def init_mesh(self, n=1, meshtype='tri'):
node = np.array([
(0, 0),
(1, 0),
(1, 1),
(0, 1)], dtype=np.float)
if meshtype == 'tri':
cell = np.array([
(1, 2, 0),
(3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
elif meshtype == 'quad':
nx = 4
ny = 4
mesh = StructureQuadMesh(self.box, nx, ny)
mesh.uniform_refine(n)
return mesh
elif meshtype == 'poly':
cell = np.array([
(1, 2, 0),
(3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
nmesh = TriangleMeshWithInfinityNode(mesh)
pnode, pcell, pcellLocation = nmesh.to_polygonmesh()
pmesh = PolygonMesh(pnode, pcell, pcellLocation)
return pmesh
def init_mesh(self, n=1, meshtype='tri'):
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float)
if meshtype == 'tri':
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
elif meshtype == 'quad':
nx = 2
ny = 2
mesh = StructureQuadMesh(self.box, nx, ny)
mesh.uniform_refine(n)
return mesh
q[i] = np.fft.ifftn(q1).real
q[i] *= E0
print(q)
test = FourierSpaceTest()
if True:
test.linear_equation_fft_solver_1d_test(10)
if True:
test.linear_equation_fft_solver_2d_test(6)
if True:
test.linear_equation_fft_solver_3d_test(6)
if True:
test.parabolic_equation_solver_test(4, 10)
if False:
qmesh = StructureQuadMesh(box, N, N)
mi = qmesh.multi_index()
fig = plt.figure()
axes = fig.gca()
qmesh.add_plot(axes)
qmesh.find_node(axes, showindex=True)
plt.show()
def __init__(self):
box = [0.0, 1.0, 0.0, 1.0]
nx = 8
ny = 8
self.mesh = StructureQuadMesh(box, nx, ny)
class StructureQuadMeshTest:
def __init__(self):
box = [0.0, 1.0, 0.0, 1.0]
nx = 8
ny = 8
self.mesh = StructureQuadMesh(box, nx, ny)
def test_cell_location(self):
start1 = time.time()
mesh = self.mesh
p = np.random.rand(10, 2)
cidx = mesh.cell_location(p)
end1 = time.time()
print('cell_location time', end1 - start1)
cell = mesh.entity('cell')
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_cell(axes, showindex=True)
mesh.find_node(axes, node=p, showindex=True)
plt.show()
def test_interpolation(self):
start2 = time.time()
pde = CosCosData()
F0 = self.mesh.interpolation(pde.solution, intertype='node')
print(F0.shape)
F1 = self.mesh.interpolation(pde.solution, intertype='edge')
print(F1.shape)
F2 = self.mesh.interpolation(pde.solution, intertype='edgex')
print(F2.shape)
F3 = self.mesh.interpolation(pde.solution, intertype='edgey')
print(F3.shape)
F4 = self.mesh.interpolation(pde.solution, intertype='cell')
print(F4.shape)
end2 = time.time()
print('time of interpolation', end2 - start2)
def test_polation_interoperator(self):
pde = CosCosData()
maxit = 4
errorType = ['$|u_I - u_h|_{max}$']
Maxerror = np.zeros((len(errorType), maxit), dtype=np.float)
NE = np.zeros(maxit, )
for i in range(maxit):
start3 = time.time()
mesh = self.mesh
isBDEdge = mesh.ds.boundary_edge_flag()
NE[i] = mesh.number_of_edges()
h = mesh.hx
bc = mesh.entity_barycenter('cell')
ec = mesh.entity_barycenter('edge')
uI = mesh.polation_interoperator(pde.solution(bc))
uh = pde.solution(ec)
Maxerror[0, i] = np.sqrt(np.sum(h**2 * (uh - uI)**2))
# Maxerror[0, i] = max(abs(uh - uI))
end3 = time.time()
print('time of %d iteration' % i, end3 - start3)
if i < maxit - 1:
mesh.uniform_refine()
showmultirate(plt, 0, NE, Maxerror, errorType)
print('Maxerror', Maxerror)
plt.show()
def test_cbar(self):
dt = 0
start4 = time.time()
mesh = self.mesh
pde = CosCosData()
bc = mesh.entity_barycenter('cell')
ch = pde.solution(bc)
NC = mesh.number_of_cells()
cellidx = np.arange(NC)
xbar = bc - dt
cbar = mesh.cbar_interpolation(ch, cellidx, xbar)
end4 = time.time()
print('test_cbar time', end4 - start4)
print('cbar', sum(cbar - ch))