def plot_basis(self, p=2, q=20, plot=True):
node = np.array([
(0.0, 0.0), (1.0, 0.0), (0.5, np.sqrt(3)/2)], dtype=np.float)
cell = np.array([(0, 1, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
space = LagrangeFiniteElementSpace(mesh, p=p)
bc = space.multi_index_matrix[1](q)/q
node = mesh.bc_to_point(bc) #( NQ, 1, 2)
phi = space.basis(bc) # (NQ, 1, ldof)
fig = plt.figure()
axes = fig.gca(projection='3d')
axes.plot_trisurf(
node[..., 0].reshape(-1),
node[..., 1].reshape(-1),
phi[..., 0].reshape(-1),
cmap='rainbow', lw=0.0, antialiased=True)
axes.plot_trisurf(
node[..., 0].reshape(-1),
node[..., 1].reshape(-1),
phi[..., 1].reshape(-1),
cmap='rainbow', lw=0.0, antialiased=True)
plt.show()
def uuu(p):
x = p[..., 0]
y = p[..., 1]
pi = np.float128('3.141592653589793238462643383279502884197')
val = np.sin(pi*x)*np.sin(pi*y)
return val
one = np.float128('1.0')
zero = np.float128('0.0')
node = np.array([
(zero, zero),
(one, zero),
(one, one),
(zero, one)], dtype=np.float128)
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.uint32)
mesh = TriangleMesh(node, cell)
area = mesh.entity_measure('cell')
qf = TriangleQuadrature(k, ftype=node.dtype.type)
bcs, ws = qf.quadpts, qf.weights
p = mesh.bc_to_point(bcs)
val = uu(p)
a = np.float128('2.952492442012559756509852517869682817665821383151928174153192567074420535371962574241548128028788940')
b = np.einsum('i, ij, j->', ws, val, area)
print(np.abs(b - a))
