Anderson Acceleration for Numerical PDEs

An in-depth exploration of Anderson Acceleration unites recent theoretical insights with practical methods to enhance nonlinear PDE solvers used in science, engineering, and economics. It details convergence for diverse operators, innovative filtering strategies, and blending AA with Newton’s method, supported by proofs and code.
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.

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