TY - JOUR

T1 - A memory saving fast A-EFIE solver for modeling low-frequency large-scale problems?

AU - Liu, Yang G.

AU - Chew, Weng Cho

AU - Jiang, Lijun

AU - Qian, Zhiguo

N1 - Funding Information:
✩ This work was supported by GRF grants: RGC Ref Nos. 711508 and 711609.

PY - 2012/6

Y1 - 2012/6

N2 - 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'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'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.

AB - 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'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'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.

KW - Augmented electric field integral equation

KW - Low frequency

KW - Memory savings

KW - Vector addition theorem

KW - Vector fast multipole algorithm

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U2 - 10.1016/j.apnum.2010.11.012

DO - 10.1016/j.apnum.2010.11.012

M3 - Article

AN - SCOPUS:84859749448

VL - 62

SP - 682

EP - 698

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

IS - 6

ER -