A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices.
A center of a polytope: An expository review and a parallel implementation.
A Decomposition-Dualization Approach for Solving Constraint Convex Minimization Problems with Applications to Discretized Obstacle Problems.
A Divide and Conquer Method for Unitary and Orthogonal Eigenproblems.
A Domain Decomposition Algorithm for Contact Problems: Analysis and Implementation
The paper deals with an iterative method for numerical solving frictionless contact problems for two elastic bodies. Each iterative step consists of a Dirichlet problem for the one body, a contact problem for the other one and two Neumann problems to coordinate contact stresses. Convergence is proved by the Banach fixed point theorem in both continuous and discrete case. Numerical experiments indicate scalability of the algorithm for some choices of the relaxation parameter.
A Fast Iterative Method for Solving Stationary Heat Conduction Problems on Regions Partitioned into Rectangles.
A fully parallel method for tridiagonal eigenvalue problem.
A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations
We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space spanned...
A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations
We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space WN spanned...
A nested decomposition algorithm for parallel computations of very large sparse systems.
A novel parallel algorithm based on the Gram-Schmidt method for tridiagonal linear systems of equations.
A parallel algorithm for computing the group inverse via Perron complementation.
A parallel algorithm for discrete least squares rational approximation.
A parallel algorithm for the eigenvalues and eigenvectors of a general complex matrix.
A parallel algorithm for two phase multicomponent contaminant transport
We discuss the formulation of a simulator in three spatial dimensions for a multicomponent, two phase (air, water) system of groundwater flow and transport with biodegradation kinetics and wells with multiple screens. The simulator has been developed for parallel, distributed memory, message passing machines. The numerical procedures employed are a fully implicit expanded mixed finite element method for flow and either a characteristics-mixed method or a Godunov method for transport and reactions...
A parallel AMG for overlapping and non-overlapping domain decomposition.
A parallel block Lanczos algorithm and its implementation for the evaluation of some eigenvalues of large sparse symmetric matrices on multicomputers
In the present work we describe HPEC (High Performance Eigenvalues Computation), a parallel software package for the evaluation of some eigenvalues of a large sparse symmetric matrix. It implements an efficient and portable Block Lanczos algorithm for distributed memory multicomputers. HPEC is based on basic linear algebra operations for sparse and dense matrices, some of which have been derived by ScaLAPACK library modules. Numerical experiments have been carried out to evaluate HPEC performance...
A parallel Cholesky algorithm for the solution of symmetric linear systems.
A parallel GMRES version for general sparse matrices.
A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods.