def test_save_1d_mesh(tempdir, encoding): filename = os.path.join(tempdir, "mf_1D.xdmf") mesh = UnitIntervalMesh(MPI.comm_world, 32) mf = MeshFunction("size_t", mesh, mesh.topology.dim, 0) mf.values[:] = np.arange(mesh.num_entities(1)) with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as file: file.write(mf)
def test_save_1d_scalar(tempdir, encoding): filename2 = os.path.join(tempdir, "u1_.xdmf") mesh = UnitIntervalMesh(MPI.COMM_WORLD, 32) V = FunctionSpace(mesh, ("Lagrange", 2)) u = Function(V) u.vector.set(1.0 + (1j if has_petsc_complex else 0)) with XDMFFile(mesh.mpi_comm(), filename2, "w", encoding=encoding) as file: file.write_mesh(mesh) file.write_function(u)
def test_save_1d_scalar(tempdir, encoding): filename2 = os.path.join(tempdir, "u1_.xdmf") mesh = UnitIntervalMesh(MPI.comm_world, 32) # FIXME: This randomly hangs in parallel V = FunctionSpace(mesh, ("Lagrange", 2)) u = Function(V) u.vector.set(1.0 + (1j if has_petsc_complex else 0)) with XDMFFile(mesh.mpi_comm(), filename2, encoding=encoding) as file: file.write(u)
def test_save_1d_tensor(tempdir): mesh = UnitIntervalMesh(MPI.COMM_WORLD, 32) element = ufl.TensorElement("Lagrange", mesh.ufl_cell(), 2, shape=(2, 2)) u = Function(FunctionSpace(mesh, element)) with u.vector.localForm() as loc: loc.set(1.0) filename = os.path.join(tempdir, "u.pvd") with VTKFile(mesh.mpi_comm(), filename, "w") as vtk: vtk.write_function(u, 0.)
def test_save_and_load_1d_mesh(tempdir, encoding): filename = os.path.join(tempdir, "mesh.xdmf") mesh = UnitIntervalMesh(MPI.comm_world, 32) with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as file: file.write(mesh) with XDMFFile(MPI.comm_world, filename) as file: mesh2 = file.read_mesh(cpp.mesh.GhostMode.none) assert mesh.num_entities_global(0) == mesh2.num_entities_global(0) dim = mesh.topology.dim assert mesh.num_entities_global(dim) == mesh2.num_entities_global(dim)
def test_save_and_load_1d_mesh(tempdir, encoding): filename = os.path.join(tempdir, "mesh.xdmf") mesh = UnitIntervalMesh(MPI.COMM_WORLD, 32) with XDMFFile(mesh.mpi_comm(), filename, "w", encoding=encoding) as file: file.write_mesh(mesh) with XDMFFile(MPI.COMM_WORLD, filename, "r", encoding=encoding) as file: mesh2 = file.read_mesh() assert mesh.topology.index_map(0).size_global == mesh2.topology.index_map(0).size_global assert mesh.topology.index_map(mesh.topology.dim).size_global == mesh2.topology.index_map( mesh.topology.dim).size_global
def test_diff_then_integrate(): # Define 1D geometry n = 21 mesh = UnitIntervalMesh(MPI.COMM_WORLD, n) # Shift and scale mesh x0, x1 = 1.5, 3.14 mesh.coordinates()[:] *= (x1 - x0) mesh.coordinates()[:] += x0 x = SpatialCoordinate(mesh)[0] xs = 0.1 + 0.8 * x / x1 # scaled to be within [0.1,0.9] # Define list of expressions to test, and configure # accuracies these expressions are known to pass with. # The reason some functions are less accurately integrated is # likely that the default choice of quadrature rule is not perfect F_list = [] def reg(exprs, acc=10): for expr in exprs: F_list.append((expr, acc)) # FIXME: 0*dx and 1*dx fails in the ufl-ffcx-jit framework somewhere # reg([Constant(0.0, cell=cell)]) # reg([Constant(1.0, cell=cell)]) monomial_list = [x**q for q in range(2, 6)] reg(monomial_list) reg([2.3 * p + 4.5 * q for p in monomial_list for q in monomial_list]) reg([x**x]) reg([x**(x**2)], 8) reg([x**(x**3)], 6) reg([x**(x**4)], 2) # Special functions: reg([atan(xs)], 8) reg([sin(x), cos(x), exp(x)], 5) reg([ln(xs), pow(x, 2.7), pow(2.7, x)], 3) reg([asin(xs), acos(xs)], 1) reg([tan(xs)], 7) try: import scipy except ImportError: scipy = None if hasattr(math, 'erf') or scipy is not None: reg([erf(xs)]) else: print( "Warning: skipping test of erf, old python version and no scipy.") # if 0: # print("Warning: skipping tests of bessel functions, doesn't build on all platforms.") # elif scipy is None: # print("Warning: skipping tests of bessel functions, missing scipy.") # else: # for nu in (0, 1, 2): # # Many of these are possibly more accurately integrated, # # but 4 covers all and is sufficient for this test # reg([bessel_J(nu, xs), bessel_Y(nu, xs), bessel_I(nu, xs), bessel_K(nu, xs)], 4) # To handle tensor algebra, make an x dependent input tensor # xx and square all expressions def reg2(exprs, acc=10): for expr in exprs: F_list.append((inner(expr, expr), acc)) xx = as_matrix([[2 * x**2, 3 * x**3], [11 * x**5, 7 * x**4]]) x3v = as_vector([3 * x**2, 5 * x**3, 7 * x**4]) cc = as_matrix([[2, 3], [4, 5]]) reg2([xx]) reg2([x3v]) reg2([cross(3 * x3v, as_vector([-x3v[1], x3v[0], x3v[2]]))]) reg2([xx.T]) reg2([tr(xx)]) reg2([det(xx)]) reg2([dot(xx, 0.1 * xx)]) reg2([outer(xx, xx.T)]) reg2([dev(xx)]) reg2([sym(xx)]) reg2([skew(xx)]) reg2([elem_mult(7 * xx, cc)]) reg2([elem_div(7 * xx, xx + cc)]) reg2([elem_pow(1e-3 * xx, 1e-3 * cc)]) reg2([elem_pow(1e-3 * cc, 1e-3 * xx)]) reg2([elem_op(lambda z: sin(z) + 2, 0.03 * xx)], 2) # pretty inaccurate... # FIXME: Add tests for all UFL operators: # These cause discontinuities and may be harder to test in the # above fashion: # 'inv', 'cofac', # 'eq', 'ne', 'le', 'ge', 'lt', 'gt', 'And', 'Or', 'Not', # 'conditional', 'sign', # 'jump', 'avg', # 'LiftingFunction', 'LiftingOperator', # FIXME: Test other derivatives: (but algorithms for operator # derivatives are the same!): # 'variable', 'diff', # 'Dx', 'grad', 'div', 'curl', 'rot', 'Dn', 'exterior_derivative', # Run through all operators defined above and compare integrals debug = 0 for F, acc in F_list: # Apply UFL differentiation f = diff(F, SpatialCoordinate(mesh))[..., 0] if debug: print(F) print(x) print(f) # Apply integration with DOLFINx # (also passes through form compilation and jit) M = f * dx f_integral = assemble_scalar(M) # noqa f_integral = mesh.mpi_comm().allreduce(f_integral, op=MPI.SUM) # Compute integral of f manually from anti-derivative F # (passes through pybind11 interface and uses UFL evaluation) F_diff = F((x1, )) - F((x0, )) # Compare results. Using custom relative delta instead # of decimal digits here because some numbers are >> 1. delta = min(abs(f_integral), abs(F_diff)) * 10**-acc assert f_integral - F_diff <= delta