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Efficiency of sparse symmetric matrix solvers in finite element analysis
Thesis   Open access

Efficiency of sparse symmetric matrix solvers in finite element analysis

Jay Janak Bhatt
Master of Science (M.S.), Drexel University
Jun 1985
DOI:
https://doi.org/10.17918/00001902
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Abstract

In the computer aided design of electromagnetic devices using finite element analysis, the largest computing effort is in solving a sparse, positive definite, symmetric matrix and therefore computational efficiency is the major requirement in solving these problems. Here, the solution time varies as an exponent of matrix size and for many practical problems can vary from a few seconds to days. It is, therefore, logical to seek to bring down the solution time to make CAD more practicable. This thesis introduces a faster method of solution which couples the renumbering scheme used with direct decomposition schemes of solution and the Evan's Conjugate gradient method. By this method, for example, at matrix size 190, the solution time is cut down from 431.33 s in Evan's method without renumbering to 353.13 s in Evan's method with renumbering. The new method is implemented on the package Kantham, which forms a part of the ECE departmental facilities at Drexel university, for the solution of Poisson's equations. Having achieved this thesis's basic goal of making Kantham run faster, the new method is compared with other existing methods of solution in the context of solution time and memory requirements.

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