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Linear solver for post-process chemical potential #579

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Oct 4, 2023
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Linear solver for post-process chemical potential #579

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31 changes: 20 additions & 11 deletions festim/concentration/theta.py
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Original file line number Diff line number Diff line change
Expand Up @@ -88,26 +88,35 @@ def post_processing_solution_to_concentration(self):
The attribute post_processing_solution is fenics.Product (if self.S is
festim.ArheniusCoeff)
"""
du = f.TrialFunction(self.post_processing_solution.function_space())
J = f.derivative(self.form_post_processing, self.post_processing_solution, du)
problem = f.NonlinearVariationalProblem(
self.form_post_processing, self.post_processing_solution, [], J
problem = f.LinearVariationalProblem(
a=f.lhs(self.form_post_processing),
L=f.rhs(self.form_post_processing),
u=self.post_processing_solution,
bcs=[],
)
solver = f.NonlinearVariationalSolver(problem)
# TODO these prms should be the same as in Simulation.settings I think
solver.parameters["newton_solver"]["absolute_tolerance"] = 1e-10
solver.parameters["newton_solver"]["relative_tolerance"] = 1e-10
solver.parameters["newton_solver"]["maximum_iterations"] = 50
solver = f.LinearVariationalSolver(problem)
solver.solve()

def create_form_post_processing(self, V, materials, dx):
"""Creates a variational formulation for c = theta * S or theta**2 * S

Args:
V (fenics.FunctionSpace): the DG1 function space of the concentration field
materials (festim.Materials): the materials
dx (fenics.Measurement): the dx measure of the problem
"""
F = 0
v = f.TestFunction(V)
self.post_processing_solution = f.Function(V)
F += -self.post_processing_solution * v * dx
c = f.TrialFunction(V)

F += -c * v * dx
for mat in materials.materials:
if mat.solubility_law == "sievert":
# for sievert materials c = theta * S
F += self.solution * self.S * v * dx(mat.id)
elif mat.solubility_law == "henry":
# for henry materials c = theta**2 * S
F += self.solution**2 * self.S * v * dx(mat.id)

self.form_post_processing = F
self.post_processing_solution = f.Function(V)
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