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Published in:
2006 | OriginalPaper | Chapter
Solving Linear Systems
Authors : Joakim Sundnes, Glenn Terje Lines, Xing Cai, Bjørn Fredrik Nielsen, Kent-Andre Mardal, Aslak Tveito
Published in: Computing the Electrical Activity in the Heart
Publisher: Springer Berlin Heidelberg
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The physical relevance of computations based on the model problems arising from the electrical activity in the heart depends on high accuracy of the solution. High accuracy requires the solution of large linear or nonlinear systems of ODEs and PDEs. This chapter deals with solution algorithms for the discretization of (linear) PDEs, which is a huge research field around the world. Much of the research in this field has been centred around simple model problems such as the Poisson problem, where a solid theoretical framework has been developed. We will briefly review this theory in the simplest possible manner. Then, at the end of the chapter, we explain how the powerful concept of (block) preconditioning extends these algorithms to systems of PDEs that arise from the discretization of the Bidomain model.