Simulating wave propagation in 3D configurations is becoming a very active area of research. Themain advantage of the BEM is that only the domain boundaries are discretized. As a result, thismethod is well suited to dealing with unbounded domains. However, the standard BEM leadsto fully-populated matrices, which results in high computational costs in CPU time and mem-ory require...

We investigate the use of the Multipole-accelerated Boundary Element Method (BEM) and of the Singularity Method for studying the interaction of many bubbles rising in a volcanic conduit. Observation shows that the expression of volcanic eruption is extremely variable, from slow release of magma to catastrophic explosive manifestation. We investigate the application of the Fast Multipole Method ...

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 ...

A new fast multipole boundary element method (BEM) is presented in this paper for large-scale analysis of two-dimensional (2-D) elastostatic problems based on the direct boundary integral equation (BIE) formulation. In this new formulation, the fundamental solution for 2-D elasticity is written in a complex form using the two complex potential functions in 2-D elasticity. In this way, the multi...

Recent advances in computational chemistry have produced force fields based on a polarizable atomic multipole description of biomolecular electrostatics. In this work, the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field is applied to restrained refinement of molecular models against X-ray diffraction data from peptide crystals. A new formalism is also de...

The solution of Helmholtz and Maxwell equations by integral formulations (kernel in exp(i kr)/r) leads to large dense linear systems. Using direct solvers requires large computational costs in O(N(3)). Using iterative solvers, the computational cost is reduced to large matrix-vector products. The fast multipole method provides a fast numerical way to compute convolution integrals. Its applicati...

This paper introduces an automatic learning method based on genetic programming to derive local and multipole expansions required by the Fast Multipole Method (FMM). FMM is a well-known approximation method widely used in the field of computational physics, which was first developed to approximately evaluate the product of particular N × N dense matrices with a vector in O(N log N) operations. ...

This paper presents an efficient preconditioning technique in order to couple Partial Element Equivalent Circuit (PEEC) method with Fast Multipole algorithm (FMM).

A. V. Meremianin∗ Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187, Dresden, Germany and REC-010, Voronezh State University, 394006, Voronezh, Russia (Dated: October 24, 2005) Abstract The technique of vector differentiation is applied to the problem of the derivation of multipole expansions in four-dimensional space. Explicit expressions for the multipole expa...

Generalized Multilevel Fast Multipole Methods in d Dimensions Nail A. Gumerov,∗ Ramani Duraiswami,† and Eugene A. Borovikov‡ Perceptual Interfaces and Reality Laboratory, Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland, 20742. Abstract We present an overview of the Fast Multipole Method, explain the use of optimal data structures and present complexity re...