def __init__(self, mesh, options=None):
if options == None:
options = scftmodel_options()
self.options = options
self.vemspace = ConformingVirtualElementSpace2d(mesh,
p=options['order'])
self.mesh = self.vemspace.mesh
self.totalArea = np.sum(self.vemspace.smspace.cellmeasure)
self.count = 0
fA = options['fA']
T0 = options['T0']
T1 = options['T1']
self.timeline0 = ChebyshevTimeLine(0, fA, T0)
self.timeline1 = ChebyshevTimeLine(fA, 1, T1)
N = T0 + T1 + 1
gdof = self.vemspace.number_of_global_dofs()
self.gof = gdof
self.q0 = np.zeros((gdof, N), dtype=self.mesh.ftype)
self.q1 = np.zeros((gdof, N), dtype=self.mesh.ftype)
self.rho = np.zeros((gdof, 2), dtype=self.mesh.ftype)
self.grad = np.zeros((gdof, 2), dtype=self.mesh.ftype)
self.w = np.zeros((gdof, 2), dtype=self.mesh.ftype)
self.sQ1 = np.zeros((N, 1), dtype=self.mesh.ftype)
self.sQ = 0.0
nupdate = options['nupdate']
self.A = self.vemspace.stiff_matrix()
self.M = self.vemspace.mass_matrix()
self.solver = PDESolver(self.A, self.M, nupdate)
self.eta_ref = 0
def reinit(self, mesh):
options = self.options
self.vemspace = ConformingVirtualElementSpace2d(mesh,
p=options['order'])
self.mesh = self.vemspace.mesh
self.totalArea = np.sum(self.vemspace.smspace.cellmeasure)
fA = options['fA']
T0 = options['T0']
T1 = options['T1']
self.timeline0 = ChebyshevTimeLine(0, fA, T0)
self.timeline1 = ChebyshevTimeLine(fA, 1, T1)
N = T0 + T1 + 1
gdof = self.vemspace.number_of_global_dofs()
self.gdof = gdof
self.q0 = np.ones((gdof, N), dtype=self.mesh.ftype)
self.q1 = np.ones((gdof, N), dtype=self.mesh.ftype)
self.rho = np.zeros((gdof, 2), dtype=self.mesh.ftype)
self.grad = np.zeros((gdof, 2), dtype=self.mesh.ftype)
self.w = np.zeros((gdof, 2), dtype=self.mesh.ftype)
self.sQ = np.zeros((N, 1), dtype=self.mesh.ftype)
self.nupdate = options['nupdate']
self.A = self.vemspace.stiff_matrix()
self.M = self.vemspace.mass_matrix()
self.F = np.zeros(self.A.shape, dtype=np.float)
self.smodel = ParabolicVEMSolver2d(self.A, self.M, self.F)
self.eta_ref = 0
def interpolation(self, n=2, plot=True):
from fealpy.pde.poisson_2d import CosCosData
from fealpy.functionspace import ConformingVirtualElementSpace2d
pde = CosCosData()
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float64)
cell = np.array([(0, 1, 2, 3)], dtype=np.int_)
mesh = QuadrangleMesh(node, cell)
#mesh = PolygonMesh.from_mesh(mesh)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.uniform_refine(n=n)
#mesh.print()
space = ConformingVirtualElementSpace2d(mesh, p=1)
uI = space.interpolation(pde.solution)
up = space.project_to_smspace(uI)
error = space.integralalg.L2_error(pde.solution, up)
print(error)
if plot:
fig = plt.figure()
axes = fig.gca()
#mesh.add_halfedge_plot(axes, showindex=True)
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
(1.0, 1.0), (1.0, 2.0), (2.0, 0.0), (2.0, 1.0),
(2.0, 2.0)],
dtype=np.float)
cell = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
if False:
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 = ConformingVirtualElementSpace2d(mesh, p=1)
A0, S0 = space.chen_stability_term()
A = space.stiff_matrix()
print("A:", A.toarray())
print("A0:", A0.toarray())
print("S0:", S0.toarray())
np.savetxt('A.txt', A.toarray(), fmt='%.2e')
np.savetxt('A0.txt', A0.toarray(), fmt='%.2e')
np.savetxt('S0.txt', S0.toarray(), fmt='%.2e')
if False:
h = 0.1
maxit = 1
pde = CosCosData()
import numpy as np import matplotlib.pyplot as plt from fealpy.pde.poisson_2d import CosCosData from fealpy.functionspace import ConformingVirtualElementSpace2d, ScaledMonomialSpace2d p = 1 pde = CosCosData() quadtree = pde.init_mesh(n=5, meshtype='quadtree') options = quadtree.adaptive_options(method='numrefine', maxsize=1, HB=True) pmesh = quadtree.to_pmesh() space0 = ConformingVirtualElementSpace2d(pmesh, p=p) uh0 = space0.interpolation(pde.solution) sh0 = space0.project_to_smspace(uh0) error = space0.integralalg.L2_error(pde.solution, sh0.value) print(error) axes0 = plt.subplot(1, 2, 1) pmesh.add_plot(axes0) pmesh.find_cell(axes0, showindex=True) NC = pmesh.number_of_cells() eta = -1 * np.ones(NC, dtype=np.int) quadtree.adaptive(eta, options) pmesh = quadtree.to_pmesh() space1 = ConformingVirtualElementSpace2d(pmesh, p=p) uI = space1.interpolation(sh0, options['HB'])
