Jiangning Qin

A parallel-vector equation solver for unsymmetric matrices on supercomputers

Abstract A parallel-vector unsymmetric equation solver is presented. The solver exploits both vector and parallel capabilities provided by modern, high-performance supercomputers. A special storage scheme and loop-unrolling technique are used to optimize the vector performance. A parallel FORTRAN language is used to develop the solver on the CRAY 2 and CRAY Y-MP multiple processing computer environment. Three numerical examples are presented which demonstrate the efficiency and accuracy of this equation solver. The first two examples demonstrate the improved performance, and the third example utilizes the proposed solver to solve a highly non-linear, unsymmetric finite element formulation for panel flutter.

A new parallel-vector finite element analysis software on distributed-memory computers

A new parallel-vector finite element analysis software package MPFEA (Massively Parallel-vector Finite Element Analysis) is developed for large-scale structural analysis on massively parallel computers with distributed-memory. MPFEA is designed for parallel generation and assembly of the global finite element stiffness matrices as well as parallel solution of the simultaneous linear equations, since these are often the major time-consuming parts of a finite element analysis. Block-skyline storage scheme along with vector-unrolling techniques are used to enhance the vector performance. Communications among processors are carried out concurrently with arithmetic operations to reduce the total execution time. Numerical results on the Intel iPSC/860 computers (such as the Intel Gamma with 128 processors and the Intel Touchstone Delta with 512 processors) are presented, including an aircraft structure and some very large truss structures, to demonstrate the efficiency and accuracy of MPFEA. 9 refs.

A tridiagonal solver for massively parallel computers

This paper describes a tridiagonal solver for solving large systems of linear equations on massively parallel computers. Assume using NP processors, then the original tridiagonal matrix is divided into NP portions by NP-1 separators, with each processor storing one portion and the NP-1 separators. Communications are needed only for those arithmetic operations involved with the NP-1 separators. Numerical performance of this solver in solving 38.4 million equations on 128 Intel iPSC/860 processors (Gamma) is presented, which shows a speedup of more than 98.

A parallel-vector equation solver for distributed-memory computers

Abstract A parallel-vector equation solver is presented for solving large linear systems of equations on computers with distributed memory. Block-skyline storage scheme along with vector-unrolling techniques are used to enhance the vector performance. Communications among processors are carried out concurrently with arithmetic operations to reduce the total execution time. Numerical results (including solving an aircraft structure) on the Intel iPSC/860 parallel-vector computer are presented to demonstrate the efficiency and accuracy of the proposed equation solver.

A Parallel-Vector Simplex Algorithm on Distributed-Memory Computers

In this paper, a parallel-vector simplex algorithm is developed for solving large-scale linear programming problems on distributed-memory computers. The algorithm uses the column storage scheme to enhance its overall performance. The effect of using different pivot rules on the performance of the simplex method on high-performance computers is also studied.

Subspace and Lanczos sparse eigen-solvers for finite element structural and electromagnetic applications

Abstract Recent developments in vectorized sparse technologies are incorporated into the Subspace and Lanczos iteration algorithms for computational enhancements. Numerical evaluations of the proposed sparse strategies for Subspace and Lanczos iteration algorithms are conducted by solving the generalized eigen-value problem associated with the Exxon-off-shore structure, HSCT aircraft and a two-dimensional reverberation chamber for electromagnetic applications. Both real and complex numbers eigen-problems can be treated.

Finite element-boundary integral methods in electromagnetics

Mixed sparse-dense, symmetrical-unsymmetrical direct equation solution algorithms are developed, and utilized to fully exploit the special characteristics of the coefficient matrix of system of linear (complex numbers) simultaneous equations. Numerical performance of the developed software is conducted, by performing a simplified Northrop-Grumman finite element-integral equation cavity model on the IBM-R6000/590 workstation.

Computational aspects of linear programming Simplex method

Abstract In this paper, the Simplex method is re-examined from the computational view points. Efficient numerical implementation for the Simplex procedure is suggested. Special features of artificial variables, and variables with unrestriction in signs are exploited to reduce the com-putational efforts, and computer memory requirement. The developed Simplex code has been tested on several examples, and its performance has been compared with existing Simplex codes.

Structure/load-dependent vectors for linear structural dynamic analysis

Abstract A structure/load-dependent vectors method is developed for large-scale, linear structural dynamic analysis with complex loadings. The dynamic solution vectors are used as starting vectors so that both structure and load characteristics are included in the basis vectors. This method requires less vectors for the same accuracy, especially for structures that have external concentrated masses. Numerical results are obtained to demonstrate the advantages of the present method over other reduction methods.

Parallel-vector out-of-core equation solver for computational mechanics

Abstract A parallel/vector out-of-core equation solver is developed for shared-memory computers, such as the Cray Y-MP machine. The input/output (I/O) time is reduced by using the a synchronous BUFFER IN and BUFFER OUT, which can be executed simultaneously with the CPU instructions. The parallel and vector capability provided by the supercomputers is also exploited to enhance the performance. Numerical applications in large-scale structural analysis are given to demonstrate the efficiency of the present out-of-core solver.