As graphics processors become powerful, ubiquitous and easier to program, they have also become more amenable to general purpose high-performance computing, including the computationally expensive task of drawing large graphs. This paper describes a new parallel analysis of the multipole method of graph drawing to support its efficient GPU implementation. We use a variation of the Fast Multipol...

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...

We describe the iterative solution of dense linear systems arising from a surface integral equation of electromagnetic scattering. The complex symmetric version of QMR has been used as an iterative solver together with a sparse approximate inverse preconditioner. The preconditioner is computed using the topological information from the computational mesh. The matrix-vector products are computed...

Various characteristics of mesomorphism can be explained using intermolecular interactions between a pair of liquid crystalline molecules. The intermolecular interactions have been calculated considering multipole-multicentere expansion method and modified by second order perturbation treatments. For calculation of multipole i.e. charge, dipole, etc. at each atomic center of molecules, para-but...

The fast multipole method (FMM) has been implemented to speed up the matrix-vector multiply when an iterative method is used to solve combined eld integral equation (CFIE). FMM reduces the complexity from O(N 2) to O(N 1:5). With a multilevel fast multipole algorithm (MLFMA), it is further reduced to O(NlogN). A 110,592 unknown problem can be solved within 24 hours on a SUN Sparc10.

Ž . This paper presents an extension of the generalized multipole technique GMT for 2D anisotropic scatterers. New expansions similar to the Bessel multipole expansion are derived for arbitrary anisotropic media. Numerical simulations prove the accuracy and the rapid convergence of these expansions. As the results obtained are extremely accurate, this technique is most helpful for the evaluatio...