Domain Decomposition Based High Performance Parallel Computing\ud

The study deals with the parallelization of finite element based Navier-Stokes codes using domain decomposition and state-ofart sparse direct solvers. There has been significant improvement in the performance of sparse direct solvers. Parallel sparse direct solvers are not found to exhibit good scalability. Hence, the parallelization of sparse direct solvers is done using domain decomposition techniques. A highly efficient sparse direct solver PARDISO is used in this study. The scalability of both Newton and modified Newton algorithms are tested

Solution of linear systems with sparse matrices

For large scale problems in electric circuit simulation as well as in chemical process simulation, the linear solver often needs about 50 - 80 % of the total amount of computing time. For that purpose, we consider direct methods for the numerical solution of linear systems of equations with unsymmetric sparse coefficient matrices. The Gaussian elimination method is applied to solve the linear system. Here, the row permutation is used to provide numerical stability and the column permutation is chosen to control sparsity. In a new approach, implemented in the solver GSPAR2, the determination of the pivot columns is done with a modified algorithm, which has only a complexity of O(n). A partial pivoting technique is used to maintain numerical stability. For solving several linear systems with the same pattern structure of the coefficient matrix efficiently, we generate a list of pseudo code instructions for the factorization of the matrices. With it, the solver GSPAR2 has been proven successful within the simulation of several real life problems. For a number of linear systems arising from different technical problems, the computing times of GSPAR2 are compared to that of some recently released linear solvers

Parallel Computation of Finite Element Navier-Stokes codes using MUMPS Solver

The study deals with the parallelization of 2D and 3D finite element based Navier-Stokes codes using direct solvers. Development of sparse direct solvers using multifrontal solvers has significantly reduced the computational time of direct solution methods. Although limited by its stringent memory requirements, multifrontal solvers can be computationally efficient. First the performance of MUltifrontal Massively Parallel Solver (MUMPS) is evaluated for both 2D and 3D codes in terms of memory requirements and CPU times. The scalability of both Newton and modified Newton algorithms is tested

Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers

In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system, and the design of data structures to take advantage of serial, coarse grain parallel and massively parallel computer architectures, are considered in detail. We put forward arguments as to why integration of the system within a sparse simplex solver is important and outline how the system is designed to achieve this integration