print "dt = ", dt
print "Mesh size = ", mesh.Diam
raw_input('Press any key to start time loop')
NSteps = 200
u_old = u0
err = []
loop = True # turn this off if you already have the data and just want to plot
if loop:
for i in range(NSteps):
print 'Timestep: ', i
pde.u = u_old
M_free, vecs = pde.AssembPDE()
F = vecs[0]; G = vecs[1]
x_old = pde.wrapSol(u_old)
rhs = linsolv.mul(a = M_free, b = x_old) - dt*linsolv.mul(a = W_free, b = x_old) + dt*F + dt*G
x_new = pde.Solve(M_free, rhs)
u_new = pde.unwrapSol(x_new)
# write to file and update
np.savetxt(outfile_fmt%(i+1), u_new)
err.append(abs(u_new[:,0] - u_old[:,0]).max())
u_old = u_new
# pattern animations
print '\nTime stepping ended...'
raw_input('Press any key to start animation...')
p = fem.Plot(Mesh = mesh)
fig = plt.figure(figsize = (7,5), facecolor = 'w', edgecolor = 'w')
datafilelist = []
[datafilelist.append(outfile_fmt % x) for x in range(NSteps)]
def testLinDiff():
# init mesh
K0 = importInitMesh(matfile=initmeshfile)
m = Mesh(K0)
# set zero Neumann boundary conditions
m.NeumannEdges = m.BoundaryEdges
m.NumNeumannEdges = len(m.NeumannEdges)
def gNeumann(Mesh=m):
return [lambda p: 0.]
# get boundary partition
m.partitionNodes()
# assemble stiffness and mass matrices
a = Assemb(Mesh=m)
a.AssembStiffMat()
a.AssembMassMat()
K = a.globalStiffMat
M = a.globalMassMat
# set source function
def fsrc(Mesh=m):
return [lambda p, m, u: 0.]
# assemble LHS of final lin. alg problem
SDC = 100. # Diffusion coefficient bumped up for quick diffusion
def makeBlockMat(x):
return SDC * x
def getlhs(K, M):
return M
# define the PDE
pde = Parabolic(Mesh=m, StiffMat=a.globalStiffMat, MassMat=a.globalMassMat)
pde.setNeumannFunc = gNeumann
pde.setSrcFunc = fsrc
pde.AssembBlockStiffMat = makeBlockMat
pde.AssembBlockMassMat = makeBlockMat
pde.AssembLHS = getlhs
import linsolv
K_free = makeBlockMat(pde.getFreeNodeArray(K))
# initial condition
f0 = [lambda p: 1. if np.sqrt(p[0]**2 + p[1]**2) <= 0.1 else 0.]
u0 = np.zeros([m.NumNodes, 1])
for i, node in enumerate(m.Nodes):
u0[i, 0] = f0[0](node)
# start time loop
outfile_fmt = os.path.join(testdata_dir, 'testdiff%d.dat')
np.savetxt(outfile_fmt % 0, u0)
dt = 0.5e-3
print "dt = ", dt
print "Mesh size = ", m.Diam
print "Characteristic time step # = ", int((1. / SDC) / dt)
raw_input('Press any key to start time loop')
NSteps = 100
u_old = u0
err = []
loop = True
if loop:
for i in range(NSteps):
print 'Timestep: ', i
pde.u = u_old
M_free, vecs = pde.AssembPDE()
F = vecs[0]
G = vecs[1]
D = vecs[2]
x_old = pde.wrapSol(u_old)
rhs = linsolv.mul(a = M_free, b = x_old) - dt * linsolv.mul(a = K_free, b = x_old) + dt * F + \
dt * G - linsolv.mul(a = M_free, b = D)
x_new = pde.Solve(M_free, rhs)
u_new = pde.unwrapSol(x_new)
# write to file and update
np.savetxt(outfile_fmt % (i + 1), u_new)
err.append(abs(x_new - x_old).max())
u_old = u_new
# pattern animations
print '\nTime stepping ended...'
raw_input('Press any key to start animation...')
p = Plot(Mesh=m)
fig = plt.figure(figsize=(7, 5), facecolor='w', edgecolor='w')
datafilelist = []
[datafilelist.append(outfile_fmt % x) for x in range(NSteps)]
ax = fig.add_subplot(1, 1, 1)
p.ax = ax
p.patternAnimate(dataFileList=datafilelist,
Component=0,
delay=0.01,
frameRate=10,
Prefix='../testdata/testdiff')
# plot convergence
fig_err = plt.figure(figsize=(7, 5), facecolor='w', edgecolor='w')
ax_err = fig_err.add_subplot(1, 1, 1)
ax_err.set_xlabel('Timestep', fontsize='xx-large')
ax_err.set_ylabel('Convergence to steady state', fontsize='xx-large')
ax_err.plot(err)
def testLinDiff():
# init mesh
K0 = importInitMesh(matfile=initmeshfile)
m = Mesh(K0)
# set zero Neumann boundary conditions
m.NeumannEdges = m.BoundaryEdges
m.NumNeumannEdges = len(m.NeumannEdges)
def gNeumann(Mesh=m):
return [lambda p: 0.0]
# get boundary partition
m.partitionNodes()
# assemble stiffness and mass matrices
a = Assemb(Mesh=m)
a.AssembStiffMat()
a.AssembMassMat()
K = a.globalStiffMat
M = a.globalMassMat
# set source function
def fsrc(Mesh=m):
return [lambda p, m, u: 0.0]
# assemble LHS of final lin. alg problem
SDC = 100.0 # Diffusion coefficient bumped up for quick diffusion
def makeBlockMat(x):
return SDC * x
def getlhs(K, M):
return M
# define the PDE
pde = Parabolic(Mesh=m, StiffMat=a.globalStiffMat, MassMat=a.globalMassMat)
pde.setNeumannFunc = gNeumann
pde.setSrcFunc = fsrc
pde.AssembBlockStiffMat = makeBlockMat
pde.AssembBlockMassMat = makeBlockMat
pde.AssembLHS = getlhs
import linsolv
K_free = makeBlockMat(pde.getFreeNodeArray(K))
# initial condition
f0 = [lambda p: 1.0 if np.sqrt(p[0] ** 2 + p[1] ** 2) <= 0.1 else 0.0]
u0 = np.zeros([m.NumNodes, 1])
for i, node in enumerate(m.Nodes):
u0[i, 0] = f0[0](node)
# start time loop
outfile_fmt = os.path.join(testdata_dir, "testdiff%d.dat")
np.savetxt(outfile_fmt % 0, u0)
dt = 0.5e-3
print "dt = ", dt
print "Mesh size = ", m.Diam
print "Characteristic time step # = ", int((1.0 / SDC) / dt)
raw_input("Press any key to start time loop")
NSteps = 100
u_old = u0
err = []
loop = True
if loop:
for i in range(NSteps):
print "Timestep: ", i
pde.u = u_old
M_free, vecs = pde.AssembPDE()
F = vecs[0]
G = vecs[1]
D = vecs[2]
x_old = pde.wrapSol(u_old)
rhs = (
linsolv.mul(a=M_free, b=x_old)
- dt * linsolv.mul(a=K_free, b=x_old)
+ dt * F
+ dt * G
- linsolv.mul(a=M_free, b=D)
)
x_new = pde.Solve(M_free, rhs)
u_new = pde.unwrapSol(x_new)
# write to file and update
np.savetxt(outfile_fmt % (i + 1), u_new)
err.append(abs(x_new - x_old).max())
u_old = u_new
# pattern animations
print "\nTime stepping ended..."
raw_input("Press any key to start animation...")
p = Plot(Mesh=m)
fig = plt.figure(figsize=(7, 5), facecolor="w", edgecolor="w")
datafilelist = []
[datafilelist.append(outfile_fmt % x) for x in range(NSteps)]
ax = fig.add_subplot(1, 1, 1)
p.ax = ax
p.patternAnimate(dataFileList=datafilelist, Component=0, delay=0.01, frameRate=10, Prefix="../testdata/testdiff")
# plot convergence
fig_err = plt.figure(figsize=(7, 5), facecolor="w", edgecolor="w")
ax_err = fig_err.add_subplot(1, 1, 1)
ax_err.set_xlabel("Timestep", fontsize="xx-large")
ax_err.set_ylabel("Convergence to steady state", fontsize="xx-large")
ax_err.plot(err)