Computational Nanotechnology Using Finite Difference Time Domain

2

The FDTD Method: Essences, Evolutions, and Applications to Nano-Optics and Quantum Physics

Xiaoyan Y.Z. Xiong and Wei E.I. Sha

Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China

CONTENTS

2.1 Introduction

2.1.1 Discretization Strategies in the Time Domain

2.1.1.1 Runge-Kutta Method

2.1.1.2 Second-Order Leap-Frog (Staggered) Time-Stepping Approach

2.1.1.3 Unconditionally Stable Algorithms

2.1.1.4 High-Order Symplectic Integration Scheme

2.1.2 Space Discretization Methods

2.1.2.1 Second-Order Leap-Frog (Staggered) Difference

2.1.2.2 Fourth-Order Staggered Difference

2.1.2.3 Fourth-Order Implicit Compact Difference Algorithm

2.1.2.4 Multiresolution Expansion Method

2.1.2.5 Pseudo-Spectral Scheme