The vortex method is applied to the calculation of a decaying homogeneous isotropic turbulence of Reλ = 25, 50 and the results are compared with a spectral method calculation. Vortex method calculations were accelerated by the use of a fast multipole method for periodic boundary conditions. The core spreading method and particle strength exchange were selected as the viscous diffusion scheme. T...

We present a software framework for the transparent and portable parallelization of simulations using particle-mesh methods. Particles are used to transport physical properties and a mesh is required in order to reinitialize the distorted particle locations, ensuring the convergence of the method. Field quantities are computed on the particles using fast multipole methods or by discretizing and...

(CSP) method is applied to the method of moments prediction of radar scattering from complex geometries. Like the fast multipole method, the CSP method breaks up the geometry into groups of basis functions. The interactions between groups are computed using a CSP expansion that gives rise to Gaussian beam-like functions which are spectrally narrow. A small percentage of the beams are responsibl...

Solution of periodic boundary value problems is of interest in various branches of science and engineering such as optics, electromagnetics and mechanics. In our previous studies we have developed a periodic Fast Multipole Method (FMM) as a fast solver of wave problems in periodic domains. It has been found, however, that the convergence of the iterative solvers for linear equations slows down ...

A new adaptive fast multipole boundary element method (BEM) for solving 3-D half-space acoustic wave problems is presented in this paper. The half-space Green’s function is employed explicitly in the boundary integral equation (BIE) formulation so that a tree structure of the boundary elements only for the boundaries of the real domain need to be applied, instead of using a tree structure that ...

The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general setting and derive a relative error estimate. This analysis benefits asymmetric versions of the method, where the division of the multipole boxes is more libera...

To efficiently solve large dense complex linear system arising from electric field integral equations (EFIE) formulation of electromagnetic scattering problems, the multilevel fast multipole method (MLFMM) is used to accelerate the matrix-vector product operations. The inner-outer flexible generalized minimum residual method (FGMRES) is combined with the symmetric successive overrelaxation (SSO...