eps = 1e-6
for k in xrange(n_nodes):
x, y = pts[k]
if (np.fabs(x - 1) < eps or #np.fabs(x - (-1)) < eps or
np.fabs(y - 1) < eps): # or np.fabs(y - (-1)) < eps):
bc_nodes[k] = 1
return bc_nodes
if __name__ == "__main__":
# Try the quad mesh with Q1 elements:
if True:
import poisson_optimized as poisson
# import poisson
pts, quads, tri = create_mesh.quad_rectangle(0, 1, 0, 1, 21, 21)
bc_nodes = set_bc_nodes_square(pts)
# forcing term at mesh nodes
f_pts = f(pts)
# Dirichlet boundary conditions at *all* mesh nodes (most of these values are not used)
u_bc_pts = u_bc(pts)
# Set up the system and solve:
tic = time.clock()
A, b = poisson.poisson(pts, quads, bc_nodes, f_pts, u_bc_pts,
FEM.Q1Aligned, FEM.GaussQuad2x2())
toc = time.clock()
print "Matrix assembly took %f s" % (toc - tic)
if pts.shape[0] < 50:
x = pts[:, 0]
y = pts[:, 1]
except:
x = pts[0]
y = pts[1]
return 2.0 * (1 + y) / ((3 + x)**2 + (1 + y)**2)
errors = []
Ns = np.array([5, 11, 21, 41, 81])
for n in Ns:
print "Running with N = %d" % n
tic = time.clock()
pts, quads, tri = create_mesh.quad_rectangle(-1, 1, -1, 1, n, n)
bc_nodes = set_bc_nodes_square(pts)
toc = time.clock()
print "Mesh generation took %f s" % (toc - tic)
f_pts = f(pts)
u_bc_pts = u_exact(pts)
# Set up the system and solve:
tic = time.clock()
A, b = poisson.poisson(pts, quads, bc_nodes, f_pts, u_bc_pts, FEM.Q1,
FEM.GaussQuad2x2())
toc = time.clock()
print "Matrix assembly took %f s" % (toc - tic)
tic = time.clock()
eps = 1e-6
for k in xrange(n_nodes):
x, y = pts[k]
if np.fabs(x - 1) < eps or np.fabs(y - 1) < eps: # np.fabs(x - (-1)) < eps or # or np.fabs(y - (-1)) < eps):
bc_nodes[k] = 1
return bc_nodes
if __name__ == "__main__":
# Try the quad mesh with Q1 elements:
if True:
import poisson_optimized as poisson
# import poisson
pts, quads, tri = create_mesh.quad_rectangle(0, 1, 0, 1, 21, 21)
bc_nodes = set_bc_nodes_square(pts)
# forcing term at mesh nodes
f_pts = f(pts)
# Dirichlet boundary conditions at *all* mesh nodes (most of these values are not used)
u_bc_pts = u_bc(pts)
# Set up the system and solve:
tic = time.clock()
A, b = poisson.poisson(pts, quads, bc_nodes, f_pts, u_bc_pts, FEM.Q1Aligned, FEM.GaussQuad2x2())
toc = time.clock()
print "Matrix assembly took %f s" % (toc - tic)
if pts.shape[0] < 50:
print "cond(A) = %3.3f" % np.linalg.cond(A.todense())
x = pts[:,0]
y = pts[:,1]
except:
x = pts[0]
y = pts[1]
return 2.0*(1+y) / ((3+x)**2 + (1+y)**2)
errors = []
Ns = np.array([5, 11, 21, 41, 81])
for n in Ns:
print "Running with N = %d" % n
tic = time.clock()
pts,quads,tri = create_mesh.quad_rectangle(-1, 1, -1, 1, n, n)
bc_nodes = set_bc_nodes_square(pts)
toc = time.clock()
print "Mesh generation took %f s" % (toc - tic)
f_pts = f(pts)
u_bc_pts = u_exact(pts)
# Set up the system and solve:
tic = time.clock()
A,b = poisson.poisson(pts, quads, bc_nodes, f_pts, u_bc_pts, FEM.Q1, FEM.GaussQuad2x2())
toc = time.clock()
print "Matrix assembly took %f s" % (toc - tic)
tic = time.clock()
x = spsolve(A.tocsr(), b)
