A new row-wise parallel finite element analysis algorithm (RWPFEA) with dynamic load balancing

Ammar Taher Al-Sayegh, Purdue University

Abstract

This research is concerned with the parallel finite element analysis (PFEA) of structures. For structural engineering problems, parallelization has been typically accomplished by one, or possibly a combination of three types of algorithms; namely: node-wise algorithms, element-wise algorithms, and domain-wise algorithms. These algorithms focus on partitioning schemes that optimize one of the solution steps in PFEA, while the other steps are parallelized without optimization, or not parallelized at all. In this work, a parallel scheme is devised that efficiently parallelizes all steps of PFEA. This work introduces a new approach that considers the four steps of nonlinear finite element analysis. (i) element state determination, (ii) assembly, (iii) application of boundary conditions, and (iv) solution of the governing system of equations, as computational units. A computational unit has processing, storage, and communication requirements. It can be partitioned into blocks of rows. Each block of rows in these processing units is contained within a separate computing processor. Using this paradigm, a procedure is devised that minimizes inter-processor communication, reduces data redundancy, and balances computational workload among processor by migrating rows from one block to another. The new Row-Wise PFEA (RWPFEA) algorithm is based on a row-wise matrix distribution. Thus, it is capable of exploiting the nature of distributed compressed row sparse (CRS) matrices and multivectors to improve concurrency. As part of this research a new dynamic load balancing (DLB) technique has also been devised. The DLB technique has been designed specifically to balance the computational workload among processors most suited for nonlinear analysis of structures. This new algorithm has been implemented in ParaStruc, a parallel structural analysis system, which has been built on Trilinos, a set of parallel numerical libraries developed by researchers in the Sandia National Laboratory. ParaStruc is a lightweight fully parallelized PFEA system, which contains only two classes, a preprocessor, a postprocessor, and a math library. Preliminary studies have shown this to be a promising approach, since superior performance advantage in terms of speedup, efficiency, and isoefficiency has been achieved in the nonlinear analysis of structures under static and dynamic response. The performance and efficiency of this algorithm has been verified with numerical simulations of a high-rise 3-D building structure. The results of ParaStruc have been compared with those obtained using the ABAQUS, which is a leading commercial finite element analysis software with parallel processing and dynamic load balancing capabilities. Finally, the performance of the proposed parallel system is studied for two types of parallel architectures, namely, shared memory and distributed memory systems. It is found that its performance is excellent in both architectures. However, in general, the performance in the distributed memory system is superior to that in the shared memory system. This is because the additional local memory inherent to these systems positively affects the performance of the memory-dependent state determination step, which is the most time consuming step in the analysis.

Degree

Ph.D.

Advisors

Liu, Purdue University.

Subject Area

Civil engineering|Computer science

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