Hi all, I see a significant speed decrease when I switch to using 'snes' as my nonlinear solver, and am wondering why? Can anyone enlighten me?
Demo is a modification to the Cahn-Hilliard demo. I run it with the 'time' command and consistently see 'snes' increasing the runtime by ~10%.
Thanks!
import random
from dolfin import *
# Class representing the intial conditions
class InitialConditions(Expression):
def __init__(self):
random.seed(2 + MPI.process_number())
def eval(self, values, x):
values[0] = 0.63 + 0.02*(0.5 - random.random())
values[1] = 0.0
def value_shape(self):
return (2,)
# Class for interfacing with the Newton solver
class CahnHilliardEquation(NonlinearProblem):
def __init__(self, a, L):
NonlinearProblem.__init__(self)
self.L = L
self.a = a
self.reset_sparsity = True
def F(self, b, x):
assemble(self.L, tensor=b)
def J(self, A, x):
assemble(self.a, tensor=A, reset_sparsity=self.reset_sparsity)
self.reset_sparsity = False
# Model parameters
lmbda = 1.0e-02 # surface parameter
dt = 5.0e-06 # time step
theta = 0.5 # time stepping family, e.g. theta=1 -> backward Euler, theta=0.5 -> Crank-Nicolson
# Form compiler options
parameters["form_compiler"]["optimize"] = True
parameters["form_compiler"]["cpp_optimize"] = True
parameters["form_compiler"]["representation"] = "quadrature"
# Create mesh and define function spaces
mesh = UnitSquareMesh(96, 96)
V = FunctionSpace(mesh, "Lagrange", 1)
ME = V*V
# Define trial and test functions
du = TrialFunction(ME)
q, v = TestFunctions(ME)
# Define functions
u = Function(ME) # current solution
u0 = Function(ME) # solution from previous converged step
# Split mixed functions
dc, dmu = split(du)
c, mu = split(u)
c0, mu0 = split(u0)
# Create intial conditions and interpolate
u_init = InitialConditions()
u.interpolate(u_init)
u0.interpolate(u_init)
# Compute the chemical potential df/dc
c = variable(c)
f = 100*c**2*(1-c)**2
dfdc = diff(f, c)
# mu_(n+theta)
mu_mid = (1.0-theta)*mu0 + theta*mu
# Weak statement of the equations
L0 = c*q*dx - c0*q*dx + dt*dot(grad(mu_mid), grad(q))*dx
L1 = mu*v*dx - dfdc*v*dx - lmbda*dot(grad(c), grad(v))*dx
L = L0 + L1
# Compute directional derivative about u in the direction of du (Jacobian)
a = derivative(L, u, du)
problem = NonlinearVariationalProblem(L, u, [], a)
solver = NonlinearVariationalSolver(problem)
#solver.parameters["nonlinear_solver"] = "snes"
solver.parameters["newton_solver"]["linear_solver"] = "gmres"
#info(solver.parameters, verbose=True)
# Step in time
t = 0.0
T = 50*dt
while (t < T):
t += dt
u0.vector()[:] = u.vector()
solver.solve()
file << (u.split()[0], t)