Fast direct solvers for elliptic PDEs /
Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes and much more. This textbook provides an introduction to such solvers from the point of view of integral equation formulat...
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| Format: | Book |
| Language: | English |
| Published: |
Philadelphia :
Society for Industrial and Applied Mathematics,
[2020]
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| Series: | CBMS-NSF regional conference series in applied mathematics ;
96. |
| Subjects: |
Table of Contents:
- Scope and aims
- How global operators rise in solvers for elliptic PDEs
- I. Linear algebra
- Matrix factorizations and low-rank approximation
- Randomized methods for low-rank approximation
- Fast algorithms for rank-structured matrices
- II. The fast multipole method
- Fast summation and multipole expansions
- The fast multipole method
- Extensions and improvements to the basic FMM
- The potential evaluation map
- III. Integral equation methods
- Integral equation formulations
- Extensions of integral equation-based methods
- Discretization of integral equations
- IV. Fast direct solvers for integral equations
- A simple direct solver for integral equations
- A multilevel scheme
- Additional topics on HBS matrices
- Interpolative decompositions and skeletonization
- Constructing a rank-structured representation of a matrix
- Direct solvers based on discrete scattering matrices
- V. Fast direct solvers for sparse matrices
- An introduction to fast solvers for linear elliptic PDEs
- Direct sparse solvers
- Fast direct sparse solvers
- Linear complexity "sweeping" schemes
- A geometry-based view of nested dissection
- Spectral collocation methods
- The hierarchical Poincaré-Steklove (HPS) method
- Extensions of the HPS method
- Fast solvers for elliptic problems on lattices.