A fast algorithm for particle simulations
Journal of Computational Physics
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
Wavelet-like bases for the fast solutions of second-kind integral equations
SIAM Journal on Scientific Computing
Multipole translation theory for the three-dimensional Laplace and Helmholtz equations
SIAM Journal on Scientific Computing
Fast and Efficient Algorithms in Computational Electromagnetics
Fast and Efficient Algorithms in Computational Electromagnetics
The Fast Multipole Method I: Error Analysis and Asymptotic Complexity
SIAM Journal on Numerical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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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.