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Condensed matrix method for implicit type scheme in imaginary distance beam propagation method

机译:虚距光束传播法中隐式格式的凝聚矩阵法

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摘要

The modes of a waveguide structure can be accurately determined using finite difference imaginary distance beam propagation method. In implicit type formulation of the problem, a matrix equation has to be solved. The matrix is sparse and large. The sparsity of the matrix can be used to form a condensed matrix of much lower dimension leaving aside the zero element blocks; this condensed matrix takes much smaller storage space and consequently saves a great deal of run-time. The algorithm for the solution of the matrix equation from such a condensed matrix is developed here. This method is comparable with other sparse matrix methods in terms of CPU usage.
机译:波导结构的模式可以使用有限差分虚距射束传播方法来精确确定。在问题的隐式类型表示中,必须求解矩阵方程。矩阵稀疏且较大。矩阵的稀疏性可以用来形成一个尺寸较小的压缩矩阵,而零元素块除外。这种浓缩的矩阵占用的存储空间小得多,因此节省了大量的运行时间。这里开发了从这样一个压缩矩阵求解矩阵方程的算法。就CPU使用率而言,此方法可与其他稀疏矩阵方法相提并论。

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