One class of waveguide resonators: algorithms based on semi-inversion technique in time and frequency domain

N. Yashina
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Abstract

An approach, based on extraction and analytical inversion of the singular part of the boundary value problem (BVP) operator in the frequency and time domain is applied to the one class of resonant structures in waveguides (coaxial type plane discontinuities bifurcation's, shunts, slots, irises, steps, disks etc.). Thus the initial BVP and BVP are reduced to the matrix equation of the second kind or to the Volterra integral equation of the second kind (with a straightforward scheme of time marching). All steps of the technique are mathematically proved. The convergence of numerical algorithms is proved also and estimated analytically. Special attention is paid to computer implementation of algorithms developed and various tests of them. Thus the convergence of numerical solutions is thoroughly investigated and analytical estimates are illustrated by numerical results.
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一类波导谐振器:基于时频半反转技术的算法
将边值问题算子奇异部分在频域和时域的提取和解析反演方法应用于一类波导谐振结构(同轴型平面不连续、分岔、分流、槽、虹膜、阶梯、圆盘等)。因此,初始BVP和BVP被简化为第二类矩阵方程或第二类Volterra积分方程(具有简单的时间推进格式)。该技术的所有步骤都得到了数学证明。并对数值算法的收敛性进行了证明和分析估计。特别注意计算机实现所开发的算法和各种测试。从而深入研究了数值解的收敛性,并用数值结果说明了解析估计。
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