Class mgrid::NonlinearMultigrid

ClassList > mgrid > NonlinearMultigrid

Nonlinear full-approximation-scheme (FAS) multigrid solver. More...

#include <multigrid_nonlinear.hpp>

Inherits the following classes: mgrid::MultigridBase

Public Attributes inherited from mgrid::MultigridBase

Type	Name
int	coarsestLevel Level index of the coarsest grid (always 0).
int	finestLevel Level index of the finest grid.

Public Functions

Type	Name
	NonlinearMultigrid (const Settings & settings) Builds the solver state from `settings` .
virtual void	multigrid () override Runs the FAS full-multigrid cycle.
	~NonlinearMultigrid () override Defaulted polymorphic destructor.

Public Functions inherited from mgrid::MultigridBase

See mgrid::MultigridBase

Type	Name
	MultigridBase (const Settings & settings) Builds the solver state from `settings` .
virtual double	differential_operator (Level level, int i, int j) = 0 Evaluates the discrete PDE operator at one grid point.
void	evaluate_operator (Level level, FDArray & result) Evaluates the discrete operator over `result` .
void	evaluate_residual (Level level, FDArray & result) Evaluates the residual `source - operator(solution)` over`result` .
virtual std::string	filename (std::string root="") = 0 Builds the output file name for this problem.
bool	fully_periodic () const True when both axes of the grid hierarchy wrap periodically.
FDArray &	get_result () The current solution on the finest grid.
void	initial_guess (T arg) Sets the finest-level initial guess and flags it as provided.
virtual void	multigrid () Runs the multigrid cycle.
void	relax (Level level, unsigned long n) Smooths `solution[level]` with a fixed number of sweeps.
void	relax (Level level, double tolerance) Smooths `solution[level]` until the relative change falls below`tolerance` or`maxIterations` sweeps have run.
virtual void	relaxation_updater (Level level, int i, int j) = 0 Applies one in-place relaxation update at a single grid point.
virtual void	solve () Solves the problem.
FDArray &	source_term () Accesses the finest-level source term.
void	source_term (T arg) Sets the finest-level source term and flags it as provided.
virtual void	write (int numOfVariables, std::string root="") Writes the finest-level solution (and optional derived fields) to a netCDF-4 file.
virtual	~MultigridBase () = default Defaulted polymorphic destructor.

Protected Attributes

Type	Name
Stack	rightHandSide Per-level right-hand side (vestigial; retained from the legacy class).
Stack	truncError Per-level relative truncation error `L R u - R L u` .

Protected Attributes inherited from mgrid::MultigridBase

See mgrid::MultigridBase

Type	Name
const double	aspect Domain aspect ratio.
const int	cycleType FMG cycle type (V / W / three).
bool	initialIsSet = `{false}` Has an initial guess been provided?
const unsigned long	maxIterations Cap on relax-to-tolerance sweeps.
int	nxfine = `{0}`
int	nzfine = `{0}` Finest-grid extents (rows, columns).
const unsigned long	postRelax Post-correction relaxation sweeps.
const unsigned long	preRelax Pre-correction relaxation sweeps.
const double	residualTolerance Convergence tolerance for the solver.
Stack	solution
Stack	source
bool	sourceIsSet = `{false}` Has a source term been provided?
Stack	temp Solution, source and scratch grid hierarchies.

Protected Functions inherited from mgrid::MultigridBase

See mgrid::MultigridBase

Type	Name
void	mark_source_set () Flags the source term as set without touching its array.
virtual void	on_cycle_end (double residual_norm)

Detailed Description

Drives a nonlinear elliptic PDE to its discrete solution with a full multigrid cycle in which every level carries the full solution (not just a correction): the solution and source are restricted down the hierarchy, the coarsest level is solved, and each successively finer level is reached by interpolation followed by Settings::mgCycleType FAS cycles. On the downstroke each coarse level is given a corrected right-hand side R f + (L R u - R L u) (the relative-truncation-error correction) so that the coarse problem shares the fine solution as its fixed point; the upstroke applies the coarse-grid correction I (u_2h - R u_h). A concrete subclass supplies the discrete PDE by overriding differential_operator, relaxation_updater and filename; this class only implements the cycle.

Note:

Modernised from the 2011 mgrid::NonlinearMultigrid: the finestLevel / coarsestLevel locals that shadowed the MultigridBase members are dropped (the base's members are used directly), not is spelled !, and the commented-out dead blocks are removed. The cycle body is otherwise transcribed verbatim from multigrid_nonlinear.cpp.

Public Functions Documentation

function NonlinearMultigrid

Builds the solver state from settings .

inline explicit mgrid::NonlinearMultigrid::NonlinearMultigrid (
    const Settings & settings
)

Parameters:

settings solver configuration, forwarded to MultigridBase; also sizes the extra truncError and rightHandSide grid hierarchies.

function multigrid

Runs the FAS full-multigrid cycle.

virtual void mgrid::NonlinearMultigrid::multigrid () override

Note:

No-op unless a source term has been provided. Restricts the solution and source to the coarsest level, solves there, then sweeps up the hierarchy running Settings::mgCycleType FAS cycles at each level.

Note:

FAS: coarse levels carry a corrected right-hand side R f + (L R u - R L u), so the coarse operator has the restricted fine solution as its fixed point.

Implements mgrid::MultigridBase::multigrid

function ~NonlinearMultigrid

Defaulted polymorphic destructor.

mgrid::NonlinearMultigrid::~NonlinearMultigrid () override

Protected Attributes Documentation

variable rightHandSide

Per-level right-hand side (vestigial; retained from the legacy class).

Stack mgrid::NonlinearMultigrid::rightHandSide;

variable truncError

Per-level relative truncation error L R u - R L u .

Stack mgrid::NonlinearMultigrid::truncError;

The documentation for this class was generated from the following file include/multigrid/multigrid_nonlinear.hpp