On the efficiency of generic BE substructuring algorithms based on Krylov solvers
نویسندگان
چکیده
This paper is concerned with the solution of boundary-element models based on substructuring. Structured matrix-vector products and the matrix-copy option are proposed to increase the efficiency of algorithms based on Krylov solvers. The former technique was designed to avoid the excessive number of conditional tests during solver iterations, and the latter one, to avoid the repeated calculation of coefficient matrices for identical subregions. Potential applications of the algorithm to composite materials, and to develop parallel codes, are noted.
منابع مشابه
Iterative Substructuring Methods for Spectral Element Discretizations of Elliptic Systems I: Compressible Linear Elasticity
An iterative substructuring method for the system of linear elasticity in three dimensions is introduced and analyzed. The pure displacement formulation for compressible materials is discretized with the spectral element method. The resulting stiiness matrix is symmetric and positive deenite. The method proposed provides a domain decomposition preconditioner constructed from local solvers for t...
متن کاملNew 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 کاملDevelopment of Krylov and AMG Linear Solvers for Large-Scale Sparse Matrices on GPUs
This research introduce our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for single GPU and multiple GPUs are implemented. A HEC matrix format and a communication mechanism are established. And also, a set of specific algorithms for solving preconditioned systems in parallel environments are designed, i...
متن کاملIterative Substructuring Methods for Spectral Element Discretizations of Elliptic Systems. II: Mixed Methods for Linear Elasticity and Stokes Flow
Iterative substructuring methods are introduced and analyzed for saddle point problems with a penalty term. Two examples of saddle point problems are considered: the mixed formulation of the linear elasticity system and the generalized Stokes system in three dimensions. These problems are discretized with spectral element methods. The resulting stiiness matrices are symmetric and indeenite. The...
متن کاملNew Solutions for Singular Lane-Emden Equations Arising in Astrophysics Based on Shifted Ultraspherical Operational Matrices of Derivatives
In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the eq...
متن کامل