def evolve(nx, C, tmax, xmax=None):
xmin = 0.0
if xmax == None:
xmax = 1.0
# create a dummy patch to store some info in the same way the MG
# solver will
myGrid = patch1d.grid1d(nx, ng=1, xmin=xmin, xmax=xmax)
# initialize the data
phi = myGrid.scratchArray()
# initial solution -- this fills the GC too
phi[:] = phi_a(myGrid, 0.0)
# time info
dt = C * 0.5 * myGrid.dx**2 / k
t = 0.0
# evolve
while (t < tmax):
if (t + dt > tmax):
dt = tmax - t
# create the multigrid object
a = multigrid.ccMG1d(nx,
xmin=xmin,
xmax=xmax,
alpha=1.0,
beta=0.5 * dt * k,
xlBCtype="neumann",
xrBCtype="neumann",
verbose=0)
# initialize the RHS
a.initRHS(phi + 0.5 * dt * k * lap(a.solnGrid, phi))
# initialize the solution to 0
a.initZeros()
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# get the solution
v = a.getSolution()
# store the new solution
phi[:] = v[:]
t += dt
return a.solnGrid, phi
def evolve(nx, C, tmax, xmax=None):
xmin = 0.0
if xmax == None: xmax = 1.0
# create a dummy patch to store some info in the same way the MG
# solver will
myGrid = patch1d.grid1d(nx, ng=1,
xmin=xmin, xmax=xmax)
# initialize the data
phi = myGrid.scratchArray()
# initial solution -- this fills the GC too
phi[:] = phi_a(myGrid, 0.0)
# time info
dt = C*0.5*myGrid.dx**2/k
t = 0.0
# evolve
while (t < tmax):
if (t + dt > tmax):
dt = tmax - t
# create the multigrid object
a = multigrid.ccMG1d(nx, xmin=xmin, xmax=xmax,
alpha = 1.0, beta = 0.5*dt*k,
xlBCtype="neumann", xrBCtype="neumann",
verbose=0)
# initialize the RHS
a.initRHS(phi + 0.5*dt*k*lap(a.solnGrid, phi))
# initialize the solution to 0
a.initZeros()
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# get the solution
v = a.getSolution()
# store the new solution
phi[:] = v[:]
t += dt
return a.solnGrid, phi
def mgsolve(nx):
# create the multigrid object
a = multigrid.ccMG1d(nx, xlBCtype="dirichlet", xrBCtype="dirichlet",
verbose=0)
# initialize the solution to 0
a.initSolution(a.solnGrid.scratchArray())
# initialize the RHS using the function f
a.initRHS(f(a.x))
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# get the solution
v = a.getSolution()
# compute the error from the analytic solution
return error(a.solnGrid, v - true(a.x))
def smoothRun(nx):
# create the multigrid object
a = multigrid.ccMG1d(nx,
xlBCtype="dirichlet",
xrBCtype="dirichlet",
verbose=0)
# initialize the solution to 0
a.initSolution(a.solnGrid.scratchArray())
# initialize the RHS using the function f
a.initRHS(f(a.x))
# smooth
n = numpy.arange(20000) + 1
e = []
r = []
for i in n:
# do 1 smoothing at the finest level
a.smooth(a.nlevels - 1, 1)
# compute the true error (wrt the analytic solution)
v = a.getSolution()
e.append(error(a.solnGrid, v - true(a.x)))
# compute the residual
a.computeResidual(a.nlevels - 1)
r.append(error(a.solnGrid, a.grids[a.nlevels - 1].getVarPtr("r")))
r = numpy.array(r)
e = numpy.array(e)
return n, r, e
# normalize
return numpy.sqrt(myg.dx * numpy.sum((r[myg.ilo:myg.ihi + 1]**2)))
# the righthand side
def f(x):
return numpy.sin(x)
# test the multigrid solver
nx = 64
# create the multigrid object
a = multigrid.ccMG1d(nx,
xlBCtype="dirichlet", xrBCtype="dirichlet",
verbose=1)
# initialize the solution to 0
init = a.solnGrid.scratchArray()
a.initSolution(init)
# initialize the RHS using the function f
rhs = f(a.x)
a.initRHS(rhs)
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# alternately, we can just use smoothing by uncommenting the following
# L2 norm of elements in r, multiplied by dx to
# normalize
return numpy.sqrt(myg.dx * numpy.sum((r[myg.ilo:myg.ihi + 1]**2)))
# the righthand side
def f(x):
return numpy.sin(x)
# test the multigrid solver
nx = 64
# create the multigrid object
a = multigrid.ccMG1d(nx, xlBCtype="dirichlet", xrBCtype="dirichlet", verbose=1)
# initialize the solution to 0
init = a.solnGrid.scratchArray()
a.initSolution(init)
# initialize the RHS using the function f
rhs = f(a.x)
a.initRHS(rhs)
# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)
# alternately, we can just use smoothing by uncommenting the following
# a.smooth(a.nlevels-1,50000)