Efficient computation of acoustical scattering from N spheres via the fast multipole method accelerated flexible generalized minimal residual method

2004 ◽  
Vol 116 (4) ◽  
pp. 2528-2528
Author(s):  
Nail A. Gumerov ◽  
Ramani Duraiswami
Keyword(s):  
Fast Multipole Method ◽  
Efficient Computation ◽  
Fast Multipole ◽  
Residual Method ◽  
Minimal Residual Method ◽  
Multipole Method ◽  
Minimal Residual

scholarly journals Efficient computation of source magnetic scalar potential

2006 ◽  
Vol 4 ◽  
pp. 59-63 ◽  
Author(s):  
W. Hafla ◽  
A. Buchau ◽  
W. M. Rucker
Keyword(s):  
Magnetic Field ◽  
Fast Multipole Method ◽  
Scalar Potential ◽  
Numerical Results ◽  
Efficient Computation ◽  
Fast Multipole ◽  
Line Integral ◽  
Source Field ◽  
Multipole Method

Abstract. Magnetic field problems are often excited by a known source field which itself is caused by free currents. Some formulations to solve the problem require knowledge of the source magnetic scalar potential whose gradient is the source field. In general, it has to be computed as a line integral. An approach for efficient computation of this potential has been developed that is based on an algorithm that gives short integration paths as well as on application of the fast multipole method. Numerical results indicate the efficiency of this approach especially when the number of current-carrying volume elements or the number of observation points are high.

Virtual Boundary Element Collocation Method with RBF Interpolation on Virtual Boundary and Diagonalization Feature in Fast Multipole Method

2011 ◽  
Vol 378-379 ◽  
pp. 166-170
Author(s):  
Wei Si ◽  
Qiang Xu
Keyword(s):  
Boundary Element ◽  
Collocation Method ◽  
Large Scale ◽  
Fast Multipole Method ◽  
Fast Multipole ◽  
Multipole Method ◽  
Elasticity Problems ◽  
Virtual Boundary ◽  
Minimal Residual ◽  
Virtual Boundary Element

The algorithm idea of virtual boundary element collocation method with RBF interpolation on virtual boundary and diagonalization feature in fast multipole method is presented to study 2-D elasticity problems in this paper. In other words, the new fast multipole method (FMM) adopting diagonalization and the generalized minimal residual (GMRES) algorithm are jointly employed to solve the equations related to virtual boundary element collocation method (VBEM) with RBF interpolation on virtual boundary. In this paper, the numerical scheme suitable for original FMM with respect to two-dimensional problem of elasticity is optimized, through the introduction of concept of diagonalization, in terms of the radial basis function to express the unknown virtual load functions, in order to further improve the efficiency of the problem to be solved. Then large-scale numerical simulations of elastostatics might be achieved by the method. Numerical examples in the paper have proved the feasibility, efficiency and calculating precision of the method.

A Fourier-series-based kernel-independent fast multipole method

2011 ◽  
Vol 230 (15) ◽  
pp. 5807-5821 ◽  
Author(s):  
Bo Zhang ◽  
Jingfang Huang ◽  
Nikos P. Pitsianis ◽  
Xiaobai Sun
Keyword(s):  
Fourier Series ◽  
Fast Multipole Method ◽  
Fast Multipole ◽  
Multipole Method

The Fast Multipole Method in Canonical Ensemble Dynamics on Massively Parallel Computers

1992 ◽  
Vol 278 ◽  
Author(s):  
Steven R. Lustig ◽  
J.J. Cristy ◽  
D.A. Pensak
Keyword(s):  
Canonical Ensemble ◽  
Yukawa Potential ◽  
Direct Method ◽  
Fast Multipole Method ◽  
Parallel Computers ◽  
Massively Parallel ◽  
Fast Multipole ◽  
Massively Parallel Computers ◽  
Multipole Method ◽  
Execution Times

AbstractThe fast multipole method (FMM) is implemented in canonical ensemble particle simulations to compute non-bonded interactions efficiently with explicit error control. Multipole and local expansions have been derived to implement the FMM efficiently in Cartesian coordinates for soft-sphere (inverse power law), Lennard- Jones, Morse and Yukawa potential functions. Significant reductions in execution times have been achieved with respect to the direct method. For a given number, N, of particles the execution times of the direct method scale asO(N2). The FMM execution times scale asO(N) on sequential workstations and vector processors and asymptotically0(logN) on massively parallel computers. Connection Machine CM-2 and WAVETRACER-DTC parallel FMM implementations execute faster than the Cray-YMP vectorized FMM for ensemble sizes larger than 28k and 35k, respectively. For 256k particle ensembles the CM-2 parallel FMM is 12 times faster than the Cray-YMP vectorized direct method and 2.2 times faster than the vectorized FMM. For 256k particle ensembles the WAVETRACER-DTC parallel FMM is 33 times faster than the Cray-YMP vectorized direct method.

Sign in / Sign up

Export Citation Format

Share Document