#include <jdbsym.hh>

Inheritance diagram for eigensolver::JdbSym:

Public Member Functions
	JdbSym (concepts::Operator< Real > &stiff, concepts::Operator< Real > &mass, Real tol, uint maxit=150, Real tau=0.0, uint jdtype=1, uint kmax=1, concepts::SolverFabric< Real > fabric=0, const concepts::Array< concepts::Vector< Real > > *start=0)

virtual const concepts::Array< Real > &	getEV ()

virtual const concepts::Array< concepts::Vector< Real > * > &	getEF ()

virtual uint	iterations () const
	Returns the number of iterations.

virtual uint	converged () const
	Returns the number of converged eigen pairs.

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.

Detailed Description

Eigenvalue solver using JDBSYM.

JDBSYM is an implementation of the Jacobi-Davidson method optimized for symmetric eigenvalue problems. It solves eigenproblems of the form $A x = \lambda x$ and $A x = \lambda B x$ with or without preconditioning, where A is symmetric and B is symmetric positive definite. The implementation supports blocking.

See also: Roman Geus and Oscar Chinellato, JDBSYM 0.14, 2000.; Roman Geus. The Jacobi-Davidson algorithm for solving large sparse symmetric eigenvalue problems with application to the design of accelerator cavities. PhD thesis 14734, Swiss Federal Institute of Technology Zurich, 2002.

Test:

test::GolubExample

test::GolubExampleSum

test::MaxwellTransmissionEVP

Author: Norbert Fernandes, 2002

Definition at line 48 of file jdbsym.hh.

Constructor & Destructor Documentation

◆ JdbSym()

eigensolver::JdbSym::JdbSym	(	concepts::Operator< Real > &	stiff,
		concepts::Operator< Real > &	mass,
		Real	tol,
		uint	maxit = `150`,
		Real	tau = `0.0`,
		uint	jdtype = `1`,
		uint	kmax = `1`,
		concepts::SolverFabric< Real > *	fabric = `0`,
		const concepts::Array< concepts::Vector< Real > * > *	start = `0`
	)

Constructor. Initializes the JdbSym class. As parameter it takes the few most important variables that are needed for the Jacobi-Davidson algorithm. The rest of the parameters are given as default and work in most cases. The class then solves the problem $A x = \lambda B x$ where A, B are the stiffness and the mass matrices respectively.

The computation is only perfomed if getEV or getEF is called.

Parameters

stiff	Stiffness matrix A
mass	Mass matrix B
fabric	Solver fabric for a linear solver (preconditioner for the shifted stiffness matrix)
tol	Convergence tolerance for the eigenpairs. For a pair $(\lambda, u)$ convergence is defined by $\\| A u - \lambda B u \\| < tol$
maxit	Maximal number of iterations
tau	Target value of Jacobi-Davidson algorithm. The code will find the `kmax` eigenvalues closest to `tau`.
jdtype	Type of solver required. An older solver and a newer solver are possible to use.
kmax	Number of eigenpairs to be computed
start	Starting vectors. Used to build the initial search subspace