A memory saving fast A-EFIE solver for modeling low-frequency large-scale problems

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• 作者：Yang G. Liu^a ; ^{liuyang@eee.hku.hk} ; Weng Cho Chew^a ; ¹ ; ^{wcchew@hku.hk} ; Lijun Jiang^a ; ^{ljiang@eee.hku.hk} ; Zhiguo Qian^b ; ^{zhiguoqian@gmail.com}
• 关键词：Vector fast multipole algorithm ; Augmented electric field integral equation ; Low frequency ; Memory savings ; Vector addition theorem
• 刊名：Applied Numerical Mathematics
• 出版年：2012
• 期刊代码：8_01689274
• 类别：cp
• 出版时间：June, 2012
• 卷：62
• 期：6
• 页码：682-698
• 文件大小：764 K

摘要

We propose a new fast solver for solving the augmented electric field integral equation (A-EFIE), which realizes memory savings for modeling low-frequency large-scale problems, compared with the low-frequency fast multipole algorithm (LF-FMA). The A-EFIE has been proposed to avoid the imbalance between the vector potential and the scalar potential at low frequencies by adding the charge to the unknown list. The corresponding low frequency fast multipole algorithm (LF-FMA) was also developed for solving the A-EFIE. Instead of the factorization of the scalar Green始s function by using the scalar addition theorem in the LF-FMA, we adopt the vector addition theorem for the factorization of the dyadic Green始s function to develop a vector fast multipole algorithm (VFMA) for solving the A-EFIE. The storage of radiation and receiving patterns of the VFMA, which becomes the main part of the total storage with the increasing scale of problems, can be reduced by 25 percent compared with that of the LF-FMA, although the storage for vector translators, which is independent of the number of unknowns, is larger than that of the LF-FMA. At last, some numerical results show the validity of the VFMA for solving A-EFIE.