pymor.analyticalproblems.elliptic

Module Contents

class pymor.analyticalproblems.elliptic.StationaryProblem(domain, rhs=None, diffusion=None, advection=None, nonlinear_advection=None, nonlinear_advection_derivative=None, reaction=None, nonlinear_reaction=None, nonlinear_reaction_derivative=None, dirichlet_data=None, neumann_data=None, robin_data=None, outputs=None, parameter_ranges=None, name=None)

Bases: pymor.parameters.base.ParametricObject

Linear elliptic problem description.

The problem consists in solving

- ∇ ⋅ [d(x, μ) ∇ u(x, μ)] + ∇ ⋅ [f_l(x, μ)u(x, μ)]
+ ∇ ⋅ f_n(u(x, μ), μ) + c_l(x, μ) u(x, μ) + c_n(u(x, μ), μ) = g(x, μ)

for u.

Parameters:

• domain – A DomainDescription of the domain the problem is posed on.

• rhs – The Function g. rhs.dim_domain has to agree with the dimension of domain, whereas rhs.shape_range has to be ().

• diffusion – The Function d with shape_range of either () or (dim domain, dim domain).

• advection – The Function f_l, only depending on x, with shape_range of (dim domain,).

• nonlinear_advection – The Function f_n, only depending on u, with shape_range of (dim domain,).

• nonlinear_advection_derivative – The derivative of f_n, only depending on u, with respect to u.

• reaction – The Function c_l, only depending on x, with shape_range of ().

• nonlinear_reaction – The Function c_n, only depending on u, with shape_range of ().

• nonlinear_reaction_derivative – The derivative of the Function c_n, only depending on u, with shape_range of ().

• dirichlet_data – Function providing the Dirichlet boundary values.

• neumann_data – Function providing the Neumann boundary values.

• robin_data – Tuple of two Functions providing the Robin parameter and boundary values.

• outputs –

  Tuple of additional output functionals to assemble. Each value must be a tuple of the form (functional_type, data) where functional_type is a string defining the type of functional to assemble and data is a Function holding the corresponding coefficient function. Currently implemented functional_types are:

  l2:

  Evaluate the l2-product with the given data function.

  l2_boundary:

  Evaluate the l2-product with the given data function on the boundary.

  quadratic:

  Evaluate the integral of the data function scaled by the squared solution (u, u).

• parameter_ranges – Ranges of interest for the Parameters of the problem.

• name – Name of the problem.

domain

rhs

diffusion

advection

nonlinear_advection

nonlinear_advection_derivative

reaction

nonlinear_reaction

nonlinear_reaction_derivative

dirichlet_data

neumann_data

robin_data

outputs