Fast convolution with free-space Green's functions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:323

Article

Vico, Felipe¹  Greengard, Leslie^2,3  Ferrando, Miguel¹ 

[1] Univ Politecn Valencia, Inst Telecomunicac & Aplicac Multimedia ITEAM, E-46022 Valencia, Spain

[2] NYU, Courant Inst, New York, NY USA

[3] Simons Fdn, Simons Ctr Data Anal, New York, NY USA

关键词: Volume potential;    Free space;    Green's function;    FFT;    Convolution;   

DOI  :  10.1016/j.jcp.2016.07.028

来源: Elsevier

【 摘 要 】

We introduce a fast algorithm for computing volume potentials - that is, the convolution of a translation invariant, free-space Green's function with a compactly supported source distribution defined on a uniform grid. The algorithm relies on regularizing the Fourier transform of the Green's function by cutting off the interaction in physical space beyond the domain of interest. This permits the straightforward application of trapezoidal quadrature and the standard FFT, with superalgebraic convergence for smooth data. Moreover, the method can be interpreted as employing a Nystrom discretization of the corresponding integral operator, with matrix entries which can be obtained explicitly and rapidly. This is of use in the design of preconditioners or fast direct solvers for a variety of volume integral equations. The method proposed permits the computation of any derivative of the potential, at the cost of an additional FFT. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free