Anderson Acceleration for Numerical PDEs

Research on Anderson acceleration (AA) has surged over the last 15 years. This book compiles recent fundamental advancements in AA and its application to nonlinear solvers for partial differential equations (PDEs). These solvers play an important role across mathematics, science, engineering, and economics, serving as a critical technology for determining solutions to predictive models for a wide range of important phenomena. This book covers AA convergence theory for both contractive and noncontractive operators, as well as filtering techniques for AA. It includes examples of how convergence theory can be adapted to various application problems. It also includes AA’s impact on sublinear convergence and integration of AA with Newton’s method. The authors provide detailed proofs of key theorems and results from numerous test examples. Code for the examples is available in an online repository.

Sara Pollock is an associate professor of mathematics at the University of Florida. Her research focuses on developing and analyzing efficient and accurate computational methods. Her most recent work has contributed fundamental insights into acceleration methods for discretized nonlinear PDEs and eigenvalue problems. She was awarded the prestigious NSF CAREER award in 2021. Beyond mathematics, she is a classically trained artist, and enjoys nature, gardening, cats, baking, and home improvement.

Leo Rebholz is a Dean’s Distinguished Professor of Mathematical Sciences at Clemson University. His research centers on numerical methods for solving PDEs, with recent work improving nonlinear solvers through acceleration methods and data assimilation techniques. He has authored over 130 research papers and five books. Outside of mathematics and research, he enjoys golfing, boating, libations, billiards, and travel.