Python hermes2d.LinSystem類代碼示例

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 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_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_example_08():
    from hermes2d.examples.c08 import set_bc, set_forms

    set_verbose(False)

    mesh = Mesh()
    mesh.load(cylinder_mesh)
    #mesh.refine_element(0)
    #mesh.refine_all_elements()
    mesh.refine_towards_boundary(5, 3)
    shapeset = H1Shapeset()
    pss = PrecalcShapeset(shapeset)

    # create an H1 space
    xvel = H1Space(mesh, shapeset)
    yvel = H1Space(mesh, shapeset)
    press = H1Space(mesh, shapeset)
    xvel.set_uniform_order(2)
    yvel.set_uniform_order(2)
    press.set_uniform_order(1)

    set_bc(xvel, yvel, press)

    ndofs = 0
    ndofs += xvel.assign_dofs(ndofs)
    ndofs += yvel.assign_dofs(ndofs)
    ndofs += press.assign_dofs(ndofs)

    xprev = Solution()
    yprev = Solution()

    xprev.set_zero(mesh)
    yprev.set_zero(mesh)

    # initialize the discrete problem
    wf = WeakForm(3)
    set_forms(wf, xprev, yprev)

    solver = DummySolver()
    sys = LinSystem(wf, solver)
    sys.set_spaces(xvel, yvel, press)
    sys.set_pss(pss)
    #dp.set_external_fns(xprev, yprev)

    # visualize the solution

    EPS_LOW = 0.0014

    for i in range(3):
        psln = Solution()
        sys.assemble()
        sys.solve_system(xprev, yprev, psln)

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_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_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_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_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_example_02():
    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)

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

    set_verbose(False)

    mesh = Mesh()
    mesh.load(sample_mesh)
    #mesh.refine_element(0)
    #mesh.refine_all_elements()
    #mesh.refine_towards_boundary(5, 3)
    shapeset = H1Shapeset()
    pss = PrecalcShapeset(shapeset)

    # create an H1 space
    xdisp = H1Space(mesh, shapeset)
    ydisp = H1Space(mesh, shapeset)
    xdisp.set_uniform_order(8)
    ydisp.set_uniform_order(8)

    set_bc(xdisp, ydisp)

    ndofs = xdisp.assign_dofs(0)
    ndofs += ydisp.assign_dofs(ndofs)

    # initialize the discrete problem
    wf = WeakForm(2)
    set_forms(wf)

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

    xsln = Solution()
    ysln = Solution()
    old_flag = set_warn_integration(False)
    sys.assemble()
    set_warn_integration(old_flag)
    sys.solve_system(xsln, ysln)

    E = float(200e9)
    nu = 0.3
    stress = VonMisesFilter(xsln, ysln, E / (2*(1 + nu)),
            (E * nu) / ((1 + nu) * (1 - 2*nu)))

def test_example_09():
    from hermes2d.examples.c09 import set_bc, temp_ext, set_forms

    # The following parameters can be changed:
    INIT_REF_NUM = 4      # number of initial uniform mesh refinements
    INIT_REF_NUM_BDY = 1  # number of initial uniform mesh refinements towards the boundary
    P_INIT = 4            # polynomial degree of all mesh elements
    TAU = 300.0           # time step in seconds

    # Problem constants
    T_INIT = 10           # temperature of the ground (also initial temperature)
    FINAL_TIME = 86400    # length of time interval (24 hours) in seconds

    # Global variable
    TIME = 0;

    # Boundary markers.
    bdy_ground = 1
    bdy_air = 2

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

    # Perform initial mesh refinements
    for i in range(INIT_REF_NUM):
        mesh.refine_all_elements()
    mesh.refine_towards_boundary(bdy_air, INIT_REF_NUM_BDY)

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

    # Set initial condition
    tsln = Solution()
    tsln.set_const(mesh, T_INIT)

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

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

    # Time stepping
    nsteps = int(FINAL_TIME/TAU + 0.5)
    rhsonly = False;

    # Assemble and solve
    ls.assemble()
    rhsonly = True
    ls.solve_system(tsln, lib="scipy")

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

    set_verbose(False)

    mesh = Mesh()
    mesh.load(domain_mesh)
    # mesh.refine_element(0)
    # mesh.refine_all_elements()
    mesh.refine_towards_boundary(5, 3)
    shapeset = H1Shapeset()
    pss = PrecalcShapeset(shapeset)

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

    set_bc(space)

    space.assign_dofs()

    xprev = Solution()
    yprev = Solution()

    # initialize the discrete problem
    wf = WeakForm()
    set_forms(wf, -4)

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

    # assemble the stiffness matrix and solve the system
    sys.assemble()
    sln = Solution()
    sys.solve_system(sln)
    assert abs(sln.l2_norm() - 1.22729) < 1e-4
    assert abs(sln.h1_norm() - 2.90006) < 1e-4

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)

    mesh = Mesh()
    mesh.load(domain_mesh)
    mesh.refine_towards_vertex(3, 12)
    shapeset = H1Shapeset()
    pss = PrecalcShapeset(shapeset)

    # create an H1 space
    space = H1Space(mesh, shapeset)
    space.set_uniform_order(4)

    set_bc(space)

    space.assign_dofs()

    xprev = Solution()
    yprev = Solution()

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

    sln = Solution()
    solver = DummySolver()
    sys = LinSystem(wf, solver)
    sys.set_spaces(space)
    sys.set_pss(pss)
    sys.assemble()
    sys.solve_system(sln)
    assert abs(sln.l2_norm() - 0.535833) < 1e-4
    assert abs(sln.h1_norm() - 1.332908) < 1e-4

def poisson_solver(mesh_tuple):
    """
    Poisson solver.

    mesh_tuple ... a tuple of (nodes, elements, boundary, nurbs)
    """
    set_verbose(False)
    mesh = Mesh()
    mesh.create(*mesh_tuple)
    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)
    return sln