Issue 0050 compatibility

check_mlt.py

@@ -0,0 +1,28 @@
+import finat
+from firedrake import *
+import numpy as np
+
+
+def isDiag(M):
+    i, j = np.nonzero(M)
+    return np.all(i == j)
+
+degree = 4
+mesh = RectangleMesh(3, 2, 2.0, 1.0)
+element = FiniteElement(  # noqa: F405
+    "KMV", mesh.ufl_cell(), degree=degree, variant="KMV"
+)
+V = FunctionSpace(mesh, element)
+quad_rule = finat.quadrature.make_quadrature(V.finat_element.cell, V.ufl_element().degree(), "KMV")
+
+u = TrialFunction(V)
+v = TestFunction(V)
+
+form = u*v*dx(scheme=quad_rule)
+A = assemble(form)
+M = A.M.values
+Mdiag = M.diagonal()
+
+print(f"Matrix is diagonal:{isDiag(M)}")
+np.save("new_diag", Mdiag)
+print("END")

check_sem.py

@@ -0,0 +1,55 @@
+import finat
+import FIAT
+from firedrake import *
+import numpy as np
+
+
+def gauss_lobatto_legendre_line_rule(degree):
+    fiat_make_rule = FIAT.quadrature.GaussLobattoLegendreQuadratureLineRule
+    fiat_rule = fiat_make_rule(FIAT.ufc_simplex(1), degree + 1)
+    finat_ps = finat.point_set.GaussLobattoLegendrePointSet
+    points = finat_ps(fiat_rule.get_points())
+    weights = fiat_rule.get_weights()
+    return finat.quadrature.QuadratureRule(points, weights)
+
+def gauss_lobatto_legendre_cube_rule(dimension, degree):
+    make_tensor_rule = finat.quadrature.TensorProductQuadratureRule
+    result = gauss_lobatto_legendre_line_rule(degree)
+    for _ in range(1, dimension):
+        line_rule = gauss_lobatto_legendre_line_rule(degree)
+        result = make_tensor_rule([result, line_rule])
+    return result
+
+
+
+def isDiag(M):
+    i, j = np.nonzero(M)
+    return np.all(i == j)
+
+degree = 2
+# mesh = RectangleMesh(3, 2, 2.0, 1.0, quadrilateral=True)
+mesh = RectangleMesh(1, 1, 1.0, 1.0, quadrilateral=True)
+element = FiniteElement('CG', mesh.ufl_cell(), degree=degree, variant='spectral')
+V = FunctionSpace(mesh, element)
+quad_rule = gauss_lobatto_legendre_cube_rule(dimension=2, degree=degree)
+
+u = TrialFunction(V)
+v = TestFunction(V)
+
+form = u*v*dx(scheme=quad_rule)
+A = assemble(form)
+M = A.M.values
+Mdiag = M.diagonal()
+
+x_mesh, y_mesh = SpatialCoordinate(mesh)
+x_func = Function(V)
+y_func = Function(V)
+x_func.interpolate(x_mesh)
+y_func.interpolate(y_mesh)
+x = x_func.dat.data[:]
+y = y_func.dat.data[:]
+
+print(f"Matrix is diagonal:{isDiag(M)}")
+old_diag = np.load("/home/olender/Development/issue_50_compatibility/spyro-1/old_sem_diag.npy")
+dif = Mdiag-old_diag
+print("END")

check_u.py

@@ -0,0 +1,70 @@
+import finat
+from firedrake import *
+import numpy as np
+
+
+def analytical_solution(t, V, mesh_z, mesh_x):
+    analytical = Function(V)
+    x = mesh_z
+    y = mesh_x
+    analytical.interpolate(x * (x + 1) * y * (y - 1) * t)
+
+    return analytical
+
+
+def isDiag(M):
+    i, j = np.nonzero(M)
+    return np.all(i == j)
+
+degree = 4
+mesh = RectangleMesh(3, 2, 2.0, 1.0)
+mesh.coordinates.dat.data[:, 0] *= -1.0
+mesh_z, mesh_x = SpatialCoordinate(mesh)
+V = FunctionSpace(mesh, "KMV", degree)
+quad_rule = finat.quadrature.make_quadrature(V.finat_element.cell, V.ufl_element().degree(), "KMV")
+
+u = TrialFunction(V)
+v = TestFunction(V)
+
+c = Function(V, name="velocity")
+c.interpolate(1 + sin(pi*-mesh_z)*sin(pi*mesh_x))
+u_n = Function(V)
+u_nm1 = Function(V)
+dt = 0.0005
+t = 0.0
+u_nm1.assign(analytical_solution((t - 2 * dt), V, mesh_z, mesh_x))
+u_n.assign(analytical_solution((t - dt), V, mesh_z, mesh_x))
+
+q = Function(V)
+q.assign(1.0)
+dt = 0.001
+
+m1 = (
+    1
+    / (c * c)
+    * ((u - 2.0 * u_n + u_nm1) / Constant(dt**2))
+    * v
+    * dx(scheme=quad_rule)
+)
+a = dot(grad(u_n), grad(v)) * dx(scheme=quad_rule)
+le = q * v * dx(scheme=quad_rule)
+
+form = m1 + a - le
+
+boundary_ids = (1, 2, 3, 4)
+bcs = DirichletBC(V, 0.0, boundary_ids)
+A = assemble(lhs(form), bcs=bcs)
+solver_parameters = {
+    "ksp_type": "preonly",
+    "pc_type": "jacobi",
+}
+solver = LinearSolver(
+    A, solver_parameters=solver_parameters
+)
+M = A.M.values
+Mdiag = M.diagonal()
+
+print(f"Matrix is diagonal:{isDiag(M)}")
+np.save("/home/olender/Development/issue_50_compatibility/spyro-1/new_diag", Mdiag)
+
+print("END")

check_u2.py

@@ -0,0 +1,113 @@
+import finat
+from firedrake import *
+import numpy as np
+
+
+def analytical_solution(t, V, mesh_z, mesh_x):
+    analytical = Function(V)
+    x = mesh_z
+    y = mesh_x
+    analytical.interpolate(x * (x + 1) * y * (y - 1) * t)
+
+    return analytical
+
+
+def isDiag(M):
+    i, j = np.nonzero(M)
+    return np.all(i == j)
+
+degree = 4
+mesh = RectangleMesh(50, 50, 1.0, 1.0)
+mesh.coordinates.dat.data[:, 0] *= -1.0
+mesh_z, mesh_x = SpatialCoordinate(mesh)
+V = FunctionSpace(mesh, "KMV", degree)
+quad_rule = finat.quadrature.make_quadrature(V.finat_element.cell, V.ufl_element().degree(), "KMV")
+
+u = TrialFunction(V)
+v = TestFunction(V)
+
+c = Function(V, name="velocity")
+c.interpolate(1 + sin(pi*-mesh_z)*sin(pi*mesh_x))
+u_n = Function(V)
+u_nm1 = Function(V)
+dt = 0.0005
+t = 0.0
+final_time = 1.0
+u_nm1.assign(analytical_solution((t - 2 * dt), V, mesh_z, mesh_x))
+u_n.assign(analytical_solution((t - dt), V, mesh_z, mesh_x))
+
+q_xy = Function(V)
+q_xy.interpolate(-(mesh_z**2) - mesh_z - mesh_x**2 + mesh_x)
+q = q_xy * Constant(2 * t)
+
+nt = int((final_time - t) / dt) + 1
+
+m1 = (
+    1
+    / (c * c)
+    * ((u - 2.0 * u_n + u_nm1) / Constant(dt**2))
+    * v
+    * dx(scheme=quad_rule)
+)
+a = dot(grad(u_n), grad(v)) * dx(scheme=quad_rule)
+le = q * v * dx(scheme=quad_rule)
+
+form = m1 + a - le
+
+B = Cofunction(V.dual())
+
+boundary_ids = (1, 2, 3, 4)
+bcs = DirichletBC(V, 0.0, boundary_ids)
+A = assemble(lhs(form), bcs=bcs)
+solver_parameters = {
+    "ksp_type": "preonly",
+    "pc_type": "jacobi",
+}
+solver = LinearSolver(
+    A, solver_parameters=solver_parameters
+)
+As = solver.A
+petsc_matrix = As.petscmat
+diagonal = petsc_matrix.getDiagonal()
+Mdiag = diagonal.array
+
+np.save("/home/olender/Development/issue_50_compatibility/spyro-1/new_diag", Mdiag)
+out = File("new_firedrake_u2.pvd")
+
+u_np1 = Function(V)
+for step in range(nt):
+    q = q_xy * Constant(2 * t)
+    m1 = (
+        1
+        / (c * c)
+        * ((u - 2.0 * u_n + u_nm1) / Constant(dt**2))
+        * v
+        * dx(scheme=quad_rule)
+    )
+    a = dot(grad(u_n), grad(v)) * dx(scheme=quad_rule)
+    le = q * v * dx(scheme=quad_rule)
+
+    form = m1 + a - le
+
+    B = assemble(rhs(form), tensor=B)
+
+    solver.solve(u_np1, B)
+
+    if (step - 1) % 100 == 0:
+        print(f"Time : {t}")
+        out.write(u_n)
+        assert (
+            norm(u_n) < 1
+        ), "Numerical instability. Try reducing dt or building the \
+            mesh differently"
+
+    u_nm1.assign(u_n)
+    u_n.assign(u_np1)
+
+    t = step * float(dt)
+
+u_an = analytical_solution(t, V, mesh_z, mesh_x)
+error = errornorm(u_n, u_an)
+print(f"Error: {error}")
+
+print("END")