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)))
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 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
def runTest(self): m = MeshHex() # check that these assemble to the same matrix ec = ElementHex1() * ElementHex1() * ElementHex1() ev = ElementVectorH1(ElementHex1()) basisc = Basis(m, ec) basisv = Basis(m, ev) @BilinearForm def bilinf_ev(u, v, w): from skfem.helpers import dot return dot(u, v) @BilinearForm def bilinf_ec(ux, uy, uz, vx, vy, vz, w): return ux * vx + uy * vy + uz * vz Kv = asm(bilinf_ev, basisv) Kc = asm(bilinf_ec, basisc) self.assertAlmostEqual(np.sum(np.sum((Kv - Kc).todense())), 0.)
def createBasis(self): m = MeshHex().refined(3) self.fbasis = FacetBasis(m, ElementHex1()) self.boundary_area = 6.000
class NormalVectorTestQuad(NormalVectorTestTri): case = (MeshQuad(), ElementQuad1()) class NormalVectorTestQuadP(NormalVectorTestTri): case = (MeshQuad(), ElementQuadP(3)) test_integrate_volume = False class NormalVectorTestHex(NormalVectorTestTri): case = (MeshHex(), ElementHex1()) intorder = 3 class NormalVectorTestHexS2(NormalVectorTestTri): case = (MeshHex(), ElementHexS2()) intorder = 3 test_integrate_volume = False class NormalVectorTestHex2(NormalVectorTestTri): case = (MeshHex(), ElementHex2()) intorder = 3 test_integrate_volume = False
ElementQuad2(), ), ( MeshTri().refined(2), MeshTri1DG, ElementTriP2(), ), ( MeshLine().refined(5), MeshLine1DG, ElementLineP1(), ), ( MeshHex().refined(3), MeshHex1DG, ElementHex1(), ), ( MeshLine().refined(), MeshLine1DG, ElementLinePp(5), ), ]) def test_periodic_loading(m, mdgtype, e): def _sort(ix): # sort index arrays so that ix[0] matches return ix[np.argsort(np.sum(m.p, axis=0)[ix])] mp = mdgtype.periodic(m, _sort(m.nodes_satisfying(lambda x: x[0] == 0)), _sort(m.nodes_satisfying(lambda x: x[0] == 1))) basis = Basis(mp, e)
def create_basis(self, m): e = ElementHex1() return Basis(m, e)
def mapping(self): return MappingIsoparametric(self, ElementHex1(), ElementQuad1())
basis = CellBasis(m, e) @pytest.mark.parametrize( "mtype,e,nrefs,npoints", [ (MeshTri, ElementTriP1(), 0, 10), (MeshTri, ElementTriP2(), 1, 10), (MeshTri, ElementTriP1(), 5, 10), (MeshTri, ElementTriP1(), 1, 3e5), (MeshTet, ElementTetP2(), 1, 10), (MeshTet, ElementTetP1(), 4, 10), (MeshTet, ElementTetP1(), 1, 3e4), (MeshQuad, ElementQuad1(), 1, 10), (MeshQuad, ElementQuad1(), 1, 3e5), (MeshHex, ElementHex1(), 1, 1e5), (MeshWedge1, ElementWedge1(), 0, 10), ] ) def test_interpolator_probes(mtype, e, nrefs, npoints): m = mtype() if nrefs > 0: m = m.refined(nrefs) np.random.seed(0) X = np.random.rand(m.p.shape[0], int(npoints)) basis = CellBasis(m, e) y = projection(lambda x: x[0] + x[1], basis)
class NormalVectorTestQuad(NormalVectorTestTri): case = (MeshQuad(), ElementQuad1()) class NormalVectorTestQuadP(NormalVectorTestTri): case = (MeshQuad(), ElementQuadP(3)) test_integrate_volume = False class NormalVectorTestHex(NormalVectorTestTri): case = (MeshHex(), ElementHex1()) intorder = 3 class NormalVectorTestHexS2(NormalVectorTestTri): case = (MeshHex(), ElementHexS2()) intorder = 3 test_integrate_volume = False class NormalVectorTestHex2(NormalVectorTestTri): case = (MeshHex(), ElementHex2()) intorder = 3 test_integrate_volume = False
element = ElementQuadBFS() with self.assertRaises(ValueError): element.gdof(0, 0, -1) with self.assertRaises(ValueError): element.gdof(0, 0, 16) @pytest.mark.parametrize("m,e,edg", [ (MeshTri().refined(), ElementTriP1(), ElementTriDG), (MeshTri().refined(), ElementTriP2(), ElementTriDG), (MeshTet().refined(), ElementTetP1(), ElementTetDG), (MeshTet().refined(), ElementTetP2(), ElementTetDG), (MeshTri().refined(), ElementTriArgyris(), ElementTriDG), (MeshTri().refined(), ElementTriMorley(), ElementTriDG), (MeshTri().refined(), ElementTriHermite(), ElementTriDG), (MeshHex().refined(), ElementHex1(), ElementHexDG), (MeshQuad().refined(), ElementQuad1(), ElementQuadDG), ]) def test_dg_element(m, e, edg): edg = edg(e) @Functional def square(w): return w['random']**2 basis = InteriorBasis(m, e) basisdg = InteriorBasis(m, edg) assert_allclose( square.assemble(basis, random=basis.interpolate(basis.zeros() + 1)),
def mapping(self): from skfem.mapping import MappingIsoparametric from skfem.element import ElementHex1, ElementQuad1 return MappingIsoparametric(self, ElementHex1(), ElementQuad1())
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, lambda p: p[0:(p.shape[0] - 1)], target_elem=e2)
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, lambda p: p[0:(p.shape[0] - 1)], target_elem=e2)