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.