Synopsis
Understand how to solve tough elliptic problems with fast, scalable domain methods.
This book explains how to break a large, indefinite elliptic system into manageable pieces that can be solved in parallel, then stitched back together for accurate results.
Two-level domain decomposition is at the core. The author shows how coarse and fine meshes interact, and why a global coarse problem speeds up convergence. Readers will see theoretical guarantees for convergence and how these methods behave in practice with nonsymmetric, indefinite operators.- Learn additive Schwarz preconditioners and how they enable parallel computation on subregions.
- See how GMRES is used to solve the resulting linear systems and why spectrum placement matters.
- Explore two concrete algorithms and their convergence proofs, plus extensions to more levels of triangulation.
- Review numerical results that illustrate performance across different mesh sizes and overlap.
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