() cell_orientation = Vcell.orientation() x0 = np.fromiter(x0, dtype=float) # Columns - get all components at once all_dofs = V.dofmap().cell_dofs(cell).tolist() Vel = V.element() value_size = V.ufl_element().value_size() basis_values = np.zeros(V.element().space_dimension()*value_size) Vel.evaluate_basis_all(basis_values, x0, vertex_coordinates, cell_orientation) with petsc_serial_matrix(TV, V) as mat: # Scalar gets all if value_size == 1: component_dofs = lambda component: V.dofmap().cell_dofs(cell) # Slices else: component_dofs = lambda component: V.sub(component).dofmap().cell_dofs(cell) for row in map(int, TV.dofmap().cell_dofs(cell)): # R^n components sub_dofs = component_dofs(row) sub_dofs_local = [all_dofs.index(dof) for dof in sub_dofs] print row, sub_dofs, sub_dofs_local, basis_values[sub_dofs_local] mat.setValues([row], sub_dofs, basis_values[sub_dofs_local], PETSc.InsertMode.INSERT_VALUES) return mat
def build_grad_matrices(V, points): """Build the sparse m-by-n matrices that map a coefficient set for a function in V to the values of dx and dy at a number m of points. """ # See <https://www.allanswered.com/post/lkbkm/#zxqgk> mesh = V.mesh() bbt = BoundingBoxTree() bbt.build(mesh) dofmap = V.dofmap() el = V.element() rows = [] cols = [] datax = [] datay = [] for i, xy in enumerate(points): cell_id = bbt.compute_first_entity_collision(Point(*xy)) cell = Cell(mesh, cell_id) coordinate_dofs = cell.get_vertex_coordinates() rows.append([i, i, i]) cols.append(dofmap.cell_dofs(cell_id)) v = el.evaluate_basis_derivatives_all(1, xy, coordinate_dofs, cell_id) v = v.reshape(3, 2) datax.append(v[:, 0]) datay.append(v[:, 1]) rows = numpy.concatenate(rows) cols = numpy.concatenate(cols) datax = numpy.concatenate(datax) datay = numpy.concatenate(datay) m = len(points) n = V.dim() dx_matrix = sparse.csr_matrix((datax, (rows, cols)), shape=(m, n)) dy_matrix = sparse.csr_matrix((datay, (rows, cols)), shape=(m, n)) return dx_matrix, dy_matrix
def cell(self, value): cell_ = Cell(self.mesh, value) self.__cell_vertex_x[:] = cell_.get_vertex_coordinates() self.__cell_orientation = self.orient_cell(cell_) self.__cell = cell_
def cylinder_average_matrix(V, TV, radius, quad_degree): '''Averaging matrix''' mesh = V.mesh() line_mesh = TV.mesh() # We are going to perform the integration with Gauss quadrature at # the end (PI u)(x): # A cell of mesh (an edge) defines a normal vector. Let P be the plane # that is defined by the normal vector n and some point x on Gamma. Let L # be the circle that is the intersect of P and S. The value of q (in Q) at x # is defined as # # q(x) = (1/|L|)*\int_{L}g(x)*dL # # which simplifies to g(x) = (1/(2*pi*R))*\int_{-pi}^{pi}u(L)*R*d(theta) and # or = (1/2) * \int_{-1}^{1} u (L(pi*s)) * ds # This can be integrated no problemo once we figure out L. To this end, let # t_1 and t_2 be two unit mutually orthogonal vectors that are orthogonal to # n. Then L(pi*s) = p + R*t_1*cos(pi*s) + R*t_2*sin(pi*s) can be seen to be # such that i) |x-p| = R and ii) x.n = 0 [i.e. this the suitable # parametrization] # Clearly we can scale the weights as well as precompute # cos and sin terms. xq, wq = leggauss(quad_degree) wq *= 0.5 cos_xq = np.cos(np.pi*xq).reshape((-1, 1)) sin_xq = np.sin(np.pi*xq).reshape((-1, 1)) if is_number(radius): radius = lambda x, radius=radius: radius mesh_x = TV.mesh().coordinates() # The idea for point evaluation/computing dofs of TV is to minimize # the number of evaluation. I mean a vector dof if done naively would # have to evaluate at same x number of component times. value_size = TV.ufl_element().value_size() # Eval at points will require serch tree = mesh.bounding_box_tree() limit = mesh.num_cells() TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1)) TV_dm = TV.dofmap() V_dm = V.dofmap() # For non scalar we plan to make compoenents by shift if value_size > 1: TV_dm = TV.sub(0).dofmap() Vel = V.element() basis_values = np.zeros(V.element().space_dimension()*value_size) with petsc_serial_matrix(TV, V) as mat: for line_cell in cells(line_mesh): # Get the tangent => orthogonal tangent vectors v0, v1 = mesh_x[line_cell.entities(0)] n = v0 - v1 t1 = np.array([n[1]-n[2], n[2]-n[0], n[0]-n[1]]) t2 = np.cross(n, t1) t1 /= np.linalg.norm(t1) t2 = t2/np.linalg.norm(t2) # The idea is now to minimize the point evaluation scalar_dofs = TV_dm.cell_dofs(line_cell.index()) scalar_dofs_x = TV_coordinates[scalar_dofs] for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x): # Get radius and integration points rad = radius(avg_point) integration_points = avg_point + rad*t1*sin_xq + rad*t2*cos_xq data = {} for index, ip in enumerate(integration_points): c = tree.compute_first_entity_collision(Point(*ip)) if c >= limit: continue Vcell = Cell(mesh, c) vertex_coordinates = Vcell.get_vertex_coordinates() cell_orientation = Vcell.orientation() Vel.evaluate_basis_all(basis_values, ip, vertex_coordinates, cell_orientation) cols_ip = V_dm.cell_dofs(c) values_ip = basis_values*wq[index] # Add for col, value in zip(cols_ip, values_ip.reshape((-1, value_size))): if col in data: data[col] += value else: data[col] = value # The thing now that with data we can assign to several # rows of the matrix column_indices = np.array(data.keys(), dtype='int32') for shift in range(value_size): row = scalar_row + shift column_values = np.array([data[col][shift] for col in column_indices]) mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES) # On to next avg point # On to next cell return PETScMatrix(mat)
def sphere_average_matrix(V, TV, radius, quad_degree): '''Averaging matrix over the sphere''' mesh = V.mesh() line_mesh = TV.mesh() # Lebedev below need off degrees if quad_degree % 2 == 0: quad_degree += 1 # NOTE: this is a dependency from quadpy.sphere import Lebedev integrator = Lebedev(quad_degree) xq = integrator.points wq = integrator.weights if is_number(radius): radius = lambda x, radius=radius: radius mesh_x = TV.mesh().coordinates() # The idea for point evaluation/computing dofs of TV is to minimize # the number of evaluation. I mean a vector dof if done naively would # have to evaluate at same x number of component times. value_size = TV.ufl_element().value_size() # Eval at points will require serch tree = mesh.bounding_box_tree() limit = mesh.num_cells() TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1)) TV_dm = TV.dofmap() V_dm = V.dofmap() # For non scalar we plan to make compoenents by shift if value_size > 1: TV_dm = TV.sub(0).dofmap() Vel = V.element() basis_values = np.zeros(V.element().space_dimension()*value_size) with petsc_serial_matrix(TV, V) as mat: for line_cell in cells(line_mesh): # The idea is now to minimize the point evaluation scalar_dofs = TV_dm.cell_dofs(line_cell.index()) scalar_dofs_x = TV_coordinates[scalar_dofs] for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x): # Get radius and integration points rad = radius(avg_point) # Scale and shift the unit sphere to the point integration_points = xq*rad + avg_point data = {} for index, ip in enumerate(integration_points): c = tree.compute_first_entity_collision(Point(*ip)) if c >= limit: continue Vcell = Cell(mesh, c) vertex_coordinates = Vcell.get_vertex_coordinates() cell_orientation = Vcell.orientation() Vel.evaluate_basis_all(basis_values, ip, vertex_coordinates, cell_orientation) cols_ip = V_dm.cell_dofs(c) values_ip = basis_values*wq[index] # Add for col, value in zip(cols_ip, values_ip.reshape((-1, value_size))): if col in data: data[col] += value else: data[col] = value # The thing now that with data we can assign to several # rows of the matrix column_indices = np.array(data.keys(), dtype='int32') for shift in range(value_size): row = scalar_row + shift column_values = np.array([data[col][shift] for col in column_indices]) mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES) # On to next avg point # On to next cell return PETScMatrix(mat)
def trace_3d1d_matrix(V, TV, reduced_mesh): '''Trace from 3d to 1d. Makes sense only for CG space''' assert reduced_mesh.id() == TV.mesh().id() assert V.ufl_element().family() == 'Lagrange' mesh = V.mesh() line_mesh = TV.mesh() # The idea for point evaluation/computing dofs of TV is to minimize # the number of evaluation. I mean a vector dof if done naively would # have to evaluate at same x number of component times. value_size = TV.ufl_element().value_size() # We use the map to get (1d cell -> [3d edge) -> 3d cell] if hasattr(reduced_mesh, 'parent_entity_map'): # ( ) mapping = reduced_mesh.parent_entity_map[mesh.id()][1] # [ ] mesh.init(1) mesh.init(1, 3) e2c = mesh.topology()(1, 3) # From 1d cell (by index) get_cell3d = lambda c, d1d3=mapping, d3d3=e2c: d3d3(d1d3[c.index()])[0] # Tree collision by midpoint else: tree = mesh.bounding_box_tree() limit = mesh.num_cells() get_cell3d = lambda c, tree=tree, bound=limit: ( lambda index: index if index<bound else None )(tree.compute_first_entity_collision(c.midpoint())) TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1)) TV_dm = TV.dofmap() V_dm = V.dofmap() # For non scalar we plan to make compoenents by shift if value_size > 1: TV_dm = TV.sub(0).dofmap() Vel = V.element() basis_values = np.zeros(V.element().space_dimension()*value_size) with petsc_serial_matrix(TV, V) as mat: for line_cell in cells(line_mesh): # Get the tangent => orthogonal tangent vectors # The idea is now to minimize the point evaluation scalar_dofs = TV_dm.cell_dofs(line_cell.index()) scalar_dofs_x = TV_coordinates[scalar_dofs] # Let's get a 3d cell to use for getting the V values # CG assumption allows taking any tet_cell = get_cell3d(line_cell) if tet_cell is None: continue Vcell = Cell(mesh, tet_cell) vertex_coordinates = Vcell.get_vertex_coordinates() cell_orientation = 0 # Columns are determined by V cell! I guess the sparsity # could be improved if for x_dofs of TV only x_dofs of V # were considered column_indices = np.array(V_dm.cell_dofs(tet_cell), dtype='int32') for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x): # 3d at point Vel.evaluate_basis_all(basis_values, avg_point, vertex_coordinates, cell_orientation) # The thing now is that with data we can assign to several # rows of the matrix. Shift determines the (x, y, ... ) or # (xx, xy, yx, ...) component of Q data = basis_values.reshape((-1, value_size)).T for shift, column_values in enumerate(data): row = scalar_row + shift mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES) # On to next avg point # On to next cell return PETScMatrix(mat)
def cylinder_average_matrix(V, TV, radius, quad_degree): '''Averaging matrix''' mesh = V.mesh() line_mesh = TV.mesh() # We are going to perform the integration with Gauss quadrature at # the end (PI u)(x): # A cell of mesh (an edge) defines a normal vector. Let P be the plane # that is defined by the normal vector n and some point x on Gamma. Let L # be the circle that is the intersect of P and S. The value of q (in Q) at x # is defined as # # q(x) = (1/|L|)*\int_{L}g(x)*dL # # which simplifies to g(x) = (1/(2*pi*R))*\int_{-pi}^{pi}u(L)*R*d(theta) and # or = (1/2) * \int_{-1}^{1} u (L(pi*s)) * ds # This can be integrated no problemo once we figure out L. To this end, let # t_1 and t_2 be two unit mutually orthogonal vectors that are orthogonal to # n. Then L(pi*s) = p + R*t_1*cos(pi*s) + R*t_2*sin(pi*s) can be seen to be # such that i) |x-p| = R and ii) x.n = 0 [i.e. this the suitable # parametrization] # Clearly we can scale the weights as well as precompute # cos and sin terms. xq, wq = leggauss(quad_degree) wq *= 0.5 cos_xq = np.cos(np.pi * xq).reshape((-1, 1)) sin_xq = np.sin(np.pi * xq).reshape((-1, 1)) if is_number(radius): radius = lambda x, radius=radius: radius mesh_x = TV.mesh().coordinates() # The idea for point evaluation/computing dofs of TV is to minimize # the number of evaluation. I mean a vector dof if done naively would # have to evaluate at same x number of component times. value_size = TV.ufl_element().value_size() # Eval at points will require serch tree = mesh.bounding_box_tree() limit = mesh.num_cells() TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1)) TV_dm = TV.dofmap() V_dm = V.dofmap() # For non scalar we plan to make compoenents by shift if value_size > 1: TV_dm = TV.sub(0).dofmap() Vel = V.element() basis_values = np.zeros(V.element().space_dimension() * value_size) with petsc_serial_matrix(TV, V) as mat: for line_cell in cells(line_mesh): # Get the tangent => orthogonal tangent vectors v0, v1 = mesh_x[line_cell.entities(0)] n = v0 - v1 t1 = np.array([n[1] - n[2], n[2] - n[0], n[0] - n[1]]) t2 = np.cross(n, t1) t1 /= np.linalg.norm(t1) t2 = t2 / np.linalg.norm(t2) # The idea is now to minimize the point evaluation scalar_dofs = TV_dm.cell_dofs(line_cell.index()) scalar_dofs_x = TV_coordinates[scalar_dofs] for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x): # Get radius and integration points rad = radius(avg_point) integration_points = avg_point + rad * t1 * sin_xq + rad * t2 * cos_xq data = {} for index, ip in enumerate(integration_points): c = tree.compute_first_entity_collision(Point(*ip)) if c >= limit: continue Vcell = Cell(mesh, c) vertex_coordinates = Vcell.get_vertex_coordinates() cell_orientation = Vcell.orientation() Vel.evaluate_basis_all(basis_values, ip, vertex_coordinates, cell_orientation) cols_ip = V_dm.cell_dofs(c) values_ip = basis_values * wq[index] # Add for col, value in zip(cols_ip, values_ip.reshape((-1, value_size))): if col in data: data[col] += value else: data[col] = value # The thing now that with data we can assign to several # rows of the matrix column_indices = np.array(data.keys(), dtype='int32') for shift in range(value_size): row = scalar_row + shift column_values = np.array( [data[col][shift] for col in column_indices]) mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES) # On to next avg point # On to next cell return PETScMatrix(mat)
def sphere_average_matrix(V, TV, radius, quad_degree): '''Averaging matrix over the sphere''' mesh = V.mesh() line_mesh = TV.mesh() # Lebedev below need off degrees if quad_degree % 2 == 0: quad_degree += 1 # NOTE: this is a dependency from quadpy.sphere import Lebedev integrator = Lebedev(quad_degree) xq = integrator.points wq = integrator.weights if is_number(radius): radius = lambda x, radius=radius: radius mesh_x = TV.mesh().coordinates() # The idea for point evaluation/computing dofs of TV is to minimize # the number of evaluation. I mean a vector dof if done naively would # have to evaluate at same x number of component times. value_size = TV.ufl_element().value_size() # Eval at points will require serch tree = mesh.bounding_box_tree() limit = mesh.num_cells() TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1)) TV_dm = TV.dofmap() V_dm = V.dofmap() # For non scalar we plan to make compoenents by shift if value_size > 1: TV_dm = TV.sub(0).dofmap() Vel = V.element() basis_values = np.zeros(V.element().space_dimension() * value_size) with petsc_serial_matrix(TV, V) as mat: for line_cell in cells(line_mesh): # The idea is now to minimize the point evaluation scalar_dofs = TV_dm.cell_dofs(line_cell.index()) scalar_dofs_x = TV_coordinates[scalar_dofs] for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x): # Get radius and integration points rad = radius(avg_point) # Scale and shift the unit sphere to the point integration_points = xq * rad + avg_point data = {} for index, ip in enumerate(integration_points): c = tree.compute_first_entity_collision(Point(*ip)) if c >= limit: continue Vcell = Cell(mesh, c) vertex_coordinates = Vcell.get_vertex_coordinates() cell_orientation = Vcell.orientation() Vel.evaluate_basis_all(basis_values, ip, vertex_coordinates, cell_orientation) cols_ip = V_dm.cell_dofs(c) values_ip = basis_values * wq[index] # Add for col, value in zip(cols_ip, values_ip.reshape((-1, value_size))): if col in data: data[col] += value else: data[col] = value # The thing now that with data we can assign to several # rows of the matrix column_indices = np.array(data.keys(), dtype='int32') for shift in range(value_size): row = scalar_row + shift column_values = np.array( [data[col][shift] for col in column_indices]) mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES) # On to next avg point # On to next cell return PETScMatrix(mat)
def trace_3d1d_matrix(V, TV, reduced_mesh): '''Trace from 3d to 1d. Makes sense only for CG space''' assert reduced_mesh.id() == TV.mesh().id() assert V.ufl_element().family() == 'Lagrange' mesh = V.mesh() line_mesh = TV.mesh() # The idea for point evaluation/computing dofs of TV is to minimize # the number of evaluation. I mean a vector dof if done naively would # have to evaluate at same x number of component times. value_size = TV.ufl_element().value_size() # We use the map to get (1d cell -> [3d edge) -> 3d cell] if hasattr(reduced_mesh, 'parent_entity_map'): # ( ) mapping = reduced_mesh.parent_entity_map[mesh.id()][1] # [ ] mesh.init(1) mesh.init(1, 3) e2c = mesh.topology()(1, 3) # From 1d cell (by index) get_cell3d = lambda c, d1d3=mapping, d3d3=e2c: d3d3(d1d3[c.index()])[0] # Tree collision by midpoint else: tree = mesh.bounding_box_tree() limit = mesh.num_cells() get_cell3d = lambda c, tree=tree, bound=limit: ( lambda index: index if index < bound else None)( tree.compute_first_entity_collision(c.midpoint())) TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1)) TV_dm = TV.dofmap() V_dm = V.dofmap() # For non scalar we plan to make compoenents by shift if value_size > 1: TV_dm = TV.sub(0).dofmap() Vel = V.element() basis_values = np.zeros(V.element().space_dimension() * value_size) with petsc_serial_matrix(TV, V) as mat: for line_cell in cells(line_mesh): # Get the tangent => orthogonal tangent vectors # The idea is now to minimize the point evaluation scalar_dofs = TV_dm.cell_dofs(line_cell.index()) scalar_dofs_x = TV_coordinates[scalar_dofs] # Let's get a 3d cell to use for getting the V values # CG assumption allows taking any tet_cell = get_cell3d(line_cell) if tet_cell is None: continue Vcell = Cell(mesh, tet_cell) vertex_coordinates = Vcell.get_vertex_coordinates() cell_orientation = 0 # Columns are determined by V cell! I guess the sparsity # could be improved if for x_dofs of TV only x_dofs of V # were considered column_indices = np.array(V_dm.cell_dofs(tet_cell), dtype='int32') for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x): # 3d at point Vel.evaluate_basis_all(basis_values, avg_point, vertex_coordinates, cell_orientation) # The thing now is that with data we can assign to several # rows of the matrix. Shift determines the (x, y, ... ) or # (xx, xy, yx, ...) component of Q data = basis_values.reshape((-1, value_size)).T for shift, column_values in enumerate(data): row = scalar_row + shift mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES) # On to next avg point # On to next cell return PETScMatrix(mat)
def average_matrix(V, TV, shape): ''' Averaging matrix for reduction of g in V to TV by integration over shape. ''' # We build a matrix representation of u in V -> Pi(u) in TV where # # Pi(u)(s) = |L(s)|^-1*\int_{L(s)}u(t) dx(s) # # Here L is the shape over which u is integrated for reduction. # Its measure is |L(s)|. mesh_x = TV.mesh().coordinates() # The idea for point evaluation/computing dofs of TV is to minimize # the number of evaluation. I mean a vector dof if done naively would # have to evaluate at same x number of component times. value_size = TV.ufl_element().value_size() mesh = V.mesh() # Eval at points will require serch tree = mesh.bounding_box_tree() limit = mesh.num_cells() TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1)) line_mesh = TV.mesh() TV_dm = TV.dofmap() V_dm = V.dofmap() # For non scalar we plan to make compoenents by shift if value_size > 1: TV_dm = TV.sub(0).dofmap() Vel = V.element() basis_values = np.zeros(V.element().space_dimension() * value_size) with petsc_serial_matrix(TV, V) as mat: for line_cell in cells(line_mesh): # Get the tangent (normal of the plane which cuts the virtual # surface to yield the bdry curve v0, v1 = mesh_x[line_cell.entities(0)] n = v0 - v1 # The idea is now to minimize the point evaluation scalar_dofs = TV_dm.cell_dofs(line_cell.index()) scalar_dofs_x = TV_coordinates[scalar_dofs] for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x): # Avg point here has the role of 'height' coordinate quadrature = shape.quadrature(avg_point, n) integration_points = quadrature.points wq = quadrature.weights curve_measure = sum(wq) data = {} for index, ip in enumerate(integration_points): c = tree.compute_first_entity_collision(Point(*ip)) if c >= limit: continue cs = tree.compute_entity_collisions(Point(*ip)) # assert False for c in cs[:1]: Vcell = Cell(mesh, c) vertex_coordinates = Vcell.get_vertex_coordinates() cell_orientation = Vcell.orientation() basis_values[:] = Vel.evaluate_basis_all( ip, vertex_coordinates, cell_orientation) cols_ip = V_dm.cell_dofs(c) values_ip = basis_values * wq[index] # Add for col, value in zip( cols_ip, values_ip.reshape((-1, value_size))): if col in data: data[col] += value / curve_measure else: data[col] = value / curve_measure # The thing now that with data we can assign to several # rows of the matrix column_indices = np.array(list(data.keys()), dtype='int32') for shift in range(value_size): row = scalar_row + shift column_values = np.array( [data[col][shift] for col in column_indices]) mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES) # On to next avg point # On to next cell return mat
def surface_average_matrix(V, TV, bdry_curve): '''Averaging matrix''' mesh = V.mesh() line_mesh = TV.mesh() # We build a matrix representation of u in V -> Pi(u) in TV where # # Pi(u)(s) = |L(s)|^-1*\int_{L(s)}u(t) dL(s) # # Here L represents a curve bounding the surface at 'height' s. # # We do this numerically as |L(s)|^-1*\sum_q u(x_q)*w_q # Weights remaing fixed wq = bdry_curve.weights mesh_x = TV.mesh().coordinates() # The idea for point evaluation/computing dofs of TV is to minimize # the number of evaluation. I mean a vector dof if done naively would # have to evaluate at same x number of component times. value_size = TV.ufl_element().value_size() # Eval at points will require serch tree = mesh.bounding_box_tree() limit = mesh.num_cells() TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1)) TV_dm = TV.dofmap() V_dm = V.dofmap() # For non scalar we plan to make compoenents by shift if value_size > 1: TV_dm = TV.sub(0).dofmap() Vel = V.element() basis_values = np.zeros(V.element().space_dimension() * value_size) with petsc_serial_matrix(TV, V) as mat: for line_cell in cells(line_mesh): # Get the tangent (normal of the plane which cuts the virtual # surface to yield the bdry curve v0, v1 = mesh_x[line_cell.entities(0)] n = v0 - v1 # We can specialize quadrature points; we can have several # height points with same normal pts_at_n = bdry_curve.points(n) len_at_n = bdry_curve.length(n) # The idea is now to minimize the point evaluation scalar_dofs = TV_dm.cell_dofs(line_cell.index()) scalar_dofs_x = TV_coordinates[scalar_dofs] for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x): # Avg point here has the role of 'height' coordinate integration_points = pts_at_n(avg_point) len_bdry_curve = len_at_n(avg_point) data = {} for index, ip in enumerate(integration_points): c = tree.compute_first_entity_collision(Point(*ip)) if c >= limit: continue Vcell = Cell(mesh, c) vertex_coordinates = Vcell.get_vertex_coordinates() cell_orientation = Vcell.orientation() Vel.evaluate_basis_all(basis_values, ip, vertex_coordinates, cell_orientation) cols_ip = V_dm.cell_dofs(c) values_ip = basis_values * wq[index] # Add for col, value in zip(cols_ip, values_ip.reshape((-1, value_size))): if col in data: data[col] += value / len_bdry_curve else: data[col] = value / len_bdry_curve # The thing now that with data we can assign to several # rows of the matrix column_indices = np.array(data.keys(), dtype='int32') for shift in range(value_size): row = scalar_row + shift column_values = np.array( [data[col][shift] for col in column_indices]) mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES) # On to next avg point # On to next cell return PETScMatrix(mat)