𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell's Equations

✍ Scribed by Amir Yefet; Peter G. Petropoulos

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
444 KB
Volume
168
Category
Article
ISSN
0021-9991

No coin nor oath required. For personal study only.

✦ Synopsis

We consider a model explicit fourth-order staggered finite-difference method for the hyperbolic Maxwell's equations. Appropriate fourth-order accurate extrapolation and one-sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces. An eigenvalue analysis of the overall scheme provides a necessary, but not sufficient, stability condition and indicates longtime stability. Numerical results verify both the stability analysis, and the scheme's fourth-order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces. For a fixed error level, we find the fourth-order scheme is computationally cheaper in comparison to the Yee scheme by more than an order of magnitude. Some open problems encountered in the application of such high-order schemes are also discussed.

📜 SIMILAR VOLUMES

A novel high-order time-domain scheme fo
A novel high-order time-domain scheme for three-dimensional Maxwell's equations
✍ Zhi-Xiang Huang; Wei Sha; Xian-Liang Wu; Ming-Sheng Chen 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 84 KB

## Abstract A novel high‐order time‐domain scheme with a four‐stage optimized symplectic integrator propagator is presented for 3D electromagnetic scattering problems. The scheme is nondissipative and does not require more storage than the classical finite‐difference time‐domain (FDTD) method. The

Fourth-order finite difference scheme fo
Fourth-order finite difference scheme for the incompressible Navier–Stokes equations in a disk
✍ Ming-Chih Lai 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 212 KB 👁 1 views

## Abstract We develop an efficient fourth‐order finite difference method for solving the incompressible Navier–Stokes equations in the vorticity‐stream function formulation on a disk. We use the fourth‐order Runge–Kutta method for the time integration and treat both the convection and diffusion te

A Reflectionless Sponge Layer Absorbing
A Reflectionless Sponge Layer Absorbing Boundary Condition for the Solution of Maxwell's Equations with High-Order Staggered Finite Difference Schemes
✍ Peter G. Petropoulos; Li Zhao; Andreas C. Cangellaris 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 372 KB

We develop, implement, and demonstrate a reflectionless sponge layer for truncating computational domains in which the time-dependent Maxwell equations are discretized with high-order staggered nondissipative finite difference schemes. The well-posedness of the Cauchy problem for the sponge layer eq

A fourth-order compact finite difference
A fourth-order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations
✍ Zhenfu Tian; Yongbin Ge 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 256 KB 👁 1 views

## Abstract A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature o

Attaining exponential convergence for th
Attaining exponential convergence for the flux error with second- and fourth-order accurate finite-difference equations. I. Presentation of the basic concept and application to a pure diffusion system
✍ Manfred Rudolph 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 213 KB

## Abstract It is a well‐known phenomenon called superconvergence in the mathematical literature that the error level of an integral quantity can be much smaller than the magnitude of the local errors involved in the computation of this quantity. When discretizing an integrated form of Fick's secon