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...

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.

Possible con®gurations of the magnetic ®eld in the outer magnetosphere during geomagnetic polarity reversals are investigated by considering the idealized problem of a magnetic multipole of order m and degree n located at the centre of a spherical cavity surrounded by a boundless perfect diamagnetic medium. In this illustrative idealization, the ®xed spherical (magnetopause) boundary layer beha...

The fast multipole method is one of the most efficient methods to compute matrix-vector multiplications and accelerate the solution of linear systems of equations. In this paper, we provide all necessary theoretical statements concerning the hydrodynamical double layer potential, which enable the application of an adaptive version of the fast multipole method of Greengard and Rokhlin to the int...

A new definition of the interaction list in the fast multipole method (FMM) is introduced in this paper, which can reduce the moment-to-local (M2L) translations by about 30-40% and therefore improve the efficiency for the FMM. In addition, an adaptive tree structure is investigated, which is potentially more efficient than the oct-tree structure for thin and slender domains as in the case of mi...

The fast multipole method (FMM) has had great success in reducing the computa4 tional complexity of solving the boundary integral form of the Helmholtz equation. We present a 5 formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. 6 By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of 7 the algorithm are...

for each i = 1, 2, .., n, where K is a given (usually smooth away from origin) kernel. For example, for gravitaional interactions in 3D, K(x, y) = 1 |x−y| ; for 2D Laplacian equation, K(x, y) = log |x− y|. The direct computation has a cost of O(n). In recent decades, many algorithm has been invented and developed to accelerate the quadratic time complexity. Fast multipole method (FMM), first in...

A novel method for extracting multipole amplitudes in the nucleon resonance region from electroproduction data is presented. The method is based on statistical concepts and it relies heavily on Monte Carlo and simulation techniques; it produces precise identification and determination of the contributing multipole amplitudes in the resonance region and for the first time a rigorous determinatio...

Parasitic extraction techniques are used to estimate signal delay in VLSI chips. Inductance extraction is a critical component of the parasitic extraction process in which on-chip inductive effects are estimated with high accuracy. In earlier work [1], we described a parallel software package for inductance extraction called ParIS, which uses a novel preconditioned iterative method to solve the...