Nilsson, M. 2003. Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 916. 38 pp. Uppsala. ISBN 91-554-5827-0 The Method of Moments is a numerical technique for solving electromagnetic problems with integral equations. The method discretizes a surfa...

The fast multipole method (FMM) has been regarded as one of the top 10 algorithms in scientific computing that were developed in the 20th century. Combined with the FMM, the boundary element method (BEM) can now solve large-scale problems with several million degrees of freedom on a desktop computer within hours. This opened up a wide range of applications for the BEM that has been hindered for...

A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex not...

The purpose of this paper is to test the applicability of a fast boundary element method in the context of geoid computations of the gravity. The fast multipole method is the method of choice due to the its advantageous property of a fast evaluation in the post-processing. Several sets of trianglar meshes for the approximation of the unit sphere and several modifications of the prediscribed dat...

This is a simple introduction to fast multipole methods for the N-body summation problems. Low rank approximation plus hierarchical decomposition leads to fast O(N) or O(N logN) algorithms for the summation problem or equivalently the computation of a matrix-vector product. Code for 1-D problem is presented for a better illustration. We consider a summation problem in the form:

This paper presents a flexible mixture model (FMM) for collaborative filtering. FMM extends existing partitioning/clustering algorithms for collaborative filtering by clustering both users and items together simultaneously without assuming that each user and item should only belong to a single cluster. Furthermore, with the introduction of ‘preference’ nodes, the proposed framework is able to e...

Preface The authors would like to thank V. Rokhlin both for discovering much of the content of later parts of these notes and for elaborating the material for us while we prepared the notes. We would also like to thank R. R. Coifman and L. Greengard for many discussions related to the content of these notes, and S. Zucker for proposing that we develop the course which stimulated us to produce t...

We discuss the concept and implementation of fast multipole algorithms on a regular structured grid. In doing so, the discrte analogue of the continuous fundamental solution is evaluated numerically. We discuss the concept and implementation of fast multipole algorithms on a regular structured grid. In doing so, the discrte analogue of the continuous fundamental solution is evaluated numericall...

We propose in this work a fast numerical algorithm for solving the equation of radiative transfer (ERT) in isotropic media. The algorithm has two steps. In the first step, we derive an integral equation for the angularly averaged ERT solution by taking advantage of the isotropy of the scattering kernel, and solve the integral equation with a fast multipole method (FMM). In the second step, we s...