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A fast, higher order three-dimensional finite-element analysis of microwave waveguide devices

机译：微波波导器件的快速，高阶三维有限元分析

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摘要

A fast, higher order three-dimensional finite-element method is presented for the efficient and accurate analysis of microwave waveguide devices. Two solution algorithms ore designed. The first one uses mixed-order triangular prism elements in conjunction with a special frontal solver. It has a very low memory requirement, and is extremely fast for waveguide devices with one dimension longer than the other two. However, the solution must be repeated at each frequency. The second solution algorithm employs higher order tetrahedral elements, which are particularly suitable for modeling complex devices, in conjunction with the multifrontal solver. This algorithm has the major advantage that it can be combined with the asymptotic waveform evaluation and complex frequency-hopping techniques to perform fast frequency-sweep calculations to obtain the response of a device over a wide band. Numerical result, are presented to demonstrate the performance of both solution algorithms and their higher order convergence. It is shown that, using the first solution algorithm, the solution accuracy increases with the order of elements for a fixed number of unknowns, while the computing time and memory requirements remain basically unchanged. With the second solution algorithm, the solution accuracy improves even faster with the increase in the order of elements for a fixed number of unknowns, and very surprisingly, the computing time and memory requirements actually decrease sometimes.
机译：提出了一种快速，高阶的三维有限元方法，可以有效，准确地分析微波波导器件。设计了两种解决方案算法。第一个使用混合阶三角棱镜元素和特殊的正面求解器。它具有非常低的存储要求，并且对于一维长于另一维的波导设备来说速度非常快。但是，必须在每个频率上重复该解决方案。第二种求解算法采用了高阶四面体元素，特别适合对复杂设备建模，并结合了多面求解器。该算法的主要优点是可以与渐近波形评估和复杂的跳频技术结合使用，以执行快速的扫频计算，从而获得宽带设备的响应。数值结果表明了两种算法的性能及其高阶收敛性。结果表明，使用第一种求解算法，对于固定数量的未知数，求解精度随元素顺序增加，而计算时间和内存需求基本上保持不变。使用第二种求解算法时，对于固定数量的未知数，随着元素顺序的增加，求解精度甚至更快地提高，并且非常令人惊讶的是，有时计算时间和内存需求实际上减少了。

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