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

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Chuchu Chen Jialin Hong

Numerical Approximations of Stochastic Maxwell Equations

via Structure-Preserving Algorithms

Chuchu Chen, Jialin Hong, Lihai Ji

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English

Springer Verlag, Singapore
05 January 2024

Differential calculus & equations; Numerical analysis; Probability & statistics; Stochastics

Series: Lecture Notes in Mathematics

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

This book provides some recent advances in the investigation of numerical approximations of the stochastic 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 stochastic Maxwell equations. A friendly introduction to the simulation of the stochastic 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, stochastic 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.

By: Chuchu Chen, Jialin Hong, Lihai Ji
Imprint: Springer Verlag, Singapore
Country of Publication: Singapore
Edition: 1st ed. 2023
Volume: 2341
Dimensions: Height: 235mm, Width: 155mm,
Weight: 468g
ISBN: 9789819966851
ISBN 10: 981996685X
Series: Lecture Notes in Mathematics
Pages: 284
Publication Date: 05 January 2024
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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 stochastic partial differential equations, especially in the structure-preserving algorithms for stochastic Hamiltonian PDEs including the stochastic Maxwell equations and the stochastic Schrödinger equation, the analysis of the long-time dynamical behaviors including the ergodicity and intermittency of stochastic numerical methods, the influence of numerical discretizations on the statistical properties like the hitting probability and density function of stochastic 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 stochastic ordinary differential systems, stochastic partial differential equations, and backward stochastic 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 stochastic partial differential equations and their numerical algorithms. He has been investigating the construction and analysis of various energy-preserving algorithms, positive-preserving algorithms, stochastic symplectic and multi-symplectic algorithms for the stochastic Lotka–Volterra model and stochastic Hamiltonian PDEs including the stochastic Maxwell equations, the stochastic Schrödinger equation, and the coupled stochastic Schrödinger equation.

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

“This interesting monograph brings a self-contained account of the numerical analysis of the stochastic 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 Antoch, zbMATH 1542.65001, 2024)