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.
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.
This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an...
This book deals with the general topic "Numerical solution of partial differential equations (PDEs)" with a focus on adaptivity of discretizations in space and time. By and large, introductory...
The remarkable functionality of the brain is made possible by the metabolism (chemical reaction) of oxygen (O?) and nutrients in the brain. These metabolism components are supplied to the brain by an...
The present volume contains selected papers issued from the sixth edition of the International Conference "Numerical methods for hyperbolic problems" that took place in 2019 in Málaga (Spain). NumHyp...
Stochastic partial differential equations (PDE) are widely used in modeling complex phenomena of fluid dynamics, random media, materials science, chemistry, biology, etc, where large structures and...
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