Abstract
Linear systems of equations resulting from finite element discretizations of partial differential equations are typically large, sparse, and ill-conditioned. Their efficient numerical solution exploits properties of the underlying continuous problem or a sequence of discretizations. The chapter discusses multigrid, domain decomposition, and preconditioning methods.
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Notes
- 1.
Fundamental contributions to the development of multigrid methods, preconditioning of finite element matrices, and domain decomposition methods are the articles [2–4, 6, 9, 12, 18]. Specialized textbooks on the subjects are the references [7, 10, 11, 13, 15, 16]. The historical development of domain decomposition methods is recapitulated in [8], and the survey article [17] discusses various aspects of preconditioning techniques. Chapters on iterative solution methods are contained in the textbooks [1, 5, 14].
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Bartels, S. (2016). Iterative Solution Methods. In: Numerical Approximation of Partial Differential Equations. Texts in Applied Mathematics, vol 64. Springer, Cham. https://doi.org/10.1007/978-3-319-32354-1_5
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