# 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)[source]

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)[source]
_solve(f, kappa, bcs)[source]
solve(kappa)[source]
class TransportMaps.Distributions.Examples.PoissonProblem.PoissonProblems.PoissonSolver(*args, **kwargs)[source]

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)[source]
class TransportMaps.Distributions.Examples.PoissonProblem.PoissonProblems.PoissonSolverProblem1(ndiscr)[source]

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__()[source]
set_up(**kwargs)[source]