Source code for pymor.analyticalproblems.helmholtz

# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright 2013-2018 pyMOR developers and contributors. All rights reserved.
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)

from pymor.analyticalproblems.elliptic import StationaryProblem
from pymor.domaindescriptions.basic import RectDomain
from pymor.functions.basic import ConstantFunction, LincombFunction
from pymor.parameters.functionals import ExpressionParameterFunctional
from pymor.parameters.spaces import CubicParameterSpace


[docs]def helmholtz_problem(domain=RectDomain(), rhs=None, parameter_range=(0., 100.), dirichlet_data=None, neumann_data=None): """Helmholtz equation problem. This problem is to solve the Helmholtz equation :: - ∆ u(x, k) - k^2 u(x, k) = f(x, k) on a given domain. Parameters ---------- domain A |DomainDescription| of the domain the problem is posed on. rhs The |Function| f(x, μ). parameter_range A tuple `(k_min, k_max)` describing the interval in which k is allowd to vary. dirichlet_data |Function| providing the Dirichlet boundary values. neumann_data |Function| providing the Neumann boundary values. """ return StationaryProblem( domain=domain, rhs=rhs or ConstantFunction(1., dim_domain=domain.dim), dirichlet_data=dirichlet_data, neumann_data=neumann_data, diffusion=ConstantFunction(1., dim_domain=domain.dim), reaction=LincombFunction([ConstantFunction(1., dim_domain=domain.dim)], [ExpressionParameterFunctional('-k**2', {'k': ()})]), parameter_space=CubicParameterSpace({'k': ()}, *parameter_range), name='helmholtz_problem' )