Unsymmetrical and Symmetrical Sparse Iterative Algorithm with Multiple Right- Hand - Sides Strategies
نویسنده
چکیده
Unified unsymmetrical and symmetrical iterative solvers for handling multiple right-hand-side vectors are examined in this work. Efficient computer implementation strategies (to reduce computational time and in-core memory requirements) are proposed. In-core, out-of-core, linear, multiple right hand side (RHS) vectors, non-linear, symmetrical, and unsymmetrical capabilities of the developed software are demonstrated by solving variety of problems selected form different engineering disciplines. Results indicate that the developed algorithm and software is reliable and efficient. Key-Words: Sparse, Iterative, Linear, Nonlinear, Conjugate Gradient, Multiple RHS vectors.
منابع مشابه
New variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs
In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...
متن کاملBlock Krylov Space Methods for Linear Systems with Multiple Right-hand Sides: an Introduction
In a number of applications in scientific computing and engineering one has to solve huge sparse linear systems of equations with several right-hand sides that are given at once. Block Krylov space solvers are iterative methods that are especially designed for such problems and have fundamental advantages over the corresponding methods for systems with a single right-hand side: much larger sear...
متن کاملTwo Algorithms for Symmetric Linear Systems with Multiple Right-hand Sides
In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple right-hand sides, and show how to incorporate deeation to drop converged linear systems using a natural convergence criterion, and present an adaptive block Lanczos algorithm. We propose also a block version of Paige and Saun-ders' MINRES method for iterative solution of sym...
متن کاملBlock Algorithms for Quark Propagator Calculation
Computing quark propagators in lattice QCD is equivalent to solving large, sparse linear systems with multiple right-hand sides. Block algorithms attempt to accelerate the convergence of iterative Krylov-subspace methods by solving the multiple systems simultaneously. This paper compares a block generalisation of the quasi-minimal residual method (QMR), Block Conjugate Gradient on the normal eq...
متن کاملProduct Hybrid Block GMRES for Nonsymmetrical Linear Systems with Multiple Right-hand Sides
Recently, the complementary behavior of restarted GMRES has been studied. We observed that successive cycles of restarted block BGMRES (BGMRES(m,s)) can also complement one another harmoniously in reducing the iterative residual. In the present paper, this characterization of BGMRES(m,s) is exploited to form a hybrid block iterative scheme. In particular, a product hybrid block GMRES algorithm ...
متن کامل