A sparse direct multifrontal solver in SCAD software

Content Provider	Semantic Scholar
Author	Fialko, Sergiy Yu . Kriksunov, Edward Z. Karpilovskyy, Viktor S.
Copyright Year	2003
Abstract	Abstract A sparse direct multi-frontal method (MFM) for solving large-scale finite element linear algebraic equations is presented. Both the minimum degree algorithm (MDA) and the nested dissection method (NDM) are applied to obtain a proper ordering of equations for reduction of fill-ins during the factorization. An automatic selection of a more efficient reordering method is based on a fast symbolic factorization. This method allows to essentially reduce the computing time comparing to the prevailing skyline solver based on a reverse Cuthill-McKee algorithm (RCM). The efficiency of the proposed approach is illustrated by numerous large-scale finite element models of real buildings. This method is implemented in the SCAD commercial software (http://www.scadgroup.com/eng/). Keywords: sparse, multi-frontal, ordering, frontal tree 1. Introduction Sparse direct methods [4] make a powerful tool for solution of large-scale finite element problems, especially when ill-conditioned problems need to be solved. In such case iterative methods show a slow convergence. An efficient direct method based on sparse reordering MDA (minimum degrees algorithm) or NDM (nested dissection method) approaches and the multi-frontal technique is presented here. The principal effort of the authors is aimed at a reduction of fillings in the course of the Gauss elimination procedure [4]. The attention is focused on the proposed solver implementations with commonly popular PCs to extend the capabilities of analysing real large-scale engineering problems and to reduce the cost of the finite element analysis. A properly chosen reordering method ensures the reduction of fillings during Gauss elimination or Choletsky factorization. The more fillings are reduced, the less the computational effort. The reverse Cuthill-McKee algorithm (RCM) is a prevailing reordering method which has been implemented in commercial finite element software until recently. The development of fast problem-oriented graphic pre-processors and automatic mesh generators causes the dimensions of finite element (FE) models to grow. For example, the usual size of SCAD client FE problems is about 90 000 - 300 000 degrees of freedom for today. Such large-scale problems require the implementation of advanced solution techniques because skyline solvers are still too much time-consuming. An alternative approach is to use sparse direct solvers which appear to be more efficient even than the profile reduction techniques based on Sloan or spectral reordering methods [ 3]. The multi-frontal solution technique [1],[2],[3],[5] proves to be convenient for implementing in commercial and research FE software.
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Language	English
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Content Type	Text
Resource Type	Article