Includes bibliographical references (pages 301-311) and index.
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 matices -- 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 of lattices
Summary:
"This is a book about how to efficiently solve elliptic partial differential equations numerically"-- Provided by publisher.
Series:
CBMS-NSF regional conference series in applied math ; 96
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.