elliptic::subdomain_preconditioners::MinusLaplacian< Dim, OptionsGroup, Solver, LinearSolverRegistrars > Class Template Reference

Approximate the subdomain operator with a flat-space Laplacian for every tensor component separately. More...

#include <MinusLaplacian.hpp>

Classes
struct	BoundaryConditions
struct	SolverOptionTag

Public Types
using	options_group = OptionsGroup
using	poisson_system
using	BoundaryConditionsBase
using	SubdomainOperator
using	SubdomainData
using	BoundaryConditionsSignature
using	solver_type = Solver
using	options = tmpl::list<SolverOptionTag, BoundaryConditions>

Public Member Functions
	MinusLaplacian (MinusLaplacian &&)=default
MinusLaplacian &	operator= (MinusLaplacian &&)=default
	MinusLaplacian (const MinusLaplacian &rhs)
MinusLaplacian &	operator= (const MinusLaplacian &rhs)
	MinusLaplacian (StoredSolverType solver, std::optional< elliptic::BoundaryConditionType > boundary_condition_type)
const Solver &	solver () const
const auto &	cached_solvers () const
	The cached solvers for each unique boundary-condition signature. These are only exposed to allow verifying their consistency.
template<typename LinearOperator, typename VarsType, typename SourceType, typename... OperatorArgs>
Convergence::HasConverged	solve (gsl::not_null< VarsType * > solution, LinearOperator &&linear_operator, const SourceType &source, const std::tuple< OperatorArgs... > &operator_args) const
	Solve the equation \(Ax=b\) by approximating \(A\) with a Laplace operator for every tensor component in \(x\).
void	reset () override
void	pup (PUP::er &p) override
std::unique_ptr< Base >	get_clone () const override
template<typename LinearOperator, typename VarsType, typename SourceType, typename... OperatorArgs>
Convergence::HasConverged	solve (const gsl::not_null< VarsType * > initial_guess_in_solution_out, LinearOperator &&, const SourceType &source, const std::tuple< OperatorArgs... > &operator_args) const

Static Public Attributes
static constexpr size_t	volume_dim = Dim
static constexpr Options::String	help

Detailed Description

template<size_t Dim, typename OptionsGroup, typename Solver = LinearSolver::Serial::LinearSolver<tmpl::list< ::LinearSolver::Serial::Registrars::Gmres< ::LinearSolver::Schwarz::ElementCenteredSubdomainData< Dim, tmpl::list<Poisson::Tags::Field<DataVector>>>>, ::LinearSolver::Serial::Registrars::ExplicitInverse<double>>>, typename LinearSolverRegistrars = tmpl::list<Registrars::MinusLaplacian<Dim, OptionsGroup, Solver>>>
class elliptic::subdomain_preconditioners::MinusLaplacian< Dim, OptionsGroup, Solver, LinearSolverRegistrars >

Approximate the subdomain operator with a flat-space Laplacian for every tensor component separately.

This linear solver applies the Solver to every tensor component in turn, approximating the subdomain operator with a flat-space Laplacian. This can be a lot cheaper than solving the full subdomain operator and can provide effective preconditioning for an iterative subdomain solver. The approximation is better the closer the original PDEs are to a set of decoupled flat-space Poisson equations.

Boundary conditions

At external boundaries we impose homogeneous Dirichlet or Neumann boundary conditions on the Poisson sub-problems. For tensor components and element faces where the original boundary conditions are of Dirichlet-type we choose homogeneous Dirichlet boundary conditions, and for those where the original boundary conditions are of Neumann-type we choose homogeneous Neumann boundary conditions. This means we may end up with more than one distinct Poisson operator on subdomains with external boundaries, one per unique combination of element face and boundary-condition type among the tensor components.

Complex variables

This preconditioner can also be applied to complex variables, in which case the Laplacian just applies to the real and imaginary part separately.

Template Parameters

Dim	Spatial dimension
OptionsGroup	The options group identifying the LinearSolver::Schwarz::Schwarz solver that defines the subdomain geometry.
Solver	Any class that provides a solve and a reset function, but typically a LinearSolver::Serial::LinearSolver. The solver will be factory-created from input-file options.

Member Typedef Documentation

BoundaryConditionsBase

template<size_t Dim, typename OptionsGroup, typename Solver = LinearSolver::Serial::LinearSolver<tmpl::list< ::LinearSolver::Serial::Registrars::Gmres< ::LinearSolver::Schwarz::ElementCenteredSubdomainData< Dim, tmpl::list<Poisson::Tags::Field<DataVector>>>>, ::LinearSolver::Serial::Registrars::ExplicitInverse<double>>>, typename LinearSolverRegistrars = tmpl::list<Registrars::MinusLaplacian<Dim, OptionsGroup, Solver>>>

using elliptic::subdomain_preconditioners::MinusLaplacian< Dim, OptionsGroup, Solver, LinearSolverRegistrars >::BoundaryConditionsBase

Initial value:

 
      typename poisson_system::boundary_conditions_base

BoundaryConditionsSignature

template<size_t Dim, typename OptionsGroup, typename Solver = LinearSolver::Serial::LinearSolver<tmpl::list< ::LinearSolver::Serial::Registrars::Gmres< ::LinearSolver::Schwarz::ElementCenteredSubdomainData< Dim, tmpl::list<Poisson::Tags::Field<DataVector>>>>, ::LinearSolver::Serial::Registrars::ExplicitInverse<double>>>, typename LinearSolverRegistrars = tmpl::list<Registrars::MinusLaplacian<Dim, OptionsGroup, Solver>>>

using elliptic::subdomain_preconditioners::MinusLaplacian< Dim, OptionsGroup, Solver, LinearSolverRegistrars >::BoundaryConditionsSignature

Initial value:

 
      std::map<BoundaryId, elliptic::BoundaryConditionType>

poisson_system

template<size_t Dim, typename OptionsGroup, typename Solver = LinearSolver::Serial::LinearSolver<tmpl::list< ::LinearSolver::Serial::Registrars::Gmres< ::LinearSolver::Schwarz::ElementCenteredSubdomainData< Dim, tmpl::list<Poisson::Tags::Field<DataVector>>>>, ::LinearSolver::Serial::Registrars::ExplicitInverse<double>>>, typename LinearSolverRegistrars = tmpl::list<Registrars::MinusLaplacian<Dim, OptionsGroup, Solver>>>

using elliptic::subdomain_preconditioners::MinusLaplacian< Dim, OptionsGroup, Solver, LinearSolverRegistrars >::poisson_system

Initial value:

 
      Poisson::FirstOrderSystem<Dim, Poisson::Geometry::FlatCartesian>

SubdomainData

template<size_t Dim, typename OptionsGroup, typename Solver = LinearSolver::Serial::LinearSolver<tmpl::list< ::LinearSolver::Serial::Registrars::Gmres< ::LinearSolver::Schwarz::ElementCenteredSubdomainData< Dim, tmpl::list<Poisson::Tags::Field<DataVector>>>>, ::LinearSolver::Serial::Registrars::ExplicitInverse<double>>>, typename LinearSolverRegistrars = tmpl::list<Registrars::MinusLaplacian<Dim, OptionsGroup, Solver>>>

using elliptic::subdomain_preconditioners::MinusLaplacian< Dim, OptionsGroup, Solver, LinearSolverRegistrars >::SubdomainData

Initial value:

 ::LinearSolver::Schwarz::ElementCenteredSubdomainData<
      Dim, tmpl::list<Poisson::Tags::Field<DataVector>>>

SubdomainOperator

template<size_t Dim, typename OptionsGroup, typename Solver = LinearSolver::Serial::LinearSolver<tmpl::list< ::LinearSolver::Serial::Registrars::Gmres< ::LinearSolver::Schwarz::ElementCenteredSubdomainData< Dim, tmpl::list<Poisson::Tags::Field<DataVector>>>>, ::LinearSolver::Serial::Registrars::ExplicitInverse<double>>>, typename LinearSolverRegistrars = tmpl::list<Registrars::MinusLaplacian<Dim, OptionsGroup, Solver>>>

using elliptic::subdomain_preconditioners::MinusLaplacian< Dim, OptionsGroup, Solver, LinearSolverRegistrars >::SubdomainOperator

Initial value:

 elliptic::dg::subdomain_operator::SubdomainOperator<
      poisson_system, OptionsGroup,
      tmpl::list<Poisson::BoundaryConditions::Robin<Dim>>>

Member Data Documentation

help

template<size_t Dim, typename OptionsGroup, typename Solver = LinearSolver::Serial::LinearSolver<tmpl::list< ::LinearSolver::Serial::Registrars::Gmres< ::LinearSolver::Schwarz::ElementCenteredSubdomainData< Dim, tmpl::list<Poisson::Tags::Field<DataVector>>>>, ::LinearSolver::Serial::Registrars::ExplicitInverse<double>>>, typename LinearSolverRegistrars = tmpl::list<Registrars::MinusLaplacian<Dim, OptionsGroup, Solver>>>

Options::String elliptic::subdomain_preconditioners::MinusLaplacian< Dim, OptionsGroup, Solver, LinearSolverRegistrars >::help

staticconstexpr

Initial value:

=
      "Approximate the linear operator with a Laplace operator "
      "for every tensor component separately."

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The documentation for this class was generated from the following file:

• src/Elliptic/SubdomainPreconditioners/MinusLaplacian.hpp