晶格波茲曼在電動力學兮應用

Applications to Electrodynamics with Lattice Boltzmann Method

林英仁(Yin-Jen Lin)

指導教授 ： 闕志鴻

國立臺灣大學/理學院/物理研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.02624

摘要

晶格波茲曼方法以往應用於解流體問題，鮮少應用於電動力
學。再者亦有許多演算法專門模擬電磁波，諸如時域有限差分。因
此於零八年曼多札結合晶格波茲曼與馬克士威方程成為模擬電動力
學問題的斬新方法。若指定正確的初始及邊界，四電流與電磁場皆
會隨時演化。
我探索各式計算過程中的邊界條件諸如在波導的導體牆及不反
射邊界。亦探索波包的陡峭程度，既然晶格波茲曼方法可處理非線
性介電材料。期間若透過統一計算架構可藉顯示單元可大幅加速運
算。

關鍵字

晶格波茲曼 ； 電動力學

並列摘要

Lattice Boltzmann method (LBM) is used to solve fluid problems traditionally.
Rarely is LBM adopted to simulate electromagnetic problems.
On the other hand, there are several kinds of methods for simulating electromagnetic
problems, such as the finite-difference time-domain method.
However, a whole new algorithm developed by Mendoza in 2008 combines
lattice Boltzmann equation and Maxwell equation to simulate electrodynamics.
When correct initial and boundary conditions are specified,
the 4-current and six independent elements of electromagnetic field can be
evolved at any time under this algorithm.
I explored various non-trivial boundary conditions in the calculations,
such as conducting walls of a waveguide and non-reflecting boundary.
Since LBM can also handle nonlinear dielectric materials, I also explore
the steepening of wave packets in such a nonlinear material. I implemented
this computation algorithm using GPU. Through the CUDATMarchitecture,
the calculation can be substantially speeded up.

並列關鍵字

Lattice Boltzmann Method ； Electromagnetic Wave

參考文獻

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