On the Lagrange interpolation in multilevel fast multipole algorithm

In this paper the Lagrange interpolation employed in the multilevel fast multipole algorithm (MLFMA) is considered as part of the efforts to obtain faster and more efficient solutions for large problems of computational electromagnetics. For the translation operator, this paper presents the choice of the parameters for optimal interpolation. Also, for the aggregation and disaggregation processes, the interpolation matrices are discussed and an efficient way of improving the accuracy by employing the poles are introduced


Investigation of nanoantennas using surface integral equations and the multilevel fast multipole algorithm
Karaosmanoglu, Barıscan; Gur, Ugur Merıc; Ergül, Özgür Salih (2015-07-09)
A rigorous analysis of nanoantennas using surface integral equations and the multilevel fast multipole algorithm (MLFMA) is presented. Plasmonic properties of materials at optical frequencies are considered by using the Lorentz-Drude models and employing surface formulations for penetrable objects. The electric and magnetic current combined-field integral equation is preferred for fast and accurate solutions, which are further accelerated by an MLFMA implementation that is modified for plasmonic structures....
On the Poisson sum formula for analysis of EM radiation/scattering from large finite arrays
Aydın Çivi, Hatice Özlem; Chou, HT (1998-01-01)
A useful procedure, that has been described previously in the literature, employs the Poisson sum formula to represent the solution to the fields of a three-dimensional (3D) large periodically spaced finite planar array problem configuration as a convolution of the infinite planar periodic array solution and the Fourier transform of the equivalent aperture distribution over the finite array. It is shown here that the Poisson sum formula utilized by Felsen and Carin (see J. Opt. Soc. Am. A, vol.11, no.4, p.1...
Two-Step Lagrange Interpolation Method for the Multilevel Fast Multipole Algorithm
Ergül, Özgür Salih; Gurel, L. (Institute of Electrical and Electronics Engineers (IEEE), 2009)
We present a two-step Lagrange interpolation method for the efficient solution of large-scale electromagnetics problems with the multilevel fast multipole algorithm (MLFMA). Local interpolations are required during aggregation and disaggregation stages of MLFMA in order to match the different sampling rates for the radiated and incoming fields in consecutive levels. The conventional one-step method is decomposed into two one-dimensional interpolations, applied successively. As it provides a significant acce...
On Crank-Nicolson Adams-Bashforth timestepping for approximate deconvolution models in two dimensions
Kaya Merdan, Songül; Rebholz, Leo G. (2014-11-01)
We consider a Crank-Nicolson-Adams-Bashforth temporal discretization, together with a finite element spatial discretization, for efficiently computing solutions to approximate deconvolution models of incompressible flow in two dimensions. We prove a restriction on the timestep that will guarantee stability, and provide several numerical experiments that show the proposed method is very effective at finding accurate coarse mesh approximations for benchmark flow problems.
On maximal permissiveness of hierarchical and modular supervisory control approaches for discrete event systems
Schmidt, Klaus Verner (2008-08-26)
Recently, several efficient modular and hierarchical approaches for the control of discrete event systems (DES) have been proposed. Although these methods are very suitable for dealing with the state space explosion problem, their common limitation is that either maximal permissiveness is not addressed or unnecessarily restrictive conditions are required in order to ensure maximally permissive control. In this paper we develop a unified framework for the investigation of maximal permissiveness of modular co...
Citation Formats
Ö. S. Ergül, “On the Lagrange interpolation in multilevel fast multipole algorithm,” 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40955.