Reliable iterative methods for solving ill-conditioned algebraic systems
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[Nijmegen] : Katholieke Universiteit Nijmegen
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The finite element method is one of the most popular techniques for numerical solution of partial differential equations. The rapid performance increase of modern computer systems makes it possible to tackle increasingly more difficult finite-element models arising in engineering practice. However, the growth in the scale of finite-element applications is not as fast as one would desire. The problem is that some important numerical algorithms do not scale well with increasing problem size. One of the bottlenecks which limits the use of finite-element modelling are linear equation solvers. This problem is addressed in the present thesis. We develop and investigate a number of numerical algorithms for efficient solving large-scale algebraic systems (with 100.000 or more unknowns) which arise in certain finite-element applications. A special attention is payed to ensuring robustness of the solvers with respect to problem and discretisation parameters
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