Case Studies on The Development of ScaLAPACK and the NAG Numerical PVM Library

In this paper we look at the development of ScaLAPACK, a software library for dense and banded numerical linear algebra, and the NAG Numerical PVM Library, which includes software for dense and sparse linear algebra, quadrature, optimization and random number generation. Both libraries are aimed at distributed memory machines, including networks of workstations. The paper concentrates on the underlying design and the testing of the libraries. Keywords BLAS, LAPACK, NAG, numerical libraries, numerical linear algebra, numerical software, ScaLAPACK 2 Case Studies on The Development of ScaLAPACK and the NAG Numerical PVM Library 1 INTRODUCTION This paper looks at the development of two software libraries aimed at distributed memory machines, ScaLAPACK and the NAG Numerical PVM Library y , concentrating on the underlying design of the libraries and issues concerned with testing the components of the libraries. The development of ScaLAPACK, and related software, had a strong influen..

Nonlinear solid mechanics analysis using the parallel selective element-free Galerkin method

A variety of meshless methods have been developed in the last fifteen years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The main objective of this thesis is the development of an efficient and accurate algorithm based on meshless methods for the solution of problems involving both material and geometrical nonlinearities, which are of practical importance in many engineering applications, including geomechanics, metal forming and biomechanics. One of the most commonly used meshless methods, the element-free Galerkin method (EFGM) is used in this research, in which maximum entropy shape functions (max-ent) are used instead of the standard moving least squares shape functions, which provides direct imposition of the essential boundary conditions. Initially, theoretical background and corresponding computer implementations of the EFGM are described for linear and nonlinear problems. The Prandtl-Reuss constitutive model is used to model elasto-plasticity, both updated and total Lagrangian formulations are used to model finite deformation and consistent or algorithmic tangent is used to allow the quadratic rate of asymptotic convergence of the global Newton-Raphson algorithm. An adaptive strategy is developed for the EFGM for two- and three-dimensional nonlinear problems based on the Chung & Belytschko error estimation procedure, which was originally proposed for linear elastic problems. A new FE-EFGM coupling procedure based on max-ent shape functions is proposed for linear and geometrically nonlinear problems, in which there is no need of interface elements between the FE and EFG regions or any other special treatment, as required in the most previous research. The proposed coupling procedure is extended to become adaptive FE-EFGM coupling for two- and three-dimensional linear and nonlinear problems, in which the Zienkiewicz & Zhu error estimation procedure with the superconvergent patch recovery method for strains and stresses recovery are used in the FE region of the problem domain, while the Chung & Belytschko error estimation procedure is used in the EFG region of the problem domain. Parallel computer algorithms based on distributed memory parallel computer architecture are also developed for different numerical techniques proposed in this thesis. In the parallel program, the message passing interface library is used for inter-processor communication and open-source software packages, METIS and MUMPS are used for the automatic domain decomposition and solution of the final system of linear equations respectively. Separate numerical examples are presented for each algorithm to demonstrate its correct implementation and performance, and results are compared with the corresponding analytical or reference results

Case studies on the development of ScaLAPACK and the NAG Numerical PVM Library

In this paper we look at the development of ScaLAPACK, a software library for dense and banded numerical linear algebra, and the NAG Numerical PVM Library, which includes software for dense and sparse linear algebra, quadrature, optimization and random number generation. Both libraries are aimed at distributed memory machines, including networks of workstations. The paper concentrates on the underlying design and the testing of the libraries