Hi Thomasz, You can get the matching CG1 indicator function (to use in the custom BC) using: I_cg = Function(V) par_loop('for (int i=0; i<A.dofs; i++) A[i][0] = fmax(A[i][0], B[0][0]);', dx, {'A' : (I_cg, RW), 'B': (I_f, READ)}) This sets nodes of l_cg to 1 if they touch any cell for which the indicator function is 1. Regards, David On Fri, 15 Apr 2016 at 13:43 Tomasz Salwa [RPG] <mmtjs@leeds.ac.uk> wrote:
Ok, I extended the BCs. I'm getting indices out of bounds error. I suppose this is because I enforce the BCs in DG0, and then solve in CG space. How can I map it from one to another?
Thanks, Tomasz
Code:
from firedrake import * import numpy as np
nx = 8; ny = 4; Lx = 2.; Ly = 1.
mesh = RectangleMesh( nx, ny, Lx, Ly ) V = FunctionSpace( mesh, "CG", 1 ) V_DG0 = FunctionSpace( mesh, "DG", 0 )
def Heaviside( zero_on_left=True, Lp=0. ): sign = 1. if zero_on_left == False: sign = -1. Hx = Function( V_DG0 ) Hx_expr = Expression( "0.5*(1.0 + copysign( 1.0, sign*(x[0]-Lp) ))", sign=sign, Lp=Lp) Hx.interpolate(Hx_expr) return Hx;
I_f = Heaviside( zero_on_left=False, Lp=1. )
phi = Function( V ) trial = TrialFunction( V ) v = TestFunction( V )
a = dot( grad(trial), grad(v) ) * dx L = Constant(0.) * v * dx
bc = DirichletBC( V, Expression( "sin(pi*x[1]/Ly)", Ly=Ly ), 1 )
class MyBC(DirichletBC): def __init__(self, V, value, markers): # Call superclass init # We provide a dummy subdomain id. super(MyBC, self).__init__(V, value, 0) # Override the "nodes" property which says where the boundary # condition is to be applied. self.nodes = np.unique(np.where(markers.dat.data_ro_with_halos == 0)[0])
# Now I can use MyBC to create a "boundary condition" to zero out all # the nodes that are *not* in the fluid domain: BC_exclude_beyond_fluid = MyBC( V, 0, I_f )
solve( a==L, phi, bcs=[bc, BC_exclude_beyond_fluid] )
Error listing:
Traceback (most recent call last): File "laplace_extended_domain.py", line 51, in <module> solve( a==L, phi, bcs=[bc, BC_exclude_beyond_fluid] ) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/solving.py", line 120, in solve _solve_varproblem(*args, **kwargs) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/solving.py", line 147, in _solve_varproblem solver.solve() File "<decorator-gen-295>", line 2, in solve File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/profiling.py", line 203, in wrapper return f(*args, **kwargs) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/variational_solver.py", line 181, in solve bc.apply(self._problem.u) File "<decorator-gen-297>", line 2, in apply File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/profiling.py", line 203, in wrapper return f(*args, **kwargs) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/bcs.py", line 233, in apply r.assign(self.function_arg, subset=self.node_set) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/utils.py", line 64, in __get__ obj.__dict__[self.__name__] = result = self.fget(obj) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/bcs.py", line 162, in node_set return op2.Subset(self._function_space.node_set, self.nodes) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/backends.py", line 118, in __call__ return t(*args, **kwargs) File "<decorator-gen-7>", line 2, in __init__ File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/utils.py", line 130, in wrapper return f(*args, **kwargs) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/base.py", line 840, in __init__ (self._indices[0], self._indices[-1], self._superset.total_size)) pyop2.exceptions.SubsetIndexOutOfBounds: Out of bounds indices in Subset construction: [20, 63) not [0, 45)
________________________________________ From: firedrake-bounces@imperial.ac.uk <firedrake-bounces@imperial.ac.uk> on behalf of Lawrence Mitchell <lawrence.mitchell@imperial.ac.uk> Sent: 15 April 2016 11:22 To: firedrake@imperial.ac.uk Subject: Re: [firedrake] Laplace equation on subdomain
On 15 Apr 2016, at 11:08, Tomasz Salwa [RPG] <mmtjs@leeds.ac.uk> wrote:
Dear Firedrakers,
As an intermediate part of fluid-structure interaction problem, I would like to solve Laplace equation (with zero Neumann boundary conditions) on a subdomain of the full domain. For that reason I define the step function that is 1 in the subdomain of interest and 0 elsewhere. Multiplying LHS of the weak form (with trial function) by the step function causes a solver error. How can I correct it? Code and error listing are below.
The problem is that you've knocked out a part of your operator so that it's:
laplace 0 0 0
Particularly, it's zero on the diagonal outside the subdomain.
To correct this, you'll need to define your own custom boundary condition class that inherits from DirichletBC that identifies the nodes that are outside the subdomain and impose strong conditions there. I think we discussed this when you visited imperial a while ago.
That way you'll end up with:
laplace 0 0 I
with the identity on the diagonal outside the subdomain instead.
As to your comment (how to write 0*v*dx more succinctly) use:
L = Constant(0)*v*dx
Thanks,
Lawrence
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