![]() To minimize the rank for a given accuracy, we develop an efficient matrix algebra based method to determine the minimal rank for each admissible block. We show that the computational cost of an H-matrix-based computation of electrodynamic problems can be significantly reduced without sacrificing accuracy, by minimizing the rank of each admissible block based on accuracy requirements and by optimizing the H-partition to reduce the number of admissible blocks at each tree level for a prescribed accuracy and for each frequency point. ![]() Different from block rank, the partition rank kave contains the information of the H-matrix partition. In light of the fact that the cost of an H-matrix-based computation of high-frequency problems is not only determined by the block rank that increases with electric size, but also determined by the H-matrix partition, we propose a new parameter, average partition rank kave, to derive the storage units and operation counts of the H-matrix based computation of electrodynamic problems. In this paper, we develop an H-matrix-based fast direct integral equation solver that has a significantly reduced computational complexity, with prescribed accuracy satisfied, to solve large-scale electrodynamic problems.
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