From 7ca2f58ac285ede6ff8de75dfd68ca6ce248f82c Mon Sep 17 00:00:00 2001 From: David Schneller Date: Thu, 21 Mar 2024 20:32:17 +0100 Subject: [PATCH 01/12] Add VTK collocation --- src/seissol_matrices/base.py | 21 +++++ src/seissol_matrices/basis_functions.py | 12 +++ src/seissol_matrices/dg_matrices.py | 106 +++++++++++++++++++++--- src/seissol_matrices/generate.py | 25 ++++++ src/seissol_matrices/vtk_points.py | 79 ++++++++++++++++++ 5 files changed, 231 insertions(+), 12 deletions(-) create mode 100644 src/seissol_matrices/base.py create mode 100644 src/seissol_matrices/generate.py create mode 100644 src/seissol_matrices/vtk_points.py diff --git a/src/seissol_matrices/base.py b/src/seissol_matrices/base.py new file mode 100644 index 0000000..b396cd3 --- /dev/null +++ b/src/seissol_matrices/base.py @@ -0,0 +1,21 @@ +import numpy as np + +def collocate(basis, points): + # takes a basis object, and a points array + # of the form: npoints × dim + # outputs a collocation matrix of the form + # npoints × nbasis + + # as far as the author of these lines is aware, + # this module has no broadcasing functionality yet + # for basis functions. Which is sad. + + assert basis.dim() == points.shape[1] + + nbasis = basis.number_of_basis_functions() + + coll = np.empty((nbasis, points.shape[0])) + for i in range(nbasis): + for j in range(points.shape[0]): + coll[i,j] = basis.eval_basis(points[j,:], i) + return coll diff --git a/src/seissol_matrices/basis_functions.py b/src/seissol_matrices/basis_functions.py index 9c6a107..f37134f 100644 --- a/src/seissol_matrices/basis_functions.py +++ b/src/seissol_matrices/basis_functions.py @@ -85,11 +85,17 @@ def eval_diff_basis(self, x, i, k): def number_of_basis_functions(self, o): pass + def dim(self): + pass + ################################################################################ class BasisFunctionGenerator1D(BasisFunctionGenerator): + def dim(self): + return 1 + def eval_basis(self, x, i): r_num = 2 * x - 1.0 r_den = 1.0 @@ -113,6 +119,9 @@ def number_of_basis_functions(self): class BasisFunctionGenerator2D(BasisFunctionGenerator): + def dim(self): + return 2 + def unroll_index(self, i): n = i[0] + i[1] tri = 0.5 * n * (n + 1) @@ -171,6 +180,9 @@ def number_of_basis_functions(self): class BasisFunctionGenerator3D(BasisFunctionGenerator): + def dim(self): + return 3 + def unroll_index(self, i): n = i[0] + i[1] + i[2] tet = (n * (n + 1) * (n + 2)) / 6.0 diff --git a/src/seissol_matrices/dg_matrices.py b/src/seissol_matrices/dg_matrices.py index 05c71f1..f793c00 100644 --- a/src/seissol_matrices/dg_matrices.py +++ b/src/seissol_matrices/dg_matrices.py @@ -5,6 +5,8 @@ import quad_rules.GaussJacobi import quad_rules.Quadrature +import base + from seissol_matrices import basis_functions @@ -16,6 +18,9 @@ def __init__(self, o, d): self.order = o self.dim = d + self.M = None + self.K = self.dim * [None] + if self.dim == 3: self.generator = basis_functions.BasisFunctionGenerator3D(self.order) self.geometry = np.array( @@ -27,27 +32,95 @@ def __init__(self, o, d): ] ) self.face_generator = dg_generator(o, 2) - n, w = quad_rules.JaskowiecSukumar.JaskowiecSukumar().find_best_rule( - 2 * self.order - ) + self.quadrule_finder = quad_rules.JaskowiecSukumar.JaskowiecSukumar().find_best_rule + self.generator_finder = basis_functions.BasisFunctionGenerator3D elif self.dim == 2: self.generator = basis_functions.BasisFunctionGenerator2D(self.order) self.geometry = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]]) - n, w = quad_rules.WitherdenVincentTri.WitherdenVincentTri().find_best_rule( - 2 * self.order - ) + self.quadrule_finder = quad_rules.WitherdenVincentTri.WitherdenVincentTri().find_best_rule + self.generator_finder = basis_functions.BasisFunctionGenerator2D elif self.dim == 1: self.generator = basis_functions.BasisFunctionGenerator1D(self.order) self.geometry = np.array([[0.0], [1.0]]) - n, w = quad_rules.GaussJacobi.GaussJacobi(0, 0).find_best_rule( - 2 * self.order - ) + self.quadrule_finder = quad_rules.GaussJacobi.GaussJacobi(0, 0).find_best_rule + self.generator_finder = basis_functions.BasisFunctionGenerator1D else: raise Execption("Can only generate 1D, 2D or 2D basis functions") - self.nodes, self.weights = quad_rules.Quadrature.transform(n, w, self.geometry) - self.M = None - self.K = self.dim * [None] + self.nodes, self.weights = self.get_quadrature_rule(2 * self.order) + + def get_quadrature_rule(self, order): + n, w = self.quadrule_finder(order) + + return quad_rules.Quadrature.transform(n, w, self.geometry) + + def multilinear_form(self, face, der, order = None, side = None): + """ + Given an array der, we compute a tensor V[i...] of dimension + len(der) defined by (given in C++ parameter pack notation) + + V[i...] = integral(1 * ... * f_i^(der)) + + For example, to obtain a mass matrix, choose der = [0,0]. + For a stiffness matrix, choose der = [1,0]. + For a trilinear form, choose der = [0,0,0]. + + Optionally can supply different orders for the basis functions. (using the order parameter) + If not given, the order will assumed to be self.order for all constituents. + + Moreover, we can opt to take a projected face basis instead of a volume basis via the + side argument. If an entry is a negative number there, we assume the volume basis functions, + otherwise the respective face side. + """ + + # NOTE: we could extract the multiplication/quadrature part from the function selection part. + # I.e., eval_functions (or a list of basis functions here) could be given as an input parameter, + # instead of the two current ones. + + # we do not support higher derivatives for the time being. So let's fail here for now. + assert np.all([d in (0,1) for d in der]) + + if order is None: + order = [self.order] * len(der) + + if side is None: + side = [-1] * len(der) + + assert len(order) == len(der) + assert len(side) == len(der) + + def get_basis_function(o, d, s): + if s < 0: + basis = self.generator_finder(o) + else: + basis = self.face_generator.generator_finder(o) + basiseval_pre = basis.eval_basis if d == 0 else basis.eval_diff_basis + if face >= 0: + if side < 0: + basiseval = lambda x, i: basiseval_pre(self.volume_to_face_parametrisation(x, face), i) + else: + basiseval = lambda x, i: basiseval_pre(self.face_to_face_parametrisation(x, face), i) + else: + # volume * face does not make sense when evaluating on the whole volume + assert side < 0 + basiseval = basiseval_pre + return basiseval, basis.number_of_basis_functions() + + basis_functions = [get_basis_function(o,d,s) for o,d,s in zip(order, der, side)] + + if face < 0: + nodes, weights = self.get_quadrature_rule(np.prod(order)) + else: + nodes, weights = self.face_generator.get_quadrature_rule(np.prod(order)) + sizes = [bn for _,bn in basis_functions] + tensor = np.empty(sizes) + generic_eval_basis = lambda x, index: np.prod( + basis_functions[k][0](x, i) for k,i in enumerate(index) + ) + for index in itertools.product(range(size) for size in sizes): + eval_basis = lambda x: generic_eval_basis(x, index) + tensor[*index] = quad_rules.Quadrature.quad(nodes, weights, eval_basis) + return tensor def mass_matrix(self): if not np.any(self.M == None): @@ -197,7 +270,16 @@ def rDivM(self, side): matrix = self.rT(side) mass = self.mass_matrix() return np.linalg.solve(mass, matrix.T) + + def collocate_volume(self, points): + return base.collocate(self.generator, points) + + def collocate_face(self, points, side): + # points are meant to be 2D here + # this method wants dim × npoints; but points is given the other way. So, we transpose it twice + projected = self.volume_to_face_parametrisation(points.T, side).T + return base.collocate(self.generator, projected) if __name__ == "__main__": from seissol_matrices import json_io diff --git a/src/seissol_matrices/generate.py b/src/seissol_matrices/generate.py new file mode 100644 index 0000000..e7f86fa --- /dev/null +++ b/src/seissol_matrices/generate.py @@ -0,0 +1,25 @@ +import sys +from seissol_matrices import json_io +from dg_matrices import dg_generator +from vtk_points import vtk_lagrange_2d, vtk_lagrange_3d + +def main(): + assert len(sys.argv) > 1 + if sys.argv[1] == 'vtk': + import dg_matrices + vtkpoints2 = {} + vtkpoints3 = {} + for deg in range(0, 8): + vtkpoints2[deg] = vtk_lagrange_2d(deg) + vtkpoints3[deg] = vtk_lagrange_3d(deg) + for basisorder in range(2, 8): + dggen = dg_generator(basisorder, 3) + for deg in range(0, 8): + json_io.write_matrix(dggen.collocate_volume(vtkpoints3[deg]), + f'coll{basisorder}vd{deg}', f'vtk{basisorder}') + for f in range(4): + json_io.write_matrix(dggen.collocate_face(vtkpoints2[deg], f), + f'coll{basisorder}f{f}d{deg}', f'vtk{basisorder}') + +if __name__ == '__main__': + main() diff --git a/src/seissol_matrices/vtk_points.py b/src/seissol_matrices/vtk_points.py new file mode 100644 index 0000000..b445818 --- /dev/null +++ b/src/seissol_matrices/vtk_points.py @@ -0,0 +1,79 @@ +import numpy as np + +def vtk_lagrange_2d(d, start=0, divd=None): + if d < 0: + return np.empty((0, 2)) + if d == 0: + return np.array([[1/3, 1/3]]) + else: + if divd is None: + divd = d + s = 1 / divd + base = 0 + obase = 0 + allrings = [] + for r in range(start, d//3 + 1): + if d == 3*r: + allrings += [[s*r, s*r]] + else: + ringcorner = [[s*r, s*r], [s*(d - 2*r), s*r], [s*r, s*(d - 2*r)]] + ringborder = [[s*(r + i), s*r] for i in range(1, d - 3*r)] + ringborder += [[s*(d - 2*r - i), s*(r + i)] for i in range(1, d - 3*r)] + ringborder += [[s*r, s*(d - 2*r - i)] for i in range(1, d - 3*r)] + allrings += ringcorner + ringborder + return np.array(allrings) + +def vtk_lagrange_3d(d): + if d == 0: + return np.array([[1/4, 1/4, 1/4]]) + else: + s = 1 / d + base = 0 + obase = 0 + allrings = [] + for r in range(d//4 + 1): + if d == 4*r: + allrings += [[s*r, s*r, s*r]] + else: + ringcorner = [[s*r, s*r, s*r], [s*(d - 3*r), s*r, s*r], [s*r, s*(d - 3*r), s*r], [s*r, s*r, s*(d - 3*r)]] + ringborder = [[s*(r + i), s*r, s*r] for i in range(1, d - 4*r)] + ringborder += [[s*(d - 3*r - i), s*(r + i), s*r] for i in range(1, d - 4*r)] + ringborder += [[s*r, s*(d - 3*r - i), s*r] for i in range(1, d - 4*r)] + ringborder += [[s*r, s*r, s*(r + i)] for i in range(1, d - 4*r)] + ringborder += [[s*(d - 3*r - i), s*r, s*(r + i)] for i in range(1, d - 4*r)] + ringborder += [[s*r, s*(d - 3*r - i), s*(r + i)] for i in range(1, d - 4*r)] + subface = vtk_lagrange_2d(d - r, r + 1, d) + ringfaces = [(i, s*r, j) for i,j in subface] + ringfaces += [(j, (1 - s*r) - i - j, i) for i,j in subface] + ringfaces += [(s*r, j, i) for i,j in subface] + ringfaces += [(j, i, s*r) for i,j in subface] + allrings += ringcorner + ringborder + ringfaces + return np.array(allrings) + +def vtk_lagrange_2d_from_vtk(d): + import vtk + tet = vtk.vtkLagrangeTriangle() + points = ((d+1)*(d+2))//2 + tet.GetPointIds().SetNumberOfIds(points) + tet.GetPoints().SetNumberOfPoints(points) + tet.Initialize() + pointlist = [] + for i in range(points): + barycentric = [0,0,0] + tet.ToBarycentricIndex(i, barycentric) + pointlist += [[b / d for b in barycentric[:2]]] + return np.array(pointlist) + +def vtk_lagrange_3d_from_vtk(d): + import vtk + tet = vtk.vtkLagrangeTetra() + points = ((d+1)*(d+2)*(d+3))//6 + tet.GetPointIds().SetNumberOfIds(points) + tet.GetPoints().SetNumberOfPoints(points) + tet.Initialize() + pointlist = [] + for i in range(points): + barycentric = [0,0,0,0] + tet.ToBarycentricIndex(i, barycentric) + pointlist += [[b / d for b in barycentric[:3]]] + return np.array(pointlist) From 21d5353354d11500dfe8cab408fa90ba23474920 Mon Sep 17 00:00:00 2001 From: David Schneller Date: Thu, 21 Mar 2024 20:33:55 +0100 Subject: [PATCH 02/12] Fix generation of VTK data --- src/seissol_matrices/generate.py | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/src/seissol_matrices/generate.py b/src/seissol_matrices/generate.py index e7f86fa..c23bc19 100644 --- a/src/seissol_matrices/generate.py +++ b/src/seissol_matrices/generate.py @@ -12,14 +12,16 @@ def main(): for deg in range(0, 8): vtkpoints2[deg] = vtk_lagrange_2d(deg) vtkpoints3[deg] = vtk_lagrange_3d(deg) + json_io.write_matrix(vtkpoints2[deg], f'vtk2d{deg}', f'vtkbase.json') + json_io.write_matrix(vtkpoints3[deg], f'vtk3d{deg}', f'vtkbase.json') for basisorder in range(2, 8): dggen = dg_generator(basisorder, 3) for deg in range(0, 8): json_io.write_matrix(dggen.collocate_volume(vtkpoints3[deg]), - f'coll{basisorder}vd{deg}', f'vtk{basisorder}') + f'coll{basisorder}vd{deg}', f'vtko{basisorder}.json') for f in range(4): json_io.write_matrix(dggen.collocate_face(vtkpoints2[deg], f), - f'coll{basisorder}f{f}d{deg}', f'vtk{basisorder}') + f'coll{basisorder}f{f}d{deg}', f'vtko{basisorder}.json') if __name__ == '__main__': main() From de1e887cc2cca4aeba4da5d895c6e5a05c9875d9 Mon Sep 17 00:00:00 2001 From: David Schneller Date: Thu, 21 Mar 2024 20:48:19 +0100 Subject: [PATCH 03/12] Refactor DG matrices --- src/seissol_matrices/dg_matrices.py | 101 +++++++--------------------- 1 file changed, 23 insertions(+), 78 deletions(-) diff --git a/src/seissol_matrices/dg_matrices.py b/src/seissol_matrices/dg_matrices.py index f793c00..7663f66 100644 --- a/src/seissol_matrices/dg_matrices.py +++ b/src/seissol_matrices/dg_matrices.py @@ -61,24 +61,24 @@ def multilinear_form(self, face, der, order = None, side = None): V[i...] = integral(1 * ... * f_i^(der)) - For example, to obtain a mass matrix, choose der = [0,0]. - For a stiffness matrix, choose der = [1,0]. - For a trilinear form, choose der = [0,0,0]. + For example, to obtain a mass matrix, choose der = [None,None]. + For a stiffness matrix in x-direction, choose der = [0,None]. + For a trilinear form, choose der = [None,None,None]. Optionally can supply different orders for the basis functions. (using the order parameter) If not given, the order will assumed to be self.order for all constituents. Moreover, we can opt to take a projected face basis instead of a volume basis via the - side argument. If an entry is a negative number there, we assume the volume basis functions, - otherwise the respective face side. + side argument. If an entry is a negative number there, we assume a non-rotated face, + otherwise the respective face side. If an entry is None, then we assume the respective volume term. """ # NOTE: we could extract the multiplication/quadrature part from the function selection part. # I.e., eval_functions (or a list of basis functions here) could be given as an input parameter, # instead of the two current ones. - # we do not support higher derivatives for the time being. So let's fail here for now. - assert np.all([d in (0,1) for d in der]) + # we only support a first derivative at the moment + assert np.all([d in (None,*(i for i in range(self.dim))) for d in der]) if order is None: order = [self.order] * len(der) @@ -90,28 +90,30 @@ def multilinear_form(self, face, der, order = None, side = None): assert len(side) == len(der) def get_basis_function(o, d, s): - if s < 0: + if s is None: basis = self.generator_finder(o) else: basis = self.face_generator.generator_finder(o) - basiseval_pre = basis.eval_basis if d == 0 else basis.eval_diff_basis - if face >= 0: - if side < 0: + basiseval_pre = basis.eval_basis if d is None else lambda x,i: basis.eval_diff_basis(x,i,d) + if face: + if s is None: basiseval = lambda x, i: basiseval_pre(self.volume_to_face_parametrisation(x, face), i) + elif s < 0: + basiseval = basiseval_pre else: basiseval = lambda x, i: basiseval_pre(self.face_to_face_parametrisation(x, face), i) else: # volume * face does not make sense when evaluating on the whole volume - assert side < 0 + assert s is None basiseval = basiseval_pre return basiseval, basis.number_of_basis_functions() basis_functions = [get_basis_function(o,d,s) for o,d,s in zip(order, der, side)] - if face < 0: - nodes, weights = self.get_quadrature_rule(np.prod(order)) - else: + if face: nodes, weights = self.face_generator.get_quadrature_rule(np.prod(order)) + else: + nodes, weights = self.get_quadrature_rule(np.prod(order)) sizes = [bn for _,bn in basis_functions] tensor = np.empty(sizes) generic_eval_basis = lambda x, index: np.prod( @@ -125,33 +127,15 @@ def get_basis_function(o, d, s): def mass_matrix(self): if not np.any(self.M == None): return self.M - number_of_basis_functions = self.generator.number_of_basis_functions() - self.M = np.zeros((number_of_basis_functions, number_of_basis_functions)) - - for i in range(number_of_basis_functions): - for j in range(number_of_basis_functions): - prod = lambda x: self.generator.eval_basis( - x, i - ) * self.generator.eval_basis(x, j) - self.M[i, j] = quad_rules.Quadrature.quad( - self.nodes, self.weights, prod - ) + + self.M = self.multilinear_form(False, [None, None]) return self.M def stiffness_matrix(self, dim): if not np.any(self.K[dim] == None): return self.K[dim] - number_of_basis_functions = self.generator.number_of_basis_functions() - self.K[dim] = np.zeros((number_of_basis_functions, number_of_basis_functions)) - - for i in range(number_of_basis_functions): - for j in range(number_of_basis_functions): - prod = lambda x: self.generator.eval_diff_basis( - x, i, dim - ) * self.generator.eval_basis(x, j) - self.K[dim][i, j] = quad_rules.Quadrature.quad( - self.nodes, self.weights, prod - ) + + self.K[dim] = self.multilinear_form(False, [dim, None]) return self.K[dim] def kDivM(self, dim): @@ -186,28 +170,7 @@ def face_to_face_parametrisation(self, x, side): def face_times_face_mass_matrix(self, side): assert self.dim == 3 - number_of_face_basis_functions = ( - self.face_generator.generator.number_of_basis_functions() - ) - - projected_basis_function = ( - lambda x, i: self.face_generator.generator.eval_basis( - self.face_to_face_parametrisation(x, side), i - ) - ) - - matrix = np.zeros( - (number_of_face_basis_functions, number_of_face_basis_functions) - ) - for i in range(number_of_face_basis_functions): - for j in range(number_of_face_basis_functions): - prod = lambda x: self.face_generator.generator.eval_basis( - x, i - ) * projected_basis_function(x, j) - matrix[i, j] = quad_rules.Quadrature.quad( - self.face_generator.nodes, self.face_generator.weights, prod - ) - return matrix + return self.multilinear_form(True, [None, None], side=[-1, side]) def fP(self, side): return self.face_times_face_mass_matrix(side) @@ -237,25 +200,7 @@ def volume_to_face_parametrisation(self, x, side): def volume_times_face_mass_matrix(self, side): assert self.dim == 3 - number_of_face_basis_functions = ( - self.face_generator.generator.number_of_basis_functions() - ) - - projected_basis_function = lambda x, i: self.generator.eval_basis( - self.volume_to_face_parametrisation(x, side), i - ) - number_of_basis_functions = self.generator.number_of_basis_functions() - - matrix = np.zeros((number_of_face_basis_functions, number_of_basis_functions)) - for i in range(number_of_face_basis_functions): - for j in range(number_of_basis_functions): - prod = lambda x: self.face_generator.generator.eval_basis( - x, i - ) * projected_basis_function(x, j) - matrix[i, j] = quad_rules.Quadrature.quad( - self.face_generator.nodes, self.face_generator.weights, prod - ) - return matrix + return self.multilinear_form(True, [None, None], side=[None, side]) def fMrT(self, side): return self.volume_times_face_mass_matrix(side) From d68d23896aa0eff0e92b047eeb8823a4804226a9 Mon Sep 17 00:00:00 2001 From: David Schneller Date: Thu, 21 Mar 2024 21:49:05 +0100 Subject: [PATCH 04/12] Formatting and bugfixing --- poetry.lock | 509 ++++++++++++------------ src/seissol_matrices/base.py | 5 +- src/seissol_matrices/basis_functions.py | 4 +- src/seissol_matrices/dg_matrices.py | 66 +-- src/seissol_matrices/generate.py | 27 +- src/seissol_matrices/vtk_points.py | 84 ++-- 6 files changed, 387 insertions(+), 308 deletions(-) diff --git a/poetry.lock b/poetry.lock index e4ff2bd..783fee6 100644 --- a/poetry.lock +++ b/poetry.lock @@ -1,34 +1,34 @@ -# This file is automatically @generated by Poetry 1.7.1 and should not be changed by hand. +# This file is automatically @generated by Poetry 1.8.2 and should not be changed by hand. 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b/src/seissol_matrices/base.py index b396cd3..2137683 100644 --- a/src/seissol_matrices/base.py +++ b/src/seissol_matrices/base.py @@ -1,5 +1,6 @@ import numpy as np + def collocate(basis, points): # takes a basis object, and a points array # of the form: npoints × dim @@ -13,9 +14,9 @@ def collocate(basis, points): assert basis.dim() == points.shape[1] nbasis = basis.number_of_basis_functions() - + coll = np.empty((nbasis, points.shape[0])) for i in range(nbasis): for j in range(points.shape[0]): - coll[i,j] = basis.eval_basis(points[j,:], i) + coll[i, j] = basis.eval_basis(points[j, :], i) return coll diff --git a/src/seissol_matrices/basis_functions.py b/src/seissol_matrices/basis_functions.py index f37134f..402d3c8 100644 --- a/src/seissol_matrices/basis_functions.py +++ b/src/seissol_matrices/basis_functions.py @@ -40,7 +40,7 @@ def singularity_free_jacobi_polynomial(n, a, b, x, y): def singularity_free_jacobi_polynomial_and_derivatives(n, a, b, x, y): if n == 0: - return 1.0, 0.0, 0.0 + return np.ones(np.shape(x)), np.zeros(np.shape(x)), np.zeros(np.shape(x)) pm_1 = 1.0 ddx_pm_1 = 0.0 ddy_pm_1 = 0.0 @@ -103,7 +103,7 @@ def eval_basis(self, x, i): def eval_diff_basis(self, x, i, k): if i == 0: - return 0 + return np.zeros(x.shape) else: r_num = 2 * x - 1.0 r_den = 1.0 diff --git a/src/seissol_matrices/dg_matrices.py b/src/seissol_matrices/dg_matrices.py index 7663f66..6f34562 100644 --- a/src/seissol_matrices/dg_matrices.py +++ b/src/seissol_matrices/dg_matrices.py @@ -5,7 +5,9 @@ import quad_rules.GaussJacobi import quad_rules.Quadrature -import base +import itertools + +from seissol_matrices import base from seissol_matrices import basis_functions @@ -32,17 +34,23 @@ def __init__(self, o, d): ] ) self.face_generator = dg_generator(o, 2) - self.quadrule_finder = quad_rules.JaskowiecSukumar.JaskowiecSukumar().find_best_rule + self.quadrule_finder = ( + quad_rules.JaskowiecSukumar.JaskowiecSukumar().find_best_rule + ) self.generator_finder = basis_functions.BasisFunctionGenerator3D elif self.dim == 2: self.generator = basis_functions.BasisFunctionGenerator2D(self.order) self.geometry = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]]) - self.quadrule_finder = quad_rules.WitherdenVincentTri.WitherdenVincentTri().find_best_rule + self.quadrule_finder = ( + quad_rules.WitherdenVincentTri.WitherdenVincentTri().find_best_rule + ) self.generator_finder = basis_functions.BasisFunctionGenerator2D elif self.dim == 1: self.generator = basis_functions.BasisFunctionGenerator1D(self.order) self.geometry = np.array([[0.0], [1.0]]) - self.quadrule_finder = quad_rules.GaussJacobi.GaussJacobi(0, 0).find_best_rule + self.quadrule_finder = quad_rules.GaussJacobi.GaussJacobi( + 0, 0 + ).find_best_rule self.generator_finder = basis_functions.BasisFunctionGenerator1D else: raise Execption("Can only generate 1D, 2D or 2D basis functions") @@ -50,11 +58,11 @@ def __init__(self, o, d): self.nodes, self.weights = self.get_quadrature_rule(2 * self.order) def get_quadrature_rule(self, order): - n, w = self.quadrule_finder(order) + n, w = self.quadrule_finder(order) return quad_rules.Quadrature.transform(n, w, self.geometry) - def multilinear_form(self, face, der, order = None, side = None): + def multilinear_form(self, face, der, order=None, side=None): """ Given an array der, we compute a tensor V[i...] of dimension len(der) defined by (given in C++ parameter pack notation) @@ -78,14 +86,14 @@ def multilinear_form(self, face, der, order = None, side = None): # instead of the two current ones. # we only support a first derivative at the moment - assert np.all([d in (None,*(i for i in range(self.dim))) for d in der]) + assert np.all([d in (None, *(i for i in range(self.dim))) for d in der]) if order is None: order = [self.order] * len(der) - + if side is None: - side = [-1] * len(der) - + side = [None] * len(der) + assert len(order) == len(der) assert len(side) == len(der) @@ -94,47 +102,58 @@ def get_basis_function(o, d, s): basis = self.generator_finder(o) else: basis = self.face_generator.generator_finder(o) - basiseval_pre = basis.eval_basis if d is None else lambda x,i: basis.eval_diff_basis(x,i,d) + basiseval_pre = ( + basis.eval_basis + if d is None + else lambda x, i: basis.eval_diff_basis(x, i, d) + ) if face: if s is None: - basiseval = lambda x, i: basiseval_pre(self.volume_to_face_parametrisation(x, face), i) + basiseval = lambda x, i: basiseval_pre( + self.volume_to_face_parametrisation(x, face), i + ) elif s < 0: basiseval = basiseval_pre else: - basiseval = lambda x, i: basiseval_pre(self.face_to_face_parametrisation(x, face), i) + basiseval = lambda x, i: basiseval_pre( + self.face_to_face_parametrisation(x, face), i + ) else: # volume * face does not make sense when evaluating on the whole volume assert s is None basiseval = basiseval_pre return basiseval, basis.number_of_basis_functions() - basis_functions = [get_basis_function(o,d,s) for o,d,s in zip(order, der, side)] - + basis_functions = [ + get_basis_function(o, d, s) for o, d, s in zip(order, der, side) + ] + if face: nodes, weights = self.face_generator.get_quadrature_rule(np.prod(order)) else: nodes, weights = self.get_quadrature_rule(np.prod(order)) - sizes = [bn for _,bn in basis_functions] + + sizes = [bn for _, bn in basis_functions] tensor = np.empty(sizes) generic_eval_basis = lambda x, index: np.prod( - basis_functions[k][0](x, i) for k,i in enumerate(index) + [basis_functions[k][0](x, i) for k, i in enumerate(index)], axis=0 ) - for index in itertools.product(range(size) for size in sizes): + for index in itertools.product(*[range(size) for size in sizes]): eval_basis = lambda x: generic_eval_basis(x, index) - tensor[*index] = quad_rules.Quadrature.quad(nodes, weights, eval_basis) + tensor[index] = quad_rules.Quadrature.quad(nodes, weights, eval_basis) return tensor def mass_matrix(self): if not np.any(self.M == None): return self.M - + self.M = self.multilinear_form(False, [None, None]) return self.M def stiffness_matrix(self, dim): if not np.any(self.K[dim] == None): return self.K[dim] - + self.K[dim] = self.multilinear_form(False, [dim, None]) return self.K[dim] @@ -215,10 +234,10 @@ def rDivM(self, side): matrix = self.rT(side) mass = self.mass_matrix() return np.linalg.solve(mass, matrix.T) - + def collocate_volume(self, points): return base.collocate(self.generator, points) - + def collocate_face(self, points, side): # points are meant to be 2D here @@ -226,6 +245,7 @@ def collocate_face(self, points, side): projected = self.volume_to_face_parametrisation(points.T, side).T return base.collocate(self.generator, projected) + if __name__ == "__main__": from seissol_matrices import json_io diff --git a/src/seissol_matrices/generate.py b/src/seissol_matrices/generate.py index c23bc19..d92eca6 100644 --- a/src/seissol_matrices/generate.py +++ b/src/seissol_matrices/generate.py @@ -3,25 +3,34 @@ from dg_matrices import dg_generator from vtk_points import vtk_lagrange_2d, vtk_lagrange_3d + def main(): assert len(sys.argv) > 1 - if sys.argv[1] == 'vtk': - import dg_matrices + if sys.argv[1] == "vtk": + import dg_matrices + vtkpoints2 = {} vtkpoints3 = {} for deg in range(0, 8): vtkpoints2[deg] = vtk_lagrange_2d(deg) vtkpoints3[deg] = vtk_lagrange_3d(deg) - json_io.write_matrix(vtkpoints2[deg], f'vtk2d{deg}', f'vtkbase.json') - json_io.write_matrix(vtkpoints3[deg], f'vtk3d{deg}', f'vtkbase.json') + json_io.write_matrix(vtkpoints2[deg], f"vtk2d{deg}", f"vtkbase.json") + json_io.write_matrix(vtkpoints3[deg], f"vtk3d{deg}", f"vtkbase.json") for basisorder in range(2, 8): dggen = dg_generator(basisorder, 3) for deg in range(0, 8): - json_io.write_matrix(dggen.collocate_volume(vtkpoints3[deg]), - f'coll{basisorder}vd{deg}', f'vtko{basisorder}.json') + json_io.write_matrix( + dggen.collocate_volume(vtkpoints3[deg]), + f"coll{basisorder}vd{deg}", + f"vtko{basisorder}.json", + ) for f in range(4): - json_io.write_matrix(dggen.collocate_face(vtkpoints2[deg], f), - f'coll{basisorder}f{f}d{deg}', f'vtko{basisorder}.json') + json_io.write_matrix( + dggen.collocate_face(vtkpoints2[deg], f), + f"coll{basisorder}f{f}d{deg}", + f"vtko{basisorder}.json", + ) + -if __name__ == '__main__': +if __name__ == "__main__": main() diff --git a/src/seissol_matrices/vtk_points.py b/src/seissol_matrices/vtk_points.py index b445818..256dabd 100644 --- a/src/seissol_matrices/vtk_points.py +++ b/src/seissol_matrices/vtk_points.py @@ -1,10 +1,11 @@ import numpy as np + def vtk_lagrange_2d(d, start=0, divd=None): if d < 0: return np.empty((0, 2)) if d == 0: - return np.array([[1/3, 1/3]]) + return np.array([[1 / 3, 1 / 3]]) else: if divd is None: divd = d @@ -12,68 +13,97 @@ def vtk_lagrange_2d(d, start=0, divd=None): base = 0 obase = 0 allrings = [] - for r in range(start, d//3 + 1): - if d == 3*r: - allrings += [[s*r, s*r]] + for r in range(start, d // 3 + 1): + if d == 3 * r: + allrings += [[s * r, s * r]] else: - ringcorner = [[s*r, s*r], [s*(d - 2*r), s*r], [s*r, s*(d - 2*r)]] - ringborder = [[s*(r + i), s*r] for i in range(1, d - 3*r)] - ringborder += [[s*(d - 2*r - i), s*(r + i)] for i in range(1, d - 3*r)] - ringborder += [[s*r, s*(d - 2*r - i)] for i in range(1, d - 3*r)] + ringcorner = [ + [s * r, s * r], + [s * (d - 2 * r), s * r], + [s * r, s * (d - 2 * r)], + ] + ringborder = [[s * (r + i), s * r] for i in range(1, d - 3 * r)] + ringborder += [ + [s * (d - 2 * r - i), s * (r + i)] for i in range(1, d - 3 * r) + ] + ringborder += [ + [s * r, s * (d - 2 * r - i)] for i in range(1, d - 3 * r) + ] allrings += ringcorner + ringborder return np.array(allrings) + def vtk_lagrange_3d(d): if d == 0: - return np.array([[1/4, 1/4, 1/4]]) + return np.array([[1 / 4, 1 / 4, 1 / 4]]) else: s = 1 / d base = 0 obase = 0 allrings = [] - for r in range(d//4 + 1): - if d == 4*r: - allrings += [[s*r, s*r, s*r]] + for r in range(d // 4 + 1): + if d == 4 * r: + allrings += [[s * r, s * r, s * r]] else: - ringcorner = [[s*r, s*r, s*r], [s*(d - 3*r), s*r, s*r], [s*r, s*(d - 3*r), s*r], [s*r, s*r, s*(d - 3*r)]] - ringborder = [[s*(r + i), s*r, s*r] for i in range(1, d - 4*r)] - ringborder += [[s*(d - 3*r - i), s*(r + i), s*r] for i in range(1, d - 4*r)] - ringborder += [[s*r, s*(d - 3*r - i), s*r] for i in range(1, d - 4*r)] - ringborder += [[s*r, s*r, s*(r + i)] for i in range(1, d - 4*r)] - ringborder += [[s*(d - 3*r - i), s*r, s*(r + i)] for i in range(1, d - 4*r)] - ringborder += [[s*r, s*(d - 3*r - i), s*(r + i)] for i in range(1, d - 4*r)] + ringcorner = [ + [s * r, s * r, s * r], + [s * (d - 3 * r), s * r, s * r], + [s * r, s * (d - 3 * r), s * r], + [s * r, s * r, s * (d - 3 * r)], + ] + ringborder = [[s * (r + i), s * r, s * r] for i in range(1, d - 4 * r)] + ringborder += [ + [s * (d - 3 * r - i), s * (r + i), s * r] + for i in range(1, d - 4 * r) + ] + ringborder += [ + [s * r, s * (d - 3 * r - i), s * r] for i in range(1, d - 4 * r) + ] + ringborder += [[s * r, s * r, s * (r + i)] for i in range(1, d - 4 * r)] + ringborder += [ + [s * (d - 3 * r - i), s * r, s * (r + i)] + for i in range(1, d - 4 * r) + ] + ringborder += [ + [s * r, s * (d - 3 * r - i), s * (r + i)] + for i in range(1, d - 4 * r) + ] subface = vtk_lagrange_2d(d - r, r + 1, d) - ringfaces = [(i, s*r, j) for i,j in subface] - ringfaces += [(j, (1 - s*r) - i - j, i) for i,j in subface] - ringfaces += [(s*r, j, i) for i,j in subface] - ringfaces += [(j, i, s*r) for i,j in subface] + ringfaces = [(i, s * r, j) for i, j in subface] + ringfaces += [(j, (1 - s * r) - i - j, i) for i, j in subface] + ringfaces += [(s * r, j, i) for i, j in subface] + ringfaces += [(j, i, s * r) for i, j in subface] allrings += ringcorner + ringborder + ringfaces return np.array(allrings) + def vtk_lagrange_2d_from_vtk(d): import vtk + tet = vtk.vtkLagrangeTriangle() - points = ((d+1)*(d+2))//2 + points = ((d + 1) * (d + 2)) // 2 tet.GetPointIds().SetNumberOfIds(points) tet.GetPoints().SetNumberOfPoints(points) tet.Initialize() pointlist = [] for i in range(points): - barycentric = [0,0,0] + barycentric = [0, 0, 0] tet.ToBarycentricIndex(i, barycentric) pointlist += [[b / d for b in barycentric[:2]]] return np.array(pointlist) + def vtk_lagrange_3d_from_vtk(d): import vtk + tet = vtk.vtkLagrangeTetra() - points = ((d+1)*(d+2)*(d+3))//6 + points = ((d + 1) * (d + 2) * (d + 3)) // 6 tet.GetPointIds().SetNumberOfIds(points) tet.GetPoints().SetNumberOfPoints(points) tet.Initialize() pointlist = [] for i in range(points): - barycentric = [0,0,0,0] + barycentric = [0, 0, 0, 0] tet.ToBarycentricIndex(i, barycentric) pointlist += [[b / d for b in barycentric[:3]]] return np.array(pointlist) From c84a4fc5aeb7cfd30a829a18f2619c7b584aadd2 Mon Sep 17 00:00:00 2001 From: David Schneller Date: Thu, 21 Mar 2024 22:09:34 +0100 Subject: [PATCH 05/12] Bugfixing --- README.md | 13 +++++++++++ src/seissol_matrices/dg_matrices.py | 36 ++++++++++++++++------------- 2 files changed, 33 insertions(+), 16 deletions(-) diff --git a/README.md b/README.md index dbb5f5c..4240815 100644 --- a/README.md +++ b/README.md @@ -23,3 +23,16 @@ If we use basis functions for order $\mathcal{O}$, we have $\frac{1}{6} \times \ | $M_{kl}$ | $\int_T \Psi_k \Psi_l dx$ | `M3` | | | $\int_T \Phi_k \Phi_l dx$ | `M2` | | $F_{kl}^{-,j}$ | $\int_T \Psi_k \Psi_l dx$ | `rT` | + +## Usage + +Use poetry to install or use the package. In particular, consider the commands + +``` +# install +poetry install +# format files +poetry run black src +# run unit tests +poetry run coverage run -m nose2 +``` diff --git a/src/seissol_matrices/dg_matrices.py b/src/seissol_matrices/dg_matrices.py index 6f34562..5ffe89b 100644 --- a/src/seissol_matrices/dg_matrices.py +++ b/src/seissol_matrices/dg_matrices.py @@ -62,7 +62,7 @@ def get_quadrature_rule(self, order): return quad_rules.Quadrature.transform(n, w, self.geometry) - def multilinear_form(self, face, der, order=None, side=None): + def multilinear_form(self, face, der, order=None, dim=None, side=None): """ Given an array der, we compute a tensor V[i...] of dimension len(der) defined by (given in C++ parameter pack notation) @@ -94,11 +94,14 @@ def multilinear_form(self, face, der, order=None, side=None): if side is None: side = [None] * len(der) + if dim is None: + dim = [2] * len(der) if face else [3] * len(der) + assert len(order) == len(der) assert len(side) == len(der) - def get_basis_function(o, d, s): - if s is None: + def get_basis_function(o, d, s, r): + if r == 3: basis = self.generator_finder(o) else: basis = self.face_generator.generator_finder(o) @@ -108,30 +111,31 @@ def get_basis_function(o, d, s): else lambda x, i: basis.eval_diff_basis(x, i, d) ) if face: - if s is None: + if r == 3: basiseval = lambda x, i: basiseval_pre( - self.volume_to_face_parametrisation(x, face), i + self.volume_to_face_parametrisation(x, s), i ) - elif s < 0: - basiseval = basiseval_pre else: - basiseval = lambda x, i: basiseval_pre( - self.face_to_face_parametrisation(x, face), i - ) + if s is None: + basiseval = basiseval_pre + else: + basiseval = lambda x, i: basiseval_pre( + self.face_to_face_parametrisation(x, s), i + ) else: # volume * face does not make sense when evaluating on the whole volume - assert s is None + assert r == 3 basiseval = basiseval_pre return basiseval, basis.number_of_basis_functions() basis_functions = [ - get_basis_function(o, d, s) for o, d, s in zip(order, der, side) + get_basis_function(o, d, s, r) for o, d, s, r in zip(order, der, side, dim) ] if face: - nodes, weights = self.face_generator.get_quadrature_rule(np.prod(order)) + nodes, weights = self.face_generator.get_quadrature_rule(np.sum(order)) else: - nodes, weights = self.get_quadrature_rule(np.prod(order)) + nodes, weights = self.get_quadrature_rule(np.sum(order)) sizes = [bn for _, bn in basis_functions] tensor = np.empty(sizes) @@ -189,7 +193,7 @@ def face_to_face_parametrisation(self, x, side): def face_times_face_mass_matrix(self, side): assert self.dim == 3 - return self.multilinear_form(True, [None, None], side=[-1, side]) + return self.multilinear_form(True, [None, None], side=[None, side], dim=[2, 2]) def fP(self, side): return self.face_times_face_mass_matrix(side) @@ -219,7 +223,7 @@ def volume_to_face_parametrisation(self, x, side): def volume_times_face_mass_matrix(self, side): assert self.dim == 3 - return self.multilinear_form(True, [None, None], side=[None, side]) + return self.multilinear_form(True, [None, None], side=[None, side], dim=[2, 3]) def fMrT(self, side): return self.volume_times_face_mass_matrix(side) From bbeb25feca5e48f8924346e49f6b2a3903bcd672 Mon Sep 17 00:00:00 2001 From: David Schneller Date: Sun, 24 Mar 2024 00:14:20 +0100 Subject: [PATCH 06/12] Update VTK matrices to generate --- src/seissol_matrices/generate.py | 17 +++++++++++------ 1 file changed, 11 insertions(+), 6 deletions(-) diff --git a/src/seissol_matrices/generate.py b/src/seissol_matrices/generate.py index d92eca6..ec57b1b 100644 --- a/src/seissol_matrices/generate.py +++ b/src/seissol_matrices/generate.py @@ -14,20 +14,25 @@ def main(): for deg in range(0, 8): vtkpoints2[deg] = vtk_lagrange_2d(deg) vtkpoints3[deg] = vtk_lagrange_3d(deg) - json_io.write_matrix(vtkpoints2[deg], f"vtk2d{deg}", f"vtkbase.json") - json_io.write_matrix(vtkpoints3[deg], f"vtk3d{deg}", f"vtkbase.json") + json_io.write_matrix(vtkpoints2[deg].T, f"vtk2d({deg})", f"vtkbase.json") + json_io.write_matrix(vtkpoints3[deg].T, f"vtk3d({deg})", f"vtkbase.json") for basisorder in range(2, 8): dggen = dg_generator(basisorder, 3) for deg in range(0, 8): json_io.write_matrix( - dggen.collocate_volume(vtkpoints3[deg]), - f"coll{basisorder}vd{deg}", + dggen.collocate_volume(vtkpoints3[deg]).T, + f"collvv({basisorder},{deg})", + f"vtko{basisorder}.json", + ) + json_io.write_matrix( + dggen.face_generator.collocate_volume(vtkpoints2[deg]).T, + f"collff({basisorder},{deg})", f"vtko{basisorder}.json", ) for f in range(4): json_io.write_matrix( - dggen.collocate_face(vtkpoints2[deg], f), - f"coll{basisorder}f{f}d{deg}", + dggen.collocate_face(vtkpoints2[deg], f).T, + f"collvf({basisorder},{deg},{f})", f"vtko{basisorder}.json", ) From 287bfebaba07305c1654e20aa9aea826d98ba1bb Mon Sep 17 00:00:00 2001 From: David Schneller Date: Mon, 30 Sep 2024 16:59:21 +0200 Subject: [PATCH 07/12] Add order 8 to VTK output --- src/seissol_matrices/generate.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/src/seissol_matrices/generate.py b/src/seissol_matrices/generate.py index ec57b1b..526dbb4 100644 --- a/src/seissol_matrices/generate.py +++ b/src/seissol_matrices/generate.py @@ -11,14 +11,14 @@ def main(): vtkpoints2 = {} vtkpoints3 = {} - for deg in range(0, 8): + for deg in range(0, 9): vtkpoints2[deg] = vtk_lagrange_2d(deg) vtkpoints3[deg] = vtk_lagrange_3d(deg) json_io.write_matrix(vtkpoints2[deg].T, f"vtk2d({deg})", f"vtkbase.json") json_io.write_matrix(vtkpoints3[deg].T, f"vtk3d({deg})", f"vtkbase.json") - for basisorder in range(2, 8): + for basisorder in range(2, 9): dggen = dg_generator(basisorder, 3) - for deg in range(0, 8): + for deg in range(0, 9): json_io.write_matrix( dggen.collocate_volume(vtkpoints3[deg]).T, f"collvv({basisorder},{deg})", From e9ac15d36942a46ab2498b99a5e4230dce0e1c31 Mon Sep 17 00:00:00 2001 From: David Schneller Date: Mon, 30 Sep 2024 16:59:31 +0200 Subject: [PATCH 08/12] Support Python 3.12 --- pyproject.toml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/pyproject.toml b/pyproject.toml index 59d82c1..02b8645 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -9,7 +9,7 @@ authors = [ readme = "README.md" [tool.poetry.dependencies] -python = ">=3.10,<3.12" +python = ">=3.10" numpy = "^1.24.2" scipy = "^1.10.0" From 1d0c4f6981372bada2461e76efbdb8e7fabb2a3b Mon Sep 17 00:00:00 2001 From: David Schneller Date: Mon, 30 Sep 2024 17:00:09 +0200 Subject: [PATCH 09/12] Remove lock --- .gitignore | 4 + poetry.lock | 517 ---------------------------------------------------- 2 files changed, 4 insertions(+), 517 deletions(-) delete mode 100644 poetry.lock diff --git a/.gitignore b/.gitignore index bee8a64..d8beb52 100644 --- a/.gitignore +++ b/.gitignore @@ -1 +1,5 @@ __pycache__ + +# don't commit the lock; it may get outdated to quickly +poetry.lock + diff --git a/poetry.lock b/poetry.lock deleted file mode 100644 index 783fee6..0000000 --- a/poetry.lock +++ /dev/null @@ -1,517 +0,0 @@ -# This file is automatically @generated by Poetry 1.8.2 and should not be changed by hand. - 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def kDivM(self, dim): - stiffness = self.stiffness_matrix(dim) + def kDivM(self, dim, matorder=None): mass = self.mass_matrix() - + if matorder is None: + stiffness = self.stiffness_matrix(dim) + else: + stiffness = self.multilinear_form( + False, [None, dim, None], order=[matorder, self.order, self.order] + ) return np.linalg.solve(mass, stiffness) - def kDivMT(self, dim): - stiffness = self.stiffness_matrix(dim) + def kDivMT(self, dim, matorder=None): mass = self.mass_matrix() + if matorder is None: + stiffness = self.stiffness_matrix(dim) + sT = stiffness.T + else: + correct1 = self.multilinear_form( + False, [dim, None, None], order=[matorder, self.order, self.order] + ) + correct2 = self.multilinear_form( + False, [None, None, dim], order=[matorder, self.order, self.order] + ) + sT = correct1 + correct2 - return np.linalg.solve(mass, stiffness.T) + return np.linalg.solve(mass, sT) def face_to_face_parametrisation(self, x, side): # implement Dumbser & Käser, 2006 Table 2 b) @@ -233,11 +247,22 @@ def rT(self, side): mass = self.face_generator.mass_matrix() return np.linalg.solve(mass, matrix) - def rDivM(self, side): + def rDivM(self, side, matorder=None): assert self.dim == 3 - matrix = self.rT(side) mass = self.mass_matrix() - return np.linalg.solve(mass, matrix.T) + if matorder is None: + matrix = self.rT(side).T + else: + prematrix = self.multilinear_form( + True, + [None, None, None], + order=[matorder, self.order, self.order], + side=[None, None, side], + dim=[3, 2, 3], + ) + facemass = self.face_generator.mass_matrix() + matrix = np.linalg.solve(facemass, prematrix).transpose((0, 2, 1)) + return np.linalg.solve(mass, matrix) def collocate_volume(self, points): return base.collocate(self.generator, points) diff --git a/src/seissol_matrices/dr_matrices.py b/src/seissol_matrices/dr_matrices.py index be1b7c8..a22ed1b 100755 --- a/src/seissol_matrices/dr_matrices.py +++ b/src/seissol_matrices/dr_matrices.py @@ -15,70 +15,63 @@ def __init__(self, o, q): self.dg3_generator = dg_matrices.dg_generator(self.order, 3) self.dg2_generator = dg_matrices.dg_generator(self.order, 2) - def V3mTo2n(self, a, b): + def V3mTo2n(self, a, b, matorder=None): m = self.bf3_generator.number_of_basis_functions() points = self.quadrule.points() n = points.shape[0] - matrix = np.zeros((n, m)) + if matorder is None: + evalfun = lambda q, j, k: self.bf3_generator.eval_basis(q, j) + materialdim = 1 + else: + materialbasis = basis_functions.BasisFunctionGenerator3D(matorder) + evalfun = lambda q, j, k: self.bf3_generator.eval_basis( + q, j + ) * materialbasis.eval_basis(q, k) + materialdim = materialbasis.number_of_basis_functions() + + matrix = np.zeros((materialdim, n, m)) for i, p in enumerate(points): for j in range(m): - if a == 0 and b == 0: - matrix[i, j] = self.bf3_generator.eval_basis([p[1], p[0], 0], j) - if a == 0 and b == 1: - matrix[i, j] = self.bf3_generator.eval_basis([p[0], p[1], 0], j) - if a == 0 and b == 2: - matrix[i, j] = self.bf3_generator.eval_basis( - [p[1], 1 - p[0] - p[1], 0], j - ) - if a == 0 and b == 3: - matrix[i, j] = self.bf3_generator.eval_basis( - [1 - p[0] - p[1], p[0], 0], j - ) - if a == 1 and b == 0: - matrix[i, j] = self.bf3_generator.eval_basis([p[0], 0, p[1]], j) - if a == 1 and b == 1: - matrix[i, j] = self.bf3_generator.eval_basis([p[1], 0, p[0]], j) - if a == 1 and b == 2: - matrix[i, j] = self.bf3_generator.eval_basis( - [1 - p[0] - p[1], 0, p[1]], j - ) - if a == 1 and b == 3: - matrix[i, j] = self.bf3_generator.eval_basis( - [p[0], 0, 1 - p[0] - p[1]], j - ) - if a == 2 and b == 0: - matrix[i, j] = self.bf3_generator.eval_basis([0, p[1], p[0]], j) - if a == 2 and b == 1: - matrix[i, j] = self.bf3_generator.eval_basis([0, p[0], p[1]], j) - if a == 2 and b == 2: - matrix[i, j] = self.bf3_generator.eval_basis( - [0, p[1], 1 - p[0] - p[1]], j - ) - if a == 2 and b == 3: - matrix[i, j] = self.bf3_generator.eval_basis( - [0, 1 - p[0] - p[1], p[0]], j - ) - if a == 3 and b == 0: - matrix[i, j] = self.bf3_generator.eval_basis( - [1 - p[0] - p[1], p[0], p[1]], j - ) - if a == 3 and b == 1: - matrix[i, j] = self.bf3_generator.eval_basis( - [1 - p[0] - p[1], p[1], p[0]], j - ) - if a == 3 and b == 2: - matrix[i, j] = self.bf3_generator.eval_basis( - [p[0], 1 - p[0] - p[1], p[1]], j - ) - if a == 3 and b == 3: - matrix[i, j] = self.bf3_generator.eval_basis( - [p[1], p[0], 1 - p[0] - p[1]], j - ) + for k in range(materialdim): + if a == 0 and b == 0: + matrix[k, i, j] = evalfun([p[1], p[0], 0], j, k) + if a == 0 and b == 1: + matrix[k, i, j] = evalfun([p[0], p[1], 0], j, k) + if a == 0 and b == 2: + matrix[k, i, j] = evalfun([p[1], 1 - p[0] - p[1], 0], j, k) + if a == 0 and b == 3: + matrix[k, i, j] = evalfun([1 - p[0] - p[1], p[0], 0], j, k) + if a == 1 and b == 0: + matrix[k, i, j] = evalfun([p[0], 0, p[1]], j, k) + if a == 1 and b == 1: + matrix[k, i, j] = evalfun([p[1], 0, p[0]], j, k) + if a == 1 and b == 2: + matrix[k, i, j] = evalfun([1 - p[0] - p[1], 0, p[1]], j, k) + if a == 1 and b == 3: + matrix[k, i, j] = evalfun([p[0], 0, 1 - p[0] - p[1]], j, k) + if a == 2 and b == 0: + matrix[k, i, j] = evalfun([0, p[1], p[0]], j, k) + if a == 2 and b == 1: + matrix[k, i, j] = evalfun([0, p[0], p[1]], j, k) + if a == 2 and b == 2: + matrix[k, i, j] = evalfun([0, p[1], 1 - p[0] - p[1]], j, k) + if a == 2 and b == 3: + matrix[k, i, j] = evalfun([0, 1 - p[0] - p[1], p[0]], j, k) + if a == 3 and b == 0: + matrix[k, i, j] = evalfun([1 - p[0] - p[1], p[0], p[1]], j, k) + if a == 3 and b == 1: + matrix[k, i, j] = evalfun([1 - p[0] - p[1], p[1], p[0]], j, k) + if a == 3 and b == 2: + matrix[k, i, j] = evalfun([p[0], 1 - p[0] - p[1], p[1]], j, k) + if a == 3 and b == 3: + matrix[k, i, j] = evalfun([p[1], p[0], 1 - p[0] - p[1]], j, k) + if matorder is None: + matrix = np.squeeze(matrix) return matrix - def V3mTo2nTWDivM(self, a, b): - matrix = self.V3mTo2n(a, b) + def V3mTo2nTWDivM(self, a, b, matorder=None): + matrix = self.V3mTo2n(a, b, matorder) mass = self.dg3_generator.mass_matrix() weights = self.quadrule.weights() n = weights.shape[0] @@ -86,7 +79,9 @@ def V3mTo2nTWDivM(self, a, b): for i in range(n): W[i, i] = weights[i] - return np.linalg.solve(mass, np.dot(matrix.T, W)) + matrixT = matrix.T if matorder is None else matrix.transpose((0, 2, 1)) + + return np.linalg.solve(mass, np.dot(matrixT, W)) def quadpoints(self): points = self.quadrule.points() diff --git a/src/seissol_matrices/generate.py b/src/seissol_matrices/generate.py index 526dbb4..a22cc7f 100644 --- a/src/seissol_matrices/generate.py +++ b/src/seissol_matrices/generate.py @@ -1,7 +1,10 @@ import sys from seissol_matrices import json_io from dg_matrices import dg_generator +from dr_matrices import dr_generator from vtk_points import vtk_lagrange_2d, vtk_lagrange_3d +from seissol_matrices import quad_points +from plasticity_matrices import PlasticityGenerator def main(): @@ -35,6 +38,85 @@ def main(): f"collvf({basisorder},{deg},{f})", f"vtko{basisorder}.json", ) + elif sys.argv[1] == "ader": + materialorder = None + if len(sys.argv) > 2: + materialorder = int(sys.argv[2]) + for order in range(2, 9): + filename = f"linear-ader-{order}-h{materialorder}.json" + if materialorder is None: + filename = f"linear-ader-{order}.json" + dggen = dg_generator(order, 3) + for dim in range(3): + json_io.write_tensor( + dggen.kDivMT(dim, materialorder), + f"kDivMT({dim})", + filename, + ) + json_io.write_tensor( + dggen.kDivM(dim, materialorder), f"kDivM({dim})", filename + ) + for line in range(3): + json_io.write_tensor(dggen.fP(line), f"fP({line})", filename) + for face in range(4): + json_io.write_tensor( + dggen.rDivM(face, materialorder), f"rDivM({face})", filename + ) + json_io.write_tensor(dggen.rT(face), f"rT({face})", filename) + json_io.write_tensor(dggen.fMrT(face), f"fMrT({face})", filename) + elif sys.argv[1] == "dr": + materialorder = None + if len(sys.argv) > 2: + materialorder = int(sys.argv[2]) + for order in range(2, 9): + for quadname, quadrule in zip( + ["stroud", "dunavant", "witherden_vincent"], + [ + quad_points.stroud(order + 1), + quad_points.dunavant(order + 1), + quad_points.witherden_vincent(order + 1), + ], + ): + filename = f"dr-{quadname}-{order}-h{materialorder}.json" + if materialorder is None: + filename = f"dr-{quadname}-{order}.json" + generator = dr_generator(order, quadrule) + + quadpoints = generator.quadpoints() + quadweights = generator.quadweights() + resample = generator.resample() + V2QuadTo2m = generator.V2QuadTo2m() + V2mTo2Quad = generator.V2mTo2Quad() + + json_io.write_matrix(quadpoints, "quadpoints", filename) + json_io.write_matrix( + quadweights.reshape(-1, 1), "quadweights", filename + ) + json_io.write_matrix(resample, "resample", filename) + json_io.write_matrix(V2QuadTo2m, "V2QuadTo2m", filename) + json_io.write_matrix(V2mTo2Quad, "V2mTo2Quad", filename) + for a in range(0, 4): + for b in range(0, 4): + V3mTo2n = generator.V3mTo2n(a, b) + V3mTo2nTWDivM = generator.V3mTo2nTWDivM( + a, b, matorder=materialorder + ) + json_io.write_matrix(V3mTo2n, f"V3mTo2n({a},{b})", filename) + json_io.write_matrix( + V3mTo2nTWDivM, f"V3mTo2nTWDivM({a},{b})", filename + ) + elif sys.argv[1] == "hom": + materialorder = None + if len(sys.argv) > 2: + materialorder = int(sys.argv[2]) + for mode in ("nb", "ip"): + filename = f"hom-{mode}-h{materialorder}.json" + generator = PlasticityGenerator(materialorder) + points = generator.nodes(mode) + interpolator = generator.generate_Vandermonde_inv(mode) + + json_io.write_matrix(points, "hompoints", filename) + json_io.write_matrix(interpolator, "homproject", filename) if __name__ == "__main__": From 4cddd830e87d5895c825fc91b85fe29be8a8d9ba Mon Sep 17 00:00:00 2001 From: David Schneller Date: Mon, 10 Mar 2025 00:16:54 +0100 Subject: [PATCH 12/12] Also generate the respective DR matrices --- src/seissol_matrices/generate.py | 47 ++++++++++++++++++++++---------- 1 file changed, 33 insertions(+), 14 deletions(-) diff --git a/src/seissol_matrices/generate.py b/src/seissol_matrices/generate.py index a22cc7f..5945204 100644 --- a/src/seissol_matrices/generate.py +++ b/src/seissol_matrices/generate.py @@ -17,23 +17,23 @@ def main(): for deg in range(0, 9): vtkpoints2[deg] = vtk_lagrange_2d(deg) vtkpoints3[deg] = vtk_lagrange_3d(deg) - json_io.write_matrix(vtkpoints2[deg].T, f"vtk2d({deg})", f"vtkbase.json") - json_io.write_matrix(vtkpoints3[deg].T, f"vtk3d({deg})", f"vtkbase.json") + json_io.write_tensor(vtkpoints2[deg].T, f"vtk2d({deg})", f"vtkbase.json") + json_io.write_tensor(vtkpoints3[deg].T, f"vtk3d({deg})", f"vtkbase.json") for basisorder in range(2, 9): dggen = dg_generator(basisorder, 3) for deg in range(0, 9): - json_io.write_matrix( + json_io.write_tensor( dggen.collocate_volume(vtkpoints3[deg]).T, f"collvv({basisorder},{deg})", f"vtko{basisorder}.json", ) - json_io.write_matrix( + json_io.write_tensor( dggen.face_generator.collocate_volume(vtkpoints2[deg]).T, f"collff({basisorder},{deg})", f"vtko{basisorder}.json", ) for f in range(4): - json_io.write_matrix( + json_io.write_tensor( dggen.collocate_face(vtkpoints2[deg], f).T, f"collvf({basisorder},{deg},{f})", f"vtko{basisorder}.json", @@ -88,21 +88,21 @@ def main(): V2QuadTo2m = generator.V2QuadTo2m() V2mTo2Quad = generator.V2mTo2Quad() - json_io.write_matrix(quadpoints, "quadpoints", filename) - json_io.write_matrix( + json_io.write_tensor(quadpoints, "quadpoints", filename) + json_io.write_tensor( quadweights.reshape(-1, 1), "quadweights", filename ) - json_io.write_matrix(resample, "resample", filename) - json_io.write_matrix(V2QuadTo2m, "V2QuadTo2m", filename) - json_io.write_matrix(V2mTo2Quad, "V2mTo2Quad", filename) + json_io.write_tensor(resample, "resample", filename) + json_io.write_tensor(V2QuadTo2m, "V2QuadTo2m", filename) + json_io.write_tensor(V2mTo2Quad, "V2mTo2Quad", filename) for a in range(0, 4): for b in range(0, 4): V3mTo2n = generator.V3mTo2n(a, b) V3mTo2nTWDivM = generator.V3mTo2nTWDivM( a, b, matorder=materialorder ) - json_io.write_matrix(V3mTo2n, f"V3mTo2n({a},{b})", filename) - json_io.write_matrix( + json_io.write_tensor(V3mTo2n, f"V3mTo2n({a},{b})", filename) + json_io.write_tensor( V3mTo2nTWDivM, f"V3mTo2nTWDivM({a},{b})", filename ) elif sys.argv[1] == "hom": @@ -114,9 +114,28 @@ def main(): generator = PlasticityGenerator(materialorder) points = generator.nodes(mode) interpolator = generator.generate_Vandermonde_inv(mode) + deinterpolator = generator.generate_Vandermonde(mode) - json_io.write_matrix(points, "hompoints", filename) - json_io.write_matrix(interpolator, "homproject", filename) + json_io.write_tensor(points, "hompoints", filename) + json_io.write_tensor(interpolator, "homproject", filename) + json_io.write_tensor(deinterpolator, "homiproject", filename) + for order in range(2, 9): + for quadname, quadrule in zip( + ["stroud", "dunavant", "witherden_vincent"], + [ + quad_points.stroud(order + 1), + quad_points.dunavant(order + 1), + quad_points.witherden_vincent(order + 1), + ], + ): + filename = f"homdr-{mode}-{quadname}-{order}-h{materialorder}.json" + generator = dr_generator(materialorder, quadrule) + for a in range(0, 4): + for b in range(0, 4): + V3mTo2n = generator.V3mTo2n(a, b) + json_io.write_tensor( + V3mTo2n, f"homV3mTo2n({a},{b})", filename + ) if __name__ == "__main__":