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ABSTRACT: The Barnes-Hut algorithm is widely used in astrophysics for solving large gravitational N -body problems using O ( N log N ) time and memory. This reduction in computational cost is achieved by a hierarchical application of the classical center-of-mass approximation. As both gravitational and electrostatic potentials are subject to a 1/ R dependence, the Barnes-Hut algorithm is also a natural choice for rapidly evaluating interactions between charged particles. The contribution of this paper is an extension of the Barnes-Hut hierarchical clustering to the acceleration of charge interactions in stratified media. We derive and validate a closed-form expression for the shift of the center-of-charge location induced by the physical inhomogeneities and show that proper positioning of the center-of-charge ensures O (1/ R <sup>3</sup>) error decay in the field approximation. Hierarchical applications of the proposed clustering approximation is demonstrated for the construction of O ( N log N ) method-of-moment based capacitance extractors.
IEEE Transactions on Microwave Theory and Techniques 06/2010; · 1.85 Impact Factor
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ABSTRACT: From the results of the previous section it is apparent that kernel evaluations by means of interpolation from a pre-existing database is much more time-efficient for computing both the near-interactions and the matrix-vector product. In fact, the Best-MEM method provides completely unacceptable computational time and should not even be considered as an option unless the computational environment possesses severe memory limitations. On the other hand, for large, multiscale geometries involving millions of unknowns, it may not be possible to store the entire kernel database. In these cases, it is our recommendation to select po(p) larger than the radius of near interactions. In this way, the near-matrix-fill time will remain unchanged and both memory levels and MVP times will be acceptable. Obviously, for distributed systems with significant amounts of memory, computational time will benefit if as much of the database is stored as memory permits.
Electrical Performance of Electronic Packaging, 2007 IEEE; 11/2007
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ABSTRACT: In this paper we discuss a computational framework which allows for accuracy controlled capacitance extraction in the entire package model consisting of 2.9 million elements on the conductor boundaries. The capacity for simulation of large- scale interconnects is attained through parallel implementation of a tree-based hierarchical computational algorithm. The acceleration of dense matrix-vector product resulting from the locally corrected Nystrom (LCN) discretization of the governing integral equation is effected by means of the Barnes-Hut (BH) method. The kernel-independence of the latter provides for inclusion of the dielectric substrate into the computational model without increasing the model's size by means of creation of the pertinent Green's function databases for the substrate process.
Signal Propagation on Interconnects, 2007. SPI 2007. IEEE Workshop on; 06/2007
