Fast-Factorization Acceleration of MoM Compressive Domain-Decomposition
Fast-Factorization Acceleration of MoM Compressive Domain-Decomposition
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DOI：
10.1109/tap.2011.2165474
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发表时间：
2011-08
影响因子：
5.7
通讯作者：
A. Freni;P. Vita;P. Pirinoli;L. Matekovits;G. Vecchi
中科院分区：
文献类型：
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作者：
A. Freni;P. Vita;P. Pirinoli;L. Matekovits;G. Vecchi
积分方程组的区域分解(DD)可以通过将标准基函数聚集到每个子域上的专用基函数来实现；这导致了MOM矩阵的强压缩，这使得对于电大问题也可以得到无迭代(例如，LU分解)的解。快速矩阵向量积算法可以用于所采用的聚集函数方法的矩阵填充和压缩过程：这种混合方法在最近的文献中受到了相当大的关注。为了定量评估这类方法的性能、优势和局限性，我们首先提出并论证了使用自适应积分方法(AIM)快速因式分解来加速合成函数展开(SFX)DD方法。该方法保持了迭代自由，在内存和时间性能上有显著的提高，数值结果证实了复杂性缩放的分析预测。然后，我们讨论了独立DD及其与FAST MOM的组合使用的复杂性扩展；这是针对DD范例的各种实现的已知文献描述进行的分析和讨论，其结果不明显，突出了需求和限制，并产生了实用的迹象。
Domain-decomposition (DD) for Integral Equation can be achieved by aggregating standard basis functions into specialized basis functions on each sub-domain; this results in a strong compression of the MoM matrix, which allows an iteration-free (e.g., LU decomposition) solution also for electrically large problems. Fast matrix-vector product algorithms can be used in the matrix filling and compression process of the employed aggregate-functions approach: this hybrid approach has received considerable attention in recent literature. In order to quantitatively assess the performance, advantages and limitations of this class of methods, we start by proposing and demonstrating the use of the Adaptive Integral Method (AIM) fast factorization to accelerate the Synthetic Function eXpansion (SFX) DD approach. The method remains iteration free, with a significant boost in memory and time performances, with analytical predictions of complexity scalings confirmed by numerical results. Then, we address the complexity scaling of both stand-alone DD and its combined use with fast MoM; this is done analytically and discussed with respect to known literature accounts of various implementations of the DD paradigm, with nonobvious results that highlight needs and limitations, and yielding practical indications.