Python hermes2d.Mesh类代码示例

def test_example_03():
    from hermes2d.examples.c03 import set_bc

    set_verbose(False)

    P_INIT = 5                # Uniform polynomial degree of mesh elements.

    # Problem parameters.
    CONST_F = 2.0

    # Load the mesh file
    mesh = Mesh()
    mesh.load(get_example_mesh())

    # Sample "manual" mesh refinement
    mesh.refine_all_elements()

    # Create an H1 space with default shapeset
    space = H1Space(mesh, P_INIT)
    set_bc(space)

    # Initialize the weak formulation
    wf = WeakForm(1)
    set_forms(wf)

    # Initialize the linear system
    ls = LinSystem(wf)
    ls.set_spaces(space)

    # Assemble and solve the matrix problem.
    sln = Solution()
    ls.assemble()
    ls.solve_system(sln)

def test_example_04():
    from hermes2d.examples.c04 import set_bc

    set_verbose(False)

    # Below you can play with the parameters CONST_F, P_INIT, and UNIFORM_REF_LEVEL.
    INIT_REF_NUM = 2         # number of initial uniform mesh refinements
    P_INIT = 2               # initial polynomial degree in all elements

    # Load the mesh file
    mesh = Mesh()
    mesh.load(get_example_mesh())

    # Perform initial mesh refinements
    for i in range(INIT_REF_NUM):
        mesh.refine_all_elements()

    # Create an H1 space with default shapeset
    space = H1Space(mesh, P_INIT)
    set_bc(space)

    # Initialize the weak formulation
    wf = WeakForm()
    set_forms(wf)

    # Initialize the linear system
    ls = LinSystem(wf)
    ls.set_spaces(space)

    # Assemble and solve the matrix problem
    sln = Solution()
    ls.assemble()
    ls.solve_system(sln)

def test_example_08():
    from hermes2d.examples.c08 import set_bc, set_forms

    set_verbose(False)

    # The following parameter can be changed:
    P_INIT = 4

    # Load the mesh file
    mesh = Mesh()
    mesh.load(get_sample_mesh())

    # Perform uniform mesh refinement
    mesh.refine_all_elements()

    # Create the x- and y- displacement space using the default H1 shapeset
    xdisp = H1Space(mesh, P_INIT)
    ydisp = H1Space(mesh, P_INIT)
    set_bc(xdisp, ydisp)

    # Initialize the weak formulation
    wf = WeakForm(2)
    set_forms(wf)

    # Initialize the linear system.
    ls = LinSystem(wf)
    ls.set_spaces(xdisp, ydisp)

    # Assemble and solve the matrix problem
    xsln = Solution()
    ysln = Solution()
    ls.assemble()
    ls.solve_system(xsln, ysln, lib="scipy")

def test_plot_mesh3e():
    mesh = Mesh()
    mesh.load(domain_mesh)
    mesh.refine_all_elements()
    mesh.refine_all_elements()

    plot_mesh_mpl(mesh.nodes_dict, mesh.elements)

def test_example_07():
    from hermes2d.examples.c07 import set_bc, set_forms

    set_verbose(False)

    # The following parameters can be changed:
    P_INIT = 2             # Initial polynomial degree of all mesh elements.
    INIT_REF_NUM = 4       # Number of initial uniform refinements

    # Load the mesh
    mesh = Mesh()
    mesh.load(get_07_mesh())

    # Perform initial mesh refinements.
    for i in range(INIT_REF_NUM):
        mesh.refine_all_elements()

    # Create an H1 space with default shapeset
    space = H1Space(mesh, P_INIT)
    set_bc(space)

    # Initialize the weak formulation
    wf = WeakForm()
    set_forms(wf)

    # Initialize the linear system.
    ls = LinSystem(wf)
    ls.set_spaces(space)

    # Assemble and solve the matrix problem
    sln = Solution()
    ls.assemble()
    ls.solve_system(sln)

def test_ScalarView_mpl_unknown():
    mesh = Mesh()
    mesh.load(domain_mesh)
    mesh.refine_element(0)
    shapeset = H1Shapeset()
    pss = PrecalcShapeset(shapeset)

    # create an H1 space
    space = H1Space(mesh, shapeset)
    space.set_uniform_order(5)
    space.assign_dofs()

    # initialize the discrete problem
    wf = WeakForm(1)
    set_forms(wf)

    solver = DummySolver()
    sys = LinSystem(wf, solver)
    sys.set_spaces(space)
    sys.set_pss(pss)

    # assemble the stiffness matrix and solve the system
    sys.assemble()
    A = sys.get_matrix()
    b = sys.get_rhs()
    from scipy.sparse.linalg import cg

    x, res = cg(A, b)
    sln = Solution()
    sln.set_fe_solution(space, pss, x)

    view = ScalarView("Solution")

    def export_mesh(self, lib="hermes2d"):
        """
        Exports the mesh in various FE solver formats.

        lib == "hermes2d" ... returns the hermes2d Mesh

        Currently only hermes2d is implemented.

        Example:

        >>> m = Mesh([[0.0,1.0],[1.0,1.0],[1.0,0.0],[0.0,0.0],],[[1,0,2],[2,0,3],],[[3,2,1],[2,1,2],[1,0,3],[0,3,4],],[])
        >>> h = m.export_mesh()
        >>> h
        <hermes2d._hermes2d.Mesh object at 0x7f07284721c8>

        """
        if lib == "hermes2d":
            from hermes2d import Mesh
            m = Mesh()
            nodes = self._nodes
            elements = [list(e)+[0] for e in self._elements]
            boundaries = self._boundaries
            curves = self._curves
            m.create(nodes, elements, boundaries, curves)
            return m
        else:
            raise NotImplementedError("unknown library")

def test_example_05():
    from hermes2d.examples.c05 import set_bc
    from hermes2d.examples.c05 import set_forms as set_forms_surf

    set_verbose(False)

    P_INIT = 4                           # initial polynomial degree in all elements
    CORNER_REF_LEVEL = 12                # number of mesh refinements towards the re-entrant corner

    # Load the mesh file
    mesh = Mesh()
    mesh.load(get_example_mesh())

    # Perform initial mesh refinements.
    mesh.refine_towards_vertex(3, CORNER_REF_LEVEL)

    # Create an H1 space with default shapeset
    space = H1Space(mesh, P_INIT)
    set_bc(space)

    # Initialize the weak formulation
    wf = WeakForm()
    set_forms(wf)

    # Initialize the linear system.
    ls = LinSystem(wf)
    ls.set_spaces(space)

    # Assemble and solve the matrix problem
    sln = Solution()
    ls.assemble()
    ls.solve_system(sln)

def test_matrix():
    set_verbose(False)

    mesh = Mesh()
    mesh.load(domain_mesh)
    mesh.refine_element(0)
    shapeset = H1Shapeset()
    pss = PrecalcShapeset(shapeset)

    # create an H1 space
    space = H1Space(mesh, shapeset)
    space.set_uniform_order(5)
    space.assign_dofs()

    # initialize the discrete problem
    wf = WeakForm(1)
    set_forms(wf)

    solver = DummySolver()
    sys = LinSystem(wf, solver)
    sys.set_spaces(space)
    sys.set_pss(pss)

    # assemble the stiffness matrix and solve the system
    sln = Solution()
    sys.assemble()
    A = sys.get_matrix()

def test_plot_mesh3c():
    mesh = Mesh()
    mesh.load(domain_mesh)
    mesh.refine_all_elements()
    mesh.refine_all_elements()

    plot_mesh_mpl_simple(mesh.nodes_dict, mesh.elements, plot_nodes=False)

def test_example_03():
    set_verbose(False)

    mesh = Mesh()
    mesh.load(domain_mesh)
    mesh.refine_element(0)
    shapeset = H1Shapeset()
    pss = PrecalcShapeset(shapeset)

    # create an H1 space
    space = H1Space(mesh, shapeset)
    space.set_uniform_order(5)
    from hermes2d.examples.c03 import set_bc

    set_bc(space)
    space.assign_dofs()

    # initialize the discrete problem
    wf = WeakForm(1)
    set_forms(wf)

    solver = DummySolver()
    sys = LinSystem(wf, solver)
    sys.set_spaces(space)
    sys.set_pss(pss)

    # assemble the stiffness matrix and solve the system
    sln = Solution()
    sys.assemble()
    sys.solve_system(sln)
    assert abs(sln.l2_norm() - 0.25493) < 1e-4
    assert abs(sln.h1_norm() - 0.89534) < 1e-4

def test_plot_mesh3d():
    mesh = Mesh()
    mesh.load(domain_mesh)
    mesh.refine_all_elements()
    mesh.refine_all_elements()

    view = MeshView("Solution")
    view.show(mesh, lib="mpl", method="orders", show=False)

def test_plot_mesh1b():
    mesh = Mesh()
    mesh.load(domain_mesh)

    view = MeshView("Solution")
    view.show(mesh, lib="mpl", method="orders", show=False)
    plot_mesh_mpl(mesh.nodes, mesh.elements)
    plot_mesh_mpl(mesh.nodes_dict, mesh.elements)

def test_plot_mesh1a():
    mesh = Mesh()
    mesh.load(domain_mesh)

    view = MeshView("Solution")
    view.show(mesh, lib="mpl", method="simple", show=False)
    plot_mesh_mpl_simple(mesh.nodes, mesh.elements)
    plot_mesh_mpl_simple(mesh.nodes_dict, mesh.elements)
    plot_mesh_mpl_simple(mesh.nodes, mesh.elements, plot_nodes=False)
    plot_mesh_mpl_simple(mesh.nodes_dict, mesh.elements, plot_nodes=False)

def test_plot_mesh2():
    mesh = Mesh()
    mesh.load(domain_mesh)
    mesh.refine_element(0)

    view = MeshView("Solution")
    view.show(mesh, lib="mpl", method="simple", show=False)
    plot_mesh_mpl(mesh.nodes_dict, mesh.elements)
    plot_mesh_mpl(mesh.nodes_dict, mesh.elements, plot_nodes=False)
    view.show(mesh, lib="mpl", method="orders", show=False)
    plot_mesh_mpl(mesh.nodes_dict, mesh.elements)