Topic
Multipole expansion
About: Multipole expansion is a research topic. Over the lifetime, 9675 publications have been published within this topic receiving 214783 citations.
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TL;DR: In this paper, a method of analysing molecular wavefunctions is described, which can be regarded as an extension of Mulliken population analysis, and can be used both to give a qualitative or quantitative picture of the molecular charge distribution, and in the accurate evaluation of molecular multipole moments of arbitrary order.
966 citations
TL;DR: Results from examples are given to demonstrate that the multipole acceleration can reduce required computation time and memory by more than an order of magnitude for realistic integrated circuit packaging problems.
Abstract: A mesh analysis equation formulation technique combined with a multipole-accelerated Generalized Minimal Residual (GMRES) matrix solution algorithm is used to compute the 3-D frequency dependent inductances and resistances in nearly order n time and memory where n is the number of volume-filaments. The mathematical formulation and numerical solution are discussed, including two types of preconditioners for the GMRES algorithm. Results from examples are given to demonstrate that the multipole acceleration can reduce required computation time and memory by more than an order of magnitude for realistic integrated circuit packaging problems. >
918 citations
TL;DR: In this article, a formalism for analyzing a full-sky temperature and polarization map of the cosmic microwave background is presented, where temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the two-point correlation function.
Abstract: We present a formalism for analyzing a full-sky temperature and polarization map of the cosmic microwave background. Temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the two-point correlation function. Polarization, which is described by a second-rank tensor, can be treated analogously by expanding in the appropriate tensor spherical harmonics. We provide expressions for the complete set of temperature and polarization multipole moments for scalar and tensor metric perturbations. Four sets of multipole moments completely describe isotropic temperature and polarization correlations; for scalar metric perturbations one set is identically zero, giving the possibility of a clean determination of the vector and tensor contributions. The variance with which the multipole moments can be measured in idealized experiments is evaluated, including the effects of detector noise, sky coverage, and beam width. Finally, we construct coordinate-independent polarization two-point correlation functions, express them in terms of the multipole moments, and derive small-angle limits.
896 citations
TL;DR: A new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions is introduced based on a new diagonal form for translation operators and yields high accuracy at a reasonable cost.
Abstract: We introduce a new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions. It is based on a new diagonal form for translation operators and yields high accuracy at a reasonable cost.
896 citations
TL;DR: Performance comparisons on integrated circuit bus crossing problems show that for problems with as few as 12 conductors the multipole accelerated boundary element method can be nearly 500 times faster than Gaussian-elimination-based algorithms, and five to ten times slower than the iterative method alone, depending on required accuracy.
Abstract: A fast algorithm for computing the capacitance of a complicated three-dimensional geometry of ideal conductors in a uniform dielectric is described and its performance in the capacitance extractor FastCap is examined. The algorithm is an acceleration of the boundary-element technique for solving the integral equation associated with the multiconductor capacitance extraction problem. The authors present a generalized conjugate residual iterative algorithm with a multipole approximation to compute the iterates. This combination reduces the complexity so that accurate multiconductor capacitance calculations grow nearly as nm, where m is the number of conductors. Performance comparisons on integrated circuit bus crossing problems show that for problems with as few as 12 conductors the multipole accelerated boundary element method can be nearly 500 times faster than Gaussian-elimination-based algorithms, and five to ten times faster than the iterative method alone, depending on required accuracy. >
859 citations