class TestPartitionofUnity(TestCase): """Test that elements form a partition of unity.""" elems = [ ElementLineP1(), ElementLineP2(), ElementTriP1(), ElementTriP2(), ElementQuad1(), ElementQuad2(), ElementQuadS2(), ElementTetP1(), ElementTetP2(), ElementHex1(), ElementHexS2(), ElementHex2(), ] def runTest(self): for elem in self.elems: if elem.dim == 1: y = np.array([[.15]]) elif elem.dim == 2: y = np.array([[.15], [.15]]) elif elem.dim == 3: y = np.array([[.15], [.15], [.15]]) out = 0. for i in range(elem.doflocs.shape[0]): out += elem.lbasis(y, i)[0][0] self.assertAlmostEqual(out, 1, msg='failed for {}'.format(elem))
class TestNodality(TestCase): """Test for Element.doflocs.""" elems = [ ElementLineP0(), ElementLineP1(), ElementLineP2(), ElementLinePp(1), ElementLinePp(3), ElementLineMini(), ElementTriP0(), ElementTriP1(), ElementTriP2(), ElementTriP3(), ElementTriP4(), ElementTriMini(), ElementQuad0(), ElementQuad1(), ElementQuad2(), ElementQuadS2(), ElementQuadP(1), ElementQuadP(3), ElementTetP0(), ElementTetP1(), ElementTetP2(), ElementTetMini(), ElementHex1(), ElementHexS2(), ElementHex2(), ElementTetCR(), ElementTetCCR(), ElementTriCR(), ElementTriCCR(), ElementWedge1(), ] def runTest(self): for e in self.elems: N = e.doflocs.shape[0] Ih = np.zeros((N, N)) for itr in range(N): Ih[itr] = e.lbasis(e.doflocs.T, itr)[0] # Remove nan-rows: test nodality only on non-nan doflocs. # # Some elements, such as ElementTriMini might have a combination # of nodal dofs and non-nodal dofs. # # Nodal dof is defined so that there exists a point where the # corresponding basis function is one, and other basis functions # are zero. Non-nodal dof does not satisfy this property. ix = np.isnan(np.sum(Ih, axis=1)) Nnan = np.sum(ix) ixs = np.nonzero(~ix)[0] Ih = Ih[ixs].T[ixs].T assert_allclose(Ih, np.eye(N - Nnan), atol=1e-13, err_msg="{}".format(type(e)))
def __init__(self, doflocs, t, **kwargs): warnings.warn("MeshQuad2 is an experimental feature and " "not governed by the semantic versioning. " "Several features of MeshQuad are still " "missing.") if t.shape[0] == 9: dofs, ix = np.unique(t[:4], return_inverse=True) super(MeshQuad2, self).__init__( doflocs[:, dofs], np.arange(len(dofs), dtype=np.int)[ix].reshape(t[:4].shape), **kwargs) else: # fallback for refinterp super(MeshQuad2, self).__init__(doflocs, t, **kwargs) from skfem.element import ElementQuad1, ElementQuad2 from skfem.assembly import InteriorBasis from skfem.mapping import MappingIsoparametric self._elem = ElementQuad2() self._basis = InteriorBasis(self, self._elem, MappingIsoparametric(self, ElementQuad1())) self._mesh = MeshQuad.from_basis(self._basis) if t.shape[0] == 9: self._mesh.p = doflocs self._mesh.t = t
class TestDerivatives(TestCase): """Test values of derivatives.""" elems = [ ElementLineP1(), ElementLineP2(), ElementTriP1(), ElementTriP2(), ElementTriMini(), ElementQuad1(), ElementQuad2(), ElementQuadS2(), ElementTetP1(), ElementTetP2(), ElementTetMini(), ElementHex1(), ElementHexS2(), ] def runTest(self): for elem in self.elems: eps = 1e-6 for base in [0., .3, .6, .9]: if elem.dim == 1: y = np.array([[base, base + eps]]) elif elem.dim == 2: y = np.array([[base, base + eps, base, base], [base, base, base, base + eps]]) elif elem.dim == 3: y = np.array([[base, base + eps, base, base, base, base], [base, base, base, base + eps, base, base], [base, base, base, base, base, base + eps]]) i = 0 while True: try: out = elem.lbasis(y, i) except ValueError: break diff = (out[0][1] - out[0][0]) / eps errmsg = 'x-derivative for {}th bfun failed for {}' self.assertAlmostEqual(diff, out[1][0][0], delta=1e-3, msg=errmsg.format(i, elem)) if elem.dim > 1: diff = (out[0][3] - out[0][2]) / eps errmsg = 'y-derivative for {}th bfun failed for {}' self.assertAlmostEqual(diff, out[1][1][3], delta=1e-3, msg=errmsg.format(i, elem)) if elem.dim == 3: diff = (out[0][5] - out[0][4]) / eps errmsg = 'z-derivative for {}th bfun failed for {}' self.assertAlmostEqual(diff, out[1][2][4], delta=1e-3, msg=errmsg.format(i, elem)) i += 1
class SolveInhomogeneousLaplaceQuad(SolveInhomogeneousLaplace): mesh = MeshQuad elem = ElementQuad2()
test_integrate_volume = False class NormalVectorTestHex2(NormalVectorTestTri): case = (MeshHex(), ElementHex2()) intorder = 3 test_integrate_volume = False @pytest.mark.parametrize("mtype,e,mtype2", [ (MeshTri, ElementTriP1(), None), (MeshTri, ElementTriArgyris(), None), (MeshHex, ElementHex1(), None), (MeshQuad, ElementQuad1(), None), (MeshQuad, ElementQuad2(), None), (MeshQuad, ElementQuad2(), MeshQuad2), (MeshTri, ElementTriP1(), MeshTri2), (MeshTet, ElementTetP1(), MeshTet2), (MeshHex, ElementHex1(), MeshHex2), ]) def test_evaluate_functional(mtype, e, mtype2): m = mtype().refined(3) if mtype2 is not None: m = mtype2.from_mesh(m) basis = Basis(m, e) @Functional def x_squared(w): return w.x[0]**2
maxval = 0.0405901240018571 def init_mesh(self): return self.mesh_type.init_ball().scaled(0.5) class SolveCirclePoissonTet2(SolveCirclePoisson): mesh_type = MeshTet2 element_type = ElementTetP2 filename = "quadratic_sphere_tet.msh" maxval = 0.0405901240018571 @pytest.mark.parametrize("mesh_elem", [(MeshTri, ElementTriP2()), (MeshQuad, ElementQuad2())]) @pytest.mark.parametrize("impose", [enforce, penalize]) def test_solving_inhomogeneous_laplace(mesh_elem, impose): """Adapted from example 14.""" mesh, elem = mesh_elem m = mesh().refined(4) basis = Basis(m, elem) boundary_basis = FacetBasis(m, elem) boundary_dofs = boundary_basis.get_dofs().flatten() def dirichlet(x): """return a harmonic function""" return ((x[0] + 1.j * x[1])**2).real
def create_basis(self, m): e = ElementQuad2() return Basis(m, e)
@pytest.mark.parametrize( "mtype,e1,e2,flat", [ (MeshTri, ElementTriP1(), ElementTriP0(), False), (MeshTri, ElementTriP1(), ElementTriP1(), False), (MeshTri, ElementTriP2(), ElementTriP1(), False), (MeshTri, ElementTriP2(), ElementTriP2(), False), (MeshTri, ElementTriP1(), ElementTriP0(), True), (MeshTri, ElementTriP1(), ElementTriP1(), True), (MeshTri, ElementTriP2(), ElementTriP1(), True), (MeshTri, ElementTriP2(), ElementTriP2(), True), (MeshTri, ElementTriP2(), None, False), (MeshTri, ElementTriP2(), None, True), (MeshQuad, ElementQuad1(), ElementQuad0(), False), (MeshQuad, ElementQuad1(), ElementQuad1(), False), (MeshQuad, ElementQuad2(), ElementQuad2(), False), (MeshQuad, ElementQuad1(), ElementQuad0(), True), (MeshQuad, ElementQuad1(), ElementQuad1(), True), (MeshQuad, ElementQuad2(), ElementQuad2(), True), (MeshTet, ElementTetP1(), ElementTetP0(), False), (MeshTet, ElementTetP2(), ElementTetP2(), False), (MeshHex, ElementHex1(), ElementHex0(), False), (MeshHex, ElementHex1(), ElementHex1(), False), (MeshHex, ElementHex2(), ElementHex2(), False), ], ) def test_trace(mtype, e1, e2, flat): m = mtype().refined(3) # use the boundary where last coordinate is zero
with self.assertRaises(ValueError): m = MeshTri() e = ElementTetP2() basis = InteriorBasis(m, e) @pytest.mark.parametrize("mtype,e1,e2", [ (MeshTri, ElementTriP1(), ElementTriP0()), (MeshTri, ElementTriP1(), ElementTriP1()), (MeshTri, ElementTriP2(), ElementTriP1()), (MeshTri, ElementTriP2(), ElementTriP2()), (MeshTri, ElementTriP2(), None), (MeshQuad, ElementQuad1(), ElementQuad0()), (MeshQuad, ElementQuad1(), ElementQuad1()), (MeshQuad, ElementQuad2(), ElementQuad2()), (MeshTet, ElementTetP1(), ElementTetP0()), (MeshTet, ElementTetP2(), ElementTetP2()), (MeshHex, ElementHex1(), ElementHex0()), (MeshHex, ElementHex1(), ElementHex1()), (MeshHex, ElementHex2(), ElementHex2()), ]) def test_trace(mtype, e1, e2): m = mtype().refined(3) # use the boundary where last coordinate is zero basis = FacetBasis( m, e1, facets=m.facets_satisfying(lambda x: x[x.shape[0] - 1] == 0.0)) xfun = projection(lambda x: x[0], InteriorBasis(m, e1)) nbasis, y = basis.trace(xfun,
with self.assertRaises(ValueError): m = MeshTri() e = ElementTetP2() basis = InteriorBasis(m, e) @pytest.mark.parametrize("mtype,e1,e2", [ (MeshTri, ElementTriP1(), ElementLineP0()), (MeshTri, ElementTriP1(), ElementLineP1()), (MeshTri, ElementTriP2(), ElementLineP1()), (MeshTri, ElementTriP2(), ElementLineP2()), (MeshTri, ElementTriP2(), None), (MeshQuad, ElementQuad1(), ElementLineP0()), (MeshQuad, ElementQuad1(), ElementLineP1()), (MeshQuad, ElementQuad2(), ElementLineP2()), (MeshTet, ElementTetP1(), ElementTriP0()), (MeshTet, ElementTetP2(), ElementTriP2()), (MeshHex, ElementHex1(), ElementQuad0()), (MeshHex, ElementHex1(), ElementQuad1()), (MeshHex, ElementHex2(), ElementQuad2()), ]) def test_trace(mtype, e1, e2): m = mtype().refined(3) # use the boundary where last coordinate is zero basis = FacetBasis( m, e1, facets=m.facets_satisfying(lambda x: x[x.shape[0] - 1] == 0.0)) xfun = project(lambda x: x[0], basis_to=InteriorBasis(m, e1)) nbasis, y = basis.trace(xfun,
class NormalVectorTestHex2(NormalVectorTestTri): case = (MeshHex(), ElementHex2()) intorder = 3 test_integrate_volume = False @pytest.mark.parametrize( "mtype,e,mtype2", [ (MeshTri, ElementTriP1(), None), (MeshTri, ElementTriArgyris(), None), (MeshHex, ElementHex1(), None), (MeshQuad, ElementQuad1(), None), (MeshQuad, ElementQuad2(), None), (MeshQuad, ElementQuad2(), MeshQuad2), (MeshTri, ElementTriP1(), MeshTri2), (MeshTet, ElementTetP1(), MeshTet2), (MeshHex, ElementHex1(), MeshHex2), ] ) def test_evaluate_functional(mtype, e, mtype2): m = mtype().refined(3) if mtype2 is not None: m = mtype2.from_mesh(m) basis = InteriorBasis(m, e) @Functional def x_squared(w): return w.x[0] ** 2