def vem_solve(model, quadtree):
mesh = quadtree.to_polygonmesh()
V = VirtualElementSpace2d(mesh, 1)
uh = FiniteElementFunction(V)
vem = PoissonVEMModel(model, V)
BC = DirichletBC(V, model.dirichlet)
A, b = solve(vem, uh, dirichlet=BC, solver='direct')
uI = V.interpolation(model.solution)
eta = vem.recover_estimate(uh)
uIuh = np.sqrt((uh - uI) @ A @ (uh - uI))
return uh, V.number_of_global_dofs(), eta, uIuh
model = CosCosData()
mesh = rectangledomainmesh(box, nx=n, ny=n, meshtype='tri')
maxit = 4
Ndof = np.zeros(maxit, dtype=np.int)
error = np.zeros(maxit, dtype=np.float)
ratio = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
V = function_space(mesh, 'Lagrange', degree)
uh = FiniteElementFunction(V)
Ndof[i] = V.number_of_global_dofs()
a = LaplaceSymetricForm(V, qt)
L = SourceForm(V, model.source, qt)
bc = DirichletBC(V, model.dirichlet, model.is_boundary)
point = V.interpolation_points()
solve(a, L, uh, dirichlet=bc, solver='direct')
error[i] = L2_error(model.solution, uh, order=qt)
# error[i] = np.sqrt(np.sum((uh - model.solution(point))**2)/Ndof[i])
if i < maxit-1:
mesh.uniform_refine()
# 输出结果
ratio[1:] = error[0:-1]/error[1:]
print('Ndof:', Ndof)
print('error:', error)
print('ratio:', ratio)
#fig = plt.figure()
#axes = fig.gca()
#axes.axis('tight')
#axes.axis('off')
for i in range(maxit):
if meshtype == 1: #fishbone mesh
mesh = fishbone(box,n)
integrator = mesh.integrator(3)
mesh.add_plot(plt,cellcolor='w')
V = LagrangeFiniteElementSpace(mesh,p=1)
V2 = VectorLagrangeFiniteElementSpace(mesh,p=1)
uh = FiniteElementFunction(V)
rgh = FiniteElementFunction(V2)
rlh = FiniteElementFunction(V)
fem = BiharmonicRecoveryFEMModel(mesh, pde,integrator,rtype=rtype)
bc = DirichletBC(V, pde.dirichlet)
solve(fem, uh, dirichlet=bc, solver='direct')
fem.recover_grad() #TODO
fem.recover_laplace()
eta1 = fem.grad_recover_estimate()
eta2 = fem.laplace_recover_estimate()
Ndof[i] = V.number_of_global_dofs()
errorMatrix[0, i] = fem.error.L2_error(pde.solution, uh)
errorMatrix[1, i] = fem.error.L2_error(pde.gradient, uh)
errorMatrix[2, i] = np.sqrt(np.sum(eta1**2))
errorMatrix[3, i] = fem.error.L2_error(pde.gradient, rgh)
errorMatrix[4, i] = fem.error.L2_error(pde.laplace, rgh)
errorMatrix[5, i] = fem.error.L2_error(pde.laplace, rlh)
errorMatrix[6, i] = np.sqrt(np.sum(eta2**2))
error = np.zeros((maxit, ), dtype=np.float)
derror = np.zeros((maxit, ), dtype=np.float)
gerror = np.zeros((maxit, ), dtype=np.float)
Ndof = np.zeros((maxit, ), dtype=np.int)
for i in range(maxit):
V = function_space(mesh, 'Lagrange', degree)
Ndof[i] = V.number_of_global_dofs()
uh = FiniteElementFunction(V)
a = BihamonicRecoveryForm(V, sigma=2)
L = SourceForm(V, model.source, 4)
BC = DirichletBC(V, model.dirichlet, isBoundaryDof)
solve(a, L, uh, BC, 'direct')
error[i] = L2_error(model.solution, uh, order=4)
ruh = recover_grad(uh)
derror[i] = div_error(model.laplace, ruh, order=4)
gerror[i] = L2_error(model.gradient, ruh, order=4)
if i < maxit - 1:
mesh.uniform_refine()
print(Ndof)
print('L2 error:\n', error)
order = np.log(error[0:-1] / error[1:]) / np.log(2)
print('order:\n', order)
print('div error:\n', derror)
order = np.log(derror[0:-1] / derror[1:]) / np.log(2)
model = PolynomialData()
model = ExpData()
for i in range(maxit):
# Mesh
mesh0 = rectangledomainmesh(box, nx=n, ny=n, meshtype='tri')
mesh1 = TriangleMeshWithInfinityPoint(mesh0)
point, cell, cellLocation = mesh1.to_polygonmesh()
mesh = PolygonMesh(point, cell, cellLocation)
# VEM Space
V = VirtualElementSpace2d(mesh, p)
uh = FiniteElementFunction(V)
Ndof[i] = V.number_of_global_dofs()
vem = PoissonVEMModel(model, V)
BC = DirichletBC(V, model.dirichlet)
solve(vem, uh, dirichlet=BC, solver='direct')
# error
uI = V.interpolation(model.solution)
error[i] = np.sqrt(np.sum((uh - uI)**2)/Ndof[i])
n = 2*n
print(Ndof)
print(error)
print(error[:-1]/error[1:])
Ndof = np.zeros((maxit, ), dtype=np.int)
for i in range(0, maxit):
mesh = load_mat_mesh('../data/square' + str(i + 2) + '.mat')
V = function_space(mesh, 'Lagrange', degree)
Ndof[i] = V.number_of_global_dofs()
uh = FiniteElementFunction(V)
a = BihamonicRecoveryForm(V, sigma=sigma)
L = SourceForm(V, model.source, 4)
bc0 = DirichletBC(V, model.dirichlet, model.is_boundary_dof)
bc1 = BihamonicRecoveryBC1(V, model.neuman, sigma=sigma)
solve(a, L, uh, dirichlet=bc0, neuman=bc1, solver='direct')
error[i] = L2_error(model.solution, uh, order=4)
ruh = recover_grad(uh)
derror[i] = div_error(model.laplace, ruh, order=4)
gerror[i] = L2_error(model.gradient, ruh, order=5)
# if i < maxit-1:
# mesh.uniform_refine()
print(Ndof)
print('L2 error:\n', error)
order = np.log(error[0:-1] / error[1:]) / np.log(2)
print('order:\n', order)
print('div error:\n', derror)
order = np.log(derror[0:-1] / derror[1:]) / np.log(2)
