Time Dependent Phase Space Filters : A Stable Absorbing Boundary Condition (Springerbriefs on Pdes and Data Science)

Soffer, Avy/ Stucchio, Chris/ Tran, Minh-Binh

Springer Verlag, Singapore（2023/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 125 p.
• 言語 ENG
• 商品コード 9789811968174
• DDC分類 518

Full Description

This book introduces an interesting and alternative way to design absorbing boundary conditions (ABCs) for quantum wave equations, basically the nonlinear Schrödinger equation. The focus of this book is the application of the phase space filter approach to derive accurate radiation conditions for Schrödinger equations.

Researchers who are interested in partial differential equations and mathematical physics might find this book appealing.

Contents

Introduction.- Absorbing Potentials and Perfectly Matched Layers.- Windowed Fourier Transforms and Space Phase Numerics.- Description of Time Dependent Phase Space Filters.- A More Practical Discussion: How to Choose the Parameters.- The Behavior of Gaussian Framelets under the Free Flow.- Assumptions and Accuracy Estimates.- Discussions on the Assumptions.- Proof of Theorem 7.5.6.- Proof of Theorems 7.5.4 and 7.5.5.- Numerical Experiments.