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

using	BoundaryConditionsBase = typename poisson_system::boundary_conditions_base

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

using	SubdomainData = ::LinearSolver::Schwarz::ElementCenteredSubdomainData< Dim, tmpl::list< Poisson::Tags::Field > >

using	BoundaryConditionsSignature = std::map< BoundaryId, elliptic::BoundaryConditionType >

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>>>, ::LinearSolver::Serial::Registrars::ExplicitInverse>>, 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.

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 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>>>, ::LinearSolver::Serial::Registrars::ExplicitInverse>>, typename LinearSolverRegistrars = tmpl::list<Registrars::MinusLaplacian<Dim, OptionsGroup, Solver>>>

constexpr 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."

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

src/Elliptic/SubdomainPreconditioners/MinusLaplacian.hpp

Classes

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Data Documentation

◆ help