Duc T. Nguyen

An algorithm for domain decomposition in finite element analysis

Abstract A simple and efficient algorithm is described for automatic decomposition of an arbitrary finite element domain into a specified number of subdomains for finite element and substructuring analysis in a multi-processor computer environment. The algorithm is designed to balance the work loads, to minimize the communication among processors and to minimize the bandwidths of the resulting system of equations. Small- to large-scale finite element models, which have two-node elements (truss, beam element), three-node elements (triangular element) and four-node elements (quadrilateral element), are solved on the Convex computer to illustrate the effectiveness of the proposed algorithm. A FORTRAN computer program is also included.

Parallel-vector solution of large-scale structural analysis problems on supercomputers

This direct method is based on the Choleski factorization procedure and uses a skyline storage scheme. Unique features of the method include its parallel computation at the outermost DO-loop and vector computation at the innermost DO-loop

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

Abstract Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve , is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14–16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for non-linear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on non-linear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

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.

Personalized identification of abdominal wall hernia meshes on computed tomography

An abdominal wall hernia is a protrusion of the intestine through an opening or area of weakness in the abdominal wall. Correct pre-operative identification of abdominal wall hernia meshes could help surgeons adjust the surgical plan to meet the expected difficulty and morbidity of operating through or removing the previous mesh. First, we present herein for the first time the application of image analysis for automated identification of hernia meshes. Second, we discuss the novel development of a new entropy-based image texture feature using geostatistics and indicator kriging. Third, we seek to enhance the hernia mesh identification by combining the new texture feature with the gray-level co-occurrence matrix feature of the image. The two features can characterize complementary information of anatomic details of the abdominal hernia wall and its mesh on computed tomography. Experimental results have demonstrated the effectiveness of the proposed study. The new computational tool has potential for personalized mesh identification which can assist surgeons in the diagnosis and repair of complex abdominal wall hernias.

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.

Performance of NIKE3D with PVSOLVE on vector and parallel computers

Abstract The cost of large implicit finite element calculations is dominated by the linear equation solver. In this work, several versions of the direct linear equation solver PVSOLVE were implemented in the general purpose, nonlinear finite element code NIKE3D. Timing studies were performed on Sun and IBM workstations, CRAY Y/MP and C90 supercomputers, and the distributed memory MEIKO CS-2 parallel computer. Cost breakdowns and efficiency curves are presented for a benchmark problem with several mesh densities. The distributed memory implementation is shown to be most efficient for large problems, where MEIKO performance is comparable to that of a single CRAY processor.

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.