def runTest(self):
m = self.mesh
e = ElementTriP1()
basis = InteriorBasis(m, e)
A = laplace.assemble(basis)
M = mass.assemble(basis)
D = m.boundary_nodes()
assert_almost_equal(enforce(A, D=D).toarray(), np.eye(A.shape[0]))
assert_almost_equal(enforce(M, D=D, diag=0.).toarray(),
np.zeros(M.shape))
enforce(A, D=D, overwrite=True)
assert_almost_equal(A.toarray(), np.eye(A.shape[0]))
def test_simple_cg_solver():
m = MeshTri().refined(3)
basis = CellBasis(m, ElementTriP1())
A0 = laplace.coo_data(basis)
A1 = laplace.assemble(basis)
f = unit_load.assemble(basis)
D = m.boundary_nodes()
x1 = solve(*condense(A1, f, D=D))
f[D] = 0
x0 = A0.solve(f, D=D)
assert_almost_equal(x0, x1)
def source(v, w):
x = w.x - .5
return v * np.exp(-1e3 * (x[0]**2 + x[1]**2))
# nonperiodic mesh
m = MeshTri.init_symmetric().refined(5)
# create a periodic mesh
Mp = MeshTri1DG.periodic(
m,
m.nodes_satisfying(lambda x: x[0] == 1),
m.nodes_satisfying(lambda x: x[0] == 0),
)
peclet = 1e2
basis = Basis(Mp, ElementTriP2())
A = laplace.assemble(basis) + peclet * advection.assemble(basis)
f = source.assemble(basis)
D = basis.get_dofs()
x = solve(*condense(A, f, D=D))
if __name__ == '__main__':
from os.path import splitext
from sys import argv
from skfem.visuals.matplotlib import plot, savefig
plot(basis, x, shading='gouraud')
savefig(splitext(argv[0])[0] + '_solution.png')
"""Wave equation.""" import numpy as np from scipy.sparse import bmat, identity from scipy.sparse.linalg import splu from skfem import * from skfem.models import laplace, mass m = MeshLine().refined(6) basis = Basis(m, ElementLineP1()) N = basis.N L = laplace.assemble(basis) M = mass.assemble(basis) I = identity(N) c = 1. # reduction to first order system in time A0 = bmat([[I, None], [None, M]], "csc") B0 = bmat([[None, I], [-c**2 * L, None]], "csc") # Crank-Nicolson dt = .01 theta = .5 A = A0 + theta * B0 * dt B = A0 - (1. - theta) * B0 * dt backsolve = splu(A).solve # timestepping def evolve(t, u):