Fast Direct Solvers for Elliptic PDEs

Fast Direct Solvers for Elliptic PDEs
Author :
Publisher : SIAM
Total Pages : 332
Release :
ISBN-10 : 9781611976045
ISBN-13 : 1611976049
Rating : 4/5 (049 Downloads)

Book Synopsis Fast Direct Solvers for Elliptic PDEs by : Per-Gunnar Martinsson

Download or read book Fast Direct Solvers for Elliptic PDEs written by Per-Gunnar Martinsson and published by SIAM. This book was released on 2019-12-16 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.


Fast Direct Solvers for Elliptic PDEs Related Books

Fast Direct Solvers for Elliptic PDEs
Language: en
Pages: 332
Authors: Per-Gunnar Martinsson
Categories: Mathematics
Type: BOOK - Published: 2019-12-16 - Publisher: SIAM

DOWNLOAD EBOOK

Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, bioc
Fast Direct Solvers for Elliptic PDEs
Language: en
Pages:
Authors: Per-Gunnar Martinsson
Categories: Differential equations, Elliptic
Type: BOOK - Published: 2019 - Publisher:

DOWNLOAD EBOOK

"This is a book about how to efficiently solve elliptic partial differential equations numerically"--
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1
Language: en
Pages: 571
Authors: Jens M. Melenk
Categories: Mathematics
Type: BOOK - Published: 2023-06-30 - Publisher: Springer Nature

DOWNLOAD EBOOK

The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles co
PETSc for Partial Differential Equations: Numerical Solutions in C and Python
Language: en
Pages: 407
Authors: Ed Bueler
Categories: Mathematics
Type: BOOK - Published: 2020-10-22 - Publisher: SIAM

DOWNLOAD EBOOK

The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and non
A Tutorial on Elliptic PDE Solvers and Their Parallelization
Language: en
Pages: 153
Authors: Craig C. Douglas
Categories: Technology & Engineering
Type: BOOK - Published: 2003-01-01 - Publisher: SIAM

DOWNLOAD EBOOK

This compact yet thorough tutorial is the perfect introduction to the basic concepts of solving partial differential equations (PDEs) using parallel numerical m