Numerical Approximations of Stochastic Maxwell Equations: via Structure-Preserving Algorithms

by Chuchu Chen, Jialin Hong, Lihai Ji

Overview

The shastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and shastic inverse problems.

This book provides some recent advances in the investigation of numerical approximations of the shastic Maxwell equations via structure-preserving algorithms. It presents an accessible overview of the construction and analysis of structure-preserving algorithms with an emphasis on the preservation of geometric structures, physical properties, and asymptotic behaviors of the shastic Maxwell equations. A friendly introduction to the simulation of the shastic Maxwell equations with some structure-preserving algorithms is provided using MATLAB for the reader’s convenience.

The objects considered in this book are related to several fascinating mathematical fields: numerical analysis, shastic analysis, (multi-)symplectic geometry, large deviations principle, ergodic theory, partial differential equation, probability theory, etc. This book will appeal to researchers who are interested in these topics.

Product Details

ISBN-13:	9789819966851
Publisher:	Springer Nature Singapore
Publication date:	01/05/2024
Series:	Lecture Notes in Mathematics , #2341
Edition description:	1st ed. 2023
Pages:	284
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Chuchu Chen is an associate professor at the Chinese Academy of Sciences. She obtained her Ph.D. in 2015 at the Chinese Academy of Sciences. Her research interest is in the numerical analysis of shastic partial differential equations, especially in the structure-preserving algorithms for shastic Hamiltonian PDEs including the shastic Maxwell equations and the shastic Schrödinger equation, the analysis of the long-time dynamical behaviors including the ergodicity and intermittency of shastic numerical methods, the influence of numerical discretizations on the statistical properties like the hitting probability and density function of shastic PDEs.

Jialin Hong is a professor at the Chinese Academy of Sciences. He obtained his Ph.D. in 1994 at Jilin University. He works in various directions including structure-preserving algorithms for dynamical systems involving symplectic and multi-symplectic methods for Hamiltonian ODEs andPDEs, Lie group methods and applications, numerical dynamics including chaos, bifurcations for discrete systems, numerical methods for shastic ordinary differential systems, shastic partial differential equations, and backward shastic differential equations, almost periodic dynamical systems, and ergodic theory.

Lihai Ji is an associate professor at the Institute of Applied Physics and Computational Mathematics. He obtained his Ph.D. in 2013 at the Chinese Academy of Sciences. He works in shastic partial differential equations and their numerical algorithms. He has been investigating the construction and analysis of various energy-preserving algorithms, positive-preserving algorithms, shastic symplectic and multi-symplectic algorithms for the shastic Lotka–Volterra model and shastic Hamiltonian PDEs including the shastic Maxwell equations, the shastic Schrödinger equation, and the coupled shastic Schrödinger equation.

Table of Contents

Introduction.- Solution Theory of Shastic Maxwell Equations.- Intrinsic Properties of Shastic Maxwell Equations.- Structure-Preserving Algorithms for Shastic Maxwell Equations.- Convergence Analysis of Structure-Preserving Algorithms.- Implementation of Numerical Experiments.- Appendix A: Basic Identities and Inequalities.- Appendix B: Semigroup, Sobolev Space, and Differential Calculus.- Appendix C: Estimates Related to Maxwell Operators.- Appendix D: Some Results of Shastic Partial Differential Equations.- References.

Editorial Reviews

This interesting monograph brings a self-contained account of the numerical analysis of the shastic Maxwell equations. More precisely, it includes the construction and analysis of structure-preserving algorithms with an emphasis on the preservation of geometric structures, physical properties, and asymptotic behavior of the original equations.” (Jaromír Anh, zbMATH 1542.65001, 2024)

From the Publisher