TransportMaps.Distributions.Examples.PoissonProblem.PoissonProblems

Module Contents

Classes

MixedPoissonSolver	Defines the solver (and adjoints) for the Poisson problem.
PoissonSolver	Defines the solver (and adjoints) for the Poisson problem.
PoissonSolverProblem1	Defines the solver (and adjoints) for the following setting of the Poisson problem.

Functions

get_Poisson_problem_solver(n, ndiscr)

class TransportMaps.Distributions.Examples.PoissonProblem.PoissonProblems.MixedPoissonSolver(**kwargs)

Bases: TransportMaps.DOLFIN.Solver

Defines the solver (and adjoints) for the Poisson problem.

\[\begin{split}\begin{cases} - \nabla \cdot \kappa({\bf x}) \nabla u({\bf x}) = f({\bf x}) & {\bf x} \in \Omega \\ u({\bf x}) = g({\bf x}) & {\bf x} \in \Gamma_D \\ - \frac{\partial u}{\partial n}({\bf x}) = h({\bf x}) & {\bf x} \in \Gamma_N \end{cases}\end{split}\]

where \(\Omega\), \(\Gamma_D \subset \partial\Omega\) and \(\Gamma_N \subset \partial\Omega\).

set_up(**kwargs)

_solve(f, kappa, bcs)

solve(kappa)

solve_adjoint(f, kappa)

solve_action_hess_adjoint(dx, usol, kappa)

class TransportMaps.Distributions.Examples.PoissonProblem.PoissonProblems.PoissonSolver(*args, **kwargs)

Bases: MixedPoissonSolver

Defines the solver (and adjoints) for the Poisson problem.

\[\begin{split}\begin{cases} - \nabla \cdot \kappa({\bf x}) \nabla u({\bf x}) = f({\bf x}) & {\bf x} \in \Omega \\ u({\bf x}) = g({\bf x}) & {\bf x} \in \Gamma_D \\ - \frac{\partial u}{\partial n}({\bf x}) = h({\bf x}) & {\bf x} \in \Gamma_N \end{cases}\end{split}\]

where \(\Omega\), \(\Gamma_D \subset \partial\Omega\) and \(\Gamma_N \subset \partial\Omega\).

TransportMaps.Distributions.Examples.PoissonProblem.PoissonProblems.get_Poisson_problem_solver(n, ndiscr)

class TransportMaps.Distributions.Examples.PoissonProblem.PoissonProblems.PoissonSolverProblem1(ndiscr)

Bases: MixedPoissonSolver

Defines the solver (and adjoints) for the following setting of the Poisson problem.

\[\begin{split}\begin{cases} - \nabla \cdot \kappa({\bf x}) \nabla u({\bf x}) = 0 & {\bf x} \in [0,1]^2\Omega \\ u({\bf x}) = 0 & {\bf x}_1 = 0 \\ u({\bf x}) = 1 & {\bf x}_1 = 1 \\ - \frac{\partial u}{\partial n}({\bf x}) = 0 & {\bf x}_2 \in {0,1} \end{cases}\end{split}\]

Parameters:

ndiscr (int) – number of discretization points per dimension

__getstate__()

set_up(**kwargs)