Exemple #1
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    def matrix_test(self, p=2):
        """
        node = np.array([
            (-1.0, -1.0),
            ( 0.0, -1.0),
            ( 1.0, -1.0),
            (-1.0, 0.0),
            ( 1.0, 0.0),
            (-1.0, 1.0),
            ( 0.0, 1.0),
            ( 1.0, 1.0)], dtype=np.float)
        cell = np.array([0, 1, 2, 4, 7, 6, 5, 3], dtype=np.int)
        cellLocation = np.array([0, 8], dtype=np.int)
        mesh = PolygonMesh(node, cell, cellLocation)
        """

        node = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)],
                        dtype=np.float)
        cell = np.array([0, 1, 2, 3], dtype=np.int)
        cellLocation = np.array([0, 4], dtype=np.int)
        mesh = PolygonMesh(node, cell, cellLocation)
        space = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
        print("G:", space.G)
        print("B:", space.B)
        print("R:", space.R)
        print("J:", space.J)
        print("Q:", space.Q)
        print("L:", space.L)
        print("D:", space.D)
Exemple #2
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    def stokes_equation_test(self, p=2, maxit=4):
        from scipy.sparse import bmat
        from fealpy.pde.Stokes_Model_2d import CosSinData
        from fealpy.mesh.simple_mesh_generator import triangle
        h = 0.4
        pde = CosSinData()
        error = np.zeros((maxit, ), dtype=np.float)
        for i in range(maxit):
            mesh = pde.init_mesh(n=i + 2, meshtype='poly')

            if 0:
                fig = plt.figure()
                axes = fig.gca()
                mesh.add_plot(axes)
                plt.show()

            uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
            pspace = ScaledMonomialSpace2d(mesh, p - 1)

            isBdDof = uspace.boundary_dof()

            udof = uspace.number_of_global_dofs()
            pdof = pspace.number_of_global_dofs()

            uh = uspace.function()
            ph = pspace.function()
            uspace.set_dirichlet_bc(uh, pde.dirichlet)

            A = uspace.matrix_A()
            P = uspace.matrix_P()
            F = uspace.source_vector(pde.source)

            AA = bmat([[A, P.T], [P, None]], format='csr')
            FF = np.block([F, np.zeros(pdof, dtype=uspace.ftype)])
            x = np.block([uh.T.flat, ph])
            isBdDof = np.block(
                [isBdDof, isBdDof,
                 np.zeros(pdof, dtype=np.bool)])

            gdof = 2 * udof + pdof
            FF -= AA @ x
            bdIdx = np.zeros(gdof, dtype=np.int)
            bdIdx[isBdDof] = 1
            Tbd = spdiags(bdIdx, 0, gdof, gdof)
            T = spdiags(1 - bdIdx, 0, gdof, gdof)
            AA = T @ AA @ T + Tbd
            FF[isBdDof] = x[isBdDof]
            x[:] = spsolve(AA, FF)
            uh[:, 0] = x[:udof]
            uh[:, 1] = x[udof:2 * udof]
            ph[:] = x[2 * udof:]

            up = uspace.project_to_smspace(uh)
            integralalg = uspace.integralalg
            error[i] = integralalg.L2_error(pde.velocity, up)
            h /= 2

        print(error)
        print(error[0:-1] / error[1:])
Exemple #3
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    def one_cell_test_0(self, p=2):
        from fealpy.pde.stokes_model_2d import StokesModelData_7
        pde = StokesModelData_7()
        node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)], dtype=np.float)
        cell = np.array([0, 1, 2, 3], dtype=np.int)
        cellLocation = np.array([0, 4], dtype=np.int)
        mesh = PolygonMesh(node, cell, cellLocation)

        uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
        pspace = ScaledMonomialSpace2d(mesh, p - 1)
        ldof = pspace.number_of_local_dofs()

        isBdDof = uspace.boundary_dof()

        udof = uspace.number_of_global_dofs()
        pdof = pspace.number_of_global_dofs()

        uh = uspace.function()
        ph = pspace.function()
        uspace.set_dirichlet_bc(uh, pde.dirichlet)

        A = uspace.matrix_A()
        P = uspace.matrix_P()
        C = uspace.CM[:, 0, :ldof].reshape(-1)
        F = uspace.source_vector(pde.source)

        AA = bmat([[A, P.T, None], [P, None, C[:, None]], [None, C, None]],
                  format='csr')
        FF = np.block([F, np.zeros(pdof + 1, dtype=uspace.ftype)])
        x = np.block([uh, ph, np.zeros((1, ), dtype=uspace.ftype)])
        isBdDof = np.r_['0', isBdDof, np.zeros(pdof + 1, dtype=np.bool)]
        gdof = udof + pdof + 1

        FF -= AA @ x
        bdIdx = np.zeros(gdof, dtype=np.int)
        bdIdx[isBdDof] = 1
        Tbd = spdiags(bdIdx, 0, gdof, gdof)
        T = spdiags(1 - bdIdx, 0, gdof, gdof)
        AA = T @ AA @ T + Tbd
        FF[isBdDof] = x[isBdDof]
        x[:] = spsolve(AA, FF)
        uh[:] = x[:udof]
        ph[:] = x[udof:-1]
        print('ph:', ph)

        print('uh:', uh)
        up = uspace.project_to_smspace(uh)
        print('up:', up)
        integralalg = uspace.integralalg
        error = integralalg.L2_error(pde.velocity, up)
        print(error)

        uv = uspace.project(pde.velocity)
        print('uproject:', uv)
        up = uspace.project_to_smspace(uv)
        print('up', up)

        error = integralalg.L2_error(pde.velocity, up)
        print(error)
Exemple #4
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 def matrix_A_test(self, p=2):
     node = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)],
                     dtype=np.float)
     cell = np.array([0, 1, 2, 3], dtype=np.int)
     cellLocation = np.array([0, 4], dtype=np.int)
     mesh = PolygonMesh(node, cell, cellLocation)
     space = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
     A = space.matrix_A()
     print(A)
Exemple #5
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 def index2_test(self, p=2):
     node = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)],
                     dtype=np.float)
     cell = np.array([0, 1, 2, 3], dtype=np.int)
     cellLocation = np.array([0, 4], dtype=np.int)
     mesh = PolygonMesh(node, cell, cellLocation)
     space = DivFreeNonConformingVirtualElementSpace2d(mesh, 3)
     idx = space.index2(p=p)
     print("p=", p, idx)
Exemple #6
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    def project_test(self, u, p=2, mtype=0, plot=True):
        from fealpy.mesh.simple_mesh_generator import triangle

        if mtype == 0:
            node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
                            dtype=np.float)
            cell = np.array([0, 1, 2, 3], dtype=np.int)
            cellLocation = np.array([0, 4], dtype=np.int)
            mesh = PolygonMesh(node, cell, cellLocation)
        elif mtype == 1:
            node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
                            dtype=np.float)
            cell = np.array([0, 1, 2, 3, 0, 2], dtype=np.int)
            cellLocation = np.array([0, 3, 6], dtype=np.int)
            mesh = PolygonMesh(node, cell, cellLocation)
        elif mtype == 2:
            h = 0.1
            mesh = triangle([-1, 1, -1, 1], h, meshtype='polygon')
        elif mtype == 3:
            node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
                            dtype=np.float)
            cell = np.array([[0, 1, 2, 3]], dtype=np.int)
            mesh = QuadrangleMesh(node, cell)
            mesh.uniform_refine()
            mesh = PolygonMesh.from_mesh(mesh)

        cell, cellLocation = mesh.entity('cell')
        edge = mesh.entity('edge')
        cell2edge = mesh.ds.cell_to_edge()
        uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
        up = uspace.project(u)
        print(up)
        up = uspace.project_to_smspace(up)
        print(up)

        integralalg = uspace.integralalg
        error = integralalg.L2_error(u, up)
        print(error)
        if plot:
            fig = plt.figure()
            axes = fig.gca()
            mesh.add_plot(axes)
            mesh.find_node(axes, showindex=True)
            mesh.find_edge(axes, showindex=True)
            mesh.find_cell(axes, showindex=True)
            plt.show()
Exemple #7
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 def matrix_G_test(self, p=2):
     node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)], dtype=np.float)
     cell = np.array([0, 1, 2, 3], dtype=np.int)
     cellLocation = np.array([0, 4], dtype=np.int)
     mesh = PolygonMesh(node, cell, cellLocation)
     space = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
Exemple #8
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errorMatrix = np.zeros((5, maxit), dtype=np.float)
dof = np.zeros(maxit, dtype=np.float)

for i in range(maxit):
    #mesh = pde.init_mesh(n=i+2, meshtype='poly') 
    mesh = pde.init_mesh(n=i+2, meshtype='quad') 
    mesh = PolygonMesh.from_mesh(mesh)

    NE = mesh.number_of_edges()
    NC = mesh.number_of_cells()
    idof = (p-2)*(p-1)//2

    dof[i] = NC

    # 完全非协调向量虚单元空间
    uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p, q=6)
    pspace = ScaledMonomialSpace2d(mesh, p-1)
    uh = uspace.function()
    ph = pspace.function()

    # 缩减非协调向量虚单元空间 
    tuspace = ReducedDivFreeNonConformingVirtualElementSpace2d(mesh, p, q=6)
    # 分片常数压力空间
    tpspace = ScaledMonomialSpace2d(mesh, 0)

    isBdDof = tuspace.boundary_dof()

    tudof = tuspace.number_of_global_dofs()
    tpdof = tpspace.number_of_global_dofs()

    tuh = tuspace.function()