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Proceedings of the 48th Design Automation Conference, 2011
To facilitate full chip capacitance extraction, field solvers are typically deployed for characterizing capacitance libraries for various interconnect structures and configurations. In the past decades, various algorithms for accelerating boundary element methods (BEM) have been developed to improve the efficiency of field solvers for capacitance ...
Xueqian Zhao, Zhuo Feng
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To facilitate full chip capacitance extraction, field solvers are typically deployed for characterizing capacitance libraries for various interconnect structures and configurations. In the past decades, various algorithms for accelerating boundary element methods (BEM) have been developed to improve the efficiency of field solvers for capacitance ...
Xueqian Zhao, Zhuo Feng
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Fast-multipole method: a mathematical study
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1997Summary: Realistic treatment of scattering from an object involves the use of a huge number of points; thus using ``fast methods'' is a crucial issue. The fast multipole method is one of them. We are here interested in solving the Helmholtz equation by a boundary element method. The algorithm, first introduced by \textit{V. Rokhlin} [J. Comput.
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Telescoping Fast Multipole Methods Using Chebyshev Economization
Journal of Computational Physics, 1995Chebyshev polynomials of the first kind are applied to telescope both the far-field multipole expansions and the near-field Taylor series expansions used in solving large \(N\)-body problems via fast multipole methods. The technique is demonstrated for pairwise-additive, \(1/r\) interparticle potentials in Cartesian coordinates, and a general ...
Lustig, Steven R. +2 more
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Efficient implementation of the fast multipole method
The Journal of Chemical Physics, 2006A number of computational techniques are described that reduce the effort related to the continuous fast multipole method, used for the evaluation of Coulomb matrix elements as needed in Hartree-Fock and density functional theories. A new extent definition for Gaussian charge distributions is proposed, as well as a new way of dividing distributions ...
Elias, Rudberg, Paweł, Sałek
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Fast multipole method for poroelastodynamics
Engineering Analysis with Boundary Elements, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fast field computations with the fast multipole method
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 2001The application of the fast multipole method reduces the computational costs and the memory requirements of the boundary element method from O(N2) to approximately O(N). In this paper we present that the computational costs can be strongly shortened, when the multipole method is not only used for the solution of the system of linear equations but also ...
Buchau, André +2 more
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A hierarchical fast-multipole method for stratified media
Microwave and Optical Technology Letters, 2000An efficient, static, fast-multipole method (FMM)-based algorithm is presented in this paper for the evaluation of the parasitic capacitance of 3-D microstrip signal lines above stratified dielectric media. A modified tree structure is used to perform the multilevel outgoing-to-local multipole translations. The algorithm, only marginally more expensive
Chew, WC, Pan, YC
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Fast multipole method for multidimensional integrals
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1998We give a fast algorithm to evaluate a class of d-dimensional integrals. A direct numerical evaluation of these integrals costs Nd, where d is the number of variables and N is the number of discrete points of each variable. The algorithm we present in this Note permits to reduce this cost from Nd to a cost of the order O(N).
Oliver Bokanowski, Mohammed Lemou
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Scalable Fast Multipole Accelerated Vortex Methods
2014 IEEE International Parallel & Distributed Processing Symposium Workshops, 2014The fast multipole method (FMM) is often used to accelerate the calculation of particle interactions in particle-based methods to simulate incompressible flows. To evaluate the most time-consuming kernels -- the Biot-Savart equation and stretching term of the vorticity equation, we mathematically reformulated it so that only two Laplace scalar ...
Qi Hu +4 more
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Contour Dynamics and the Fast Multipole Method
SIAM Journal on Scientific Computing, 1994Summary: Contour dynamics methods are used to evolve regions of constant vorticity moving under the Euler equations for an inviscid, incompressible fluid in two dimensions. If the induced velocity field is evaluated directly, contour dynamics methods require a CPU time per timestep proportional to \(N^ 2\) (\(N\) being the number of codes used to ...
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