CAJ | 학술논문

从圆柱坐标系下麦克斯韦方程的时域有限差分式和特征解出发,引入了二维和三维圆柱坐标系下网格波阻抗(MWI).结合完全匹配吸收层(PML)概念,推导出了二维圆柱坐标系下的MWI-PWL吸收边界条件算法.通过数值实验,研究了圆柱坐标系下网格波阻抗的正确性和它在圆柱坐标系下时域有限差分法(FDTD)中的应用.计算结果证明,当采用非均匀圆柱坐标系下FDTD法计算时,圆柱坐标系下网格波阻抗可以较准确地计算由于网格尺寸不同造成的数值反射误差.同时,网格波阻抗也为确定网格尺寸容许可变的范围提供了理论标准.二维圆柱坐标系下的MWI-PML是一种简单、低反射的吸收边界条件,与Teixeira的完全匹配吸收层相比,其引起的数值反射误差增加不大但更易于实现.
종원주좌표계하맥극사위방정적시역유한차분식화특정해출발,인입료이유화삼유원주좌표계하망격파조항(MWI).결합완전필배흡수층(PML)개념,추도출료이유원주좌표계하적MWI-PWL흡수변계조건산법.통과수치실험,연구료원주좌표계하망격파조항적정학성화타재원주좌표계하시역유한차분법(FDTD)중적응용.계산결과증명,당채용비균균원주좌표계하FDTD법계산시,원주좌표계하망격파조항가이교준학지계산유우망격척촌불동조성적수치반사오차.동시,망격파조항야위학정망격척촌용허가변적범위제공료이론표준.이유원주좌표계하적MWI-PML시일충간단、저반사적흡수변계조건,여Teixeira적완전필배흡수층상비,기인기적수치반사오차증가불대단경역우실현.
Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI-PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non-uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI-PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.