EST MINRES: An Optimal Iterative Solver for Symmetric Indefinite Systems stemming from Mixed Approximation
نویسندگان
چکیده
We discuss the design and implementation of a suite of functions for solving symmetric indefinite linear systems associated with mixed approximation of systems of PDEs. The novel feature of our iterative solver is the incorporation of error control in the natural “energy” norm in combination with an a posteriori estimator for the PDE approximation error. This leads to a robust and optimally efficient stopping criterion: the iteration is terminated as soon as the algebraic error is insignificant compared to the approximation error. We describe a “proof of concept” MATLAB implementation of this algorithm and we illustrate its effectiveness when integrated into the Incompressible Flow Iterative Solution Software (IFISS) package (cf. ACM Transactions on Mathematical Software 33, Article 14, 2007).
منابع مشابه
New Krylov-subspace Solvers for Hermitian Positive Definite Matrices with Indefinite Preconditioners
Incomplete LDL∗ factorizations sometimes produce an inde nite preconditioner even when the input matrix is Hermitian positive de nite. The two most popular iterative solvers for Hermitian systems, MINRES and CG, cannot use such preconditioners; they require a positive de nite preconditioner. We present two new Krylov-subspace solvers, a variant of MINRES and a variant of CG, both of which can b...
متن کاملSolving Hermitian positive definite systems using indefinite incomplete factorizations
Incomplete LDL factorizations sometimes produce an indefinite preconditioner evenwhen the input matrix is Hermitian positive definite. The two most popular iterative solvers for symmetric systems, CG and MINRES, cannot use such preconditioners; they require a positive definite preconditioner. One approach, that has been extensively studied to address this problem is to force positive definitene...
متن کاملALGORITHM & DOCUMENTATION: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems pdfsubject=MINRES-QLP for indefinite or singular symmetric systems
We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-...
متن کاملALGORITHM & DOCUMENTATION: MINRES-QLP for Singular Symmetric and Hermitian Linear Equations and Least-Squares Problems pdfsubject=MINRES-QLP for indefinite or singular symmetric systems
We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-...
متن کاملThe Mixed Finite Element Multigrid Method for Stokes Equations
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution o...
متن کامل