高階ADI-FDTD算法的數(shù)值色散分析
Analysis of the Numerical Dispersion of Higher Order ADI-FDTD
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摘要: 該文給出高階交替方向隱時(shí)域優(yōu)先差分(ADI-FDTD)算法，即在ADI-FDTD迭代公式的基礎(chǔ)上對(duì)時(shí)間的差分仍然采用二階中心差分格式，而對(duì)空間的差分則采用四階中心差分格式，并解析地證明了所給出的高階ADI-FDTD算法仍然滿足無(wú)條件穩(wěn)定方程，同時(shí)對(duì)增長(zhǎng)因子相位的分析，得到數(shù)值色散關(guān)系，最后對(duì)其數(shù)值色散誤差進(jìn)行了分析，研究表明與普通ADI-FDTD相比，其色散誤差較小。
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關(guān)鍵詞:
- 高階ADI-FDTD算法;數(shù)值色散
Abstract: In this paper, a new higher order Alternating Direction Implicit Finite-Difference Time-Domain (ADI-FDTD) formulation in particular, a second-order-in-time, fourth-order-in-space AD-FDTD method is presented for the first time. At the same time ,the unconditional stability of the higher order ADI-FDTD formulation is analytically proved. By analysis of the amplification factors, the numerical dispersion relation is derived. In addition, the numerical dispersion errors are investigated. Finally numerical results indicate that the higher order ADI-FDTD has s better accuracy compared to the ADI-FDTD method. -
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