Anderson Acceleration for Numerical PDEs
Published on 31. August 2025
Book
Paperback/Softback
114 pages
978-1-61197-848-3 (ISBN)
Description
Research on the Anderson Acceleration (AA) has exploded in the last 15 years. This book brings together these recent fundamental results applied to nonlinear solvers for PDEs, which are ubiquitous across mathematics, science, engineering, and economics as predictive models for a vast quantity of important phenomena. Coverage includes:
AA convergence theory for both contractive and non-contractive operators,
filtering techniques for AA, showing how the convergence theory can be fit to various application problems, and
AA's effect on sublinear convergence, and
how AA can be best combined with Newton's method.
The authors provide proofs of the main theorems and results of many of the test examples. Code for the test examples is provided in an online repository.
Audience
Anderson Acceleration for Numerical PDE is intended for mathematicians, scientists, and engineers who solve nonlinear problems when Newton's method either fails or is inefficient. Graduate students in applied mathematics and computational science will also find the book useful. It has sufficient theory and coding for use in a second-year graduate course.
AA convergence theory for both contractive and non-contractive operators,
filtering techniques for AA, showing how the convergence theory can be fit to various application problems, and
AA's effect on sublinear convergence, and
how AA can be best combined with Newton's method.
The authors provide proofs of the main theorems and results of many of the test examples. Code for the test examples is provided in an online repository.
Audience
Anderson Acceleration for Numerical PDE is intended for mathematicians, scientists, and engineers who solve nonlinear problems when Newton's method either fails or is inefficient. Graduate students in applied mathematics and computational science will also find the book useful. It has sufficient theory and coding for use in a second-year graduate course.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
ISBN-13
978-1-61197-848-3 (9781611978483)
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Schweitzer Classification
Persons
Sara Pollock is an Associate Professor of Mathematics at the University of Florida. She has a wide range of research interests relating to the development and analysis of efficient and accurate computational methods. Her most recent work has produced new fundamental results on acceleration methods for discretized nonlinear partial differential equations and for eigenvalue problems. She was recipient of the prestigious NSF CAREER award in 2021. In addition to mathematics she is also a classically trained artist. In her free time, she enjoys nature, gardening, cats - both wild and domestic - baking, and home improvement.
Leo Rebholz is Dean's Distinguished Professor of Mathematical Sciences at Clemson University. He works on numerical methods to solve partial differential equations, and his recent research has focused on improving nonlinear solvers through the development of acceleration methods and data assimilation techniques. He has published over 130 research papers and five books. Outside of mathematics and research, he enjoys golfing, boating, libations, billiards, and travel.
Leo Rebholz is Dean's Distinguished Professor of Mathematical Sciences at Clemson University. He works on numerical methods to solve partial differential equations, and his recent research has focused on improving nonlinear solvers through the development of acceleration methods and data assimilation techniques. He has published over 130 research papers and five books. Outside of mathematics and research, he enjoys golfing, boating, libations, billiards, and travel.