This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be pre-calculated and thereby effectively reduces the complexity of the problem to a calculation over the surface. Several eigenvalues are retrieved simultaneously. ...

A numerical method for solving the equations modeling acoustic scattering in three dimensions is presented. The method is capable of handling several dozen scatterers, each of which is several wave-lengths long, on a personal work station. Even for geometries involving cavities, solutions accurate to seven digits or better were obtained. The method relies on a Boundary Integral Equation formula...

A method for designing magnetic shields that do not perturb applied multipole fields in the static regime is developed. Cylindrical core-shell structures with two layers characterized by homogeneous isotropic permeabilities are found to support neutral shielding of multipole fields and unique cloaking solutions of arbitrary multipole order. An extra degree of freedom is provided by every layer ...

We present a fast multipole algorithm for the evaluation of pairwise interaction through the radial basis functions such as 1/r, ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 þ a2 p and 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 þ a2 p (with a > 0) in both two and three dimensions. Our algorithm is an extension of the kernel independent fast multipole method presented in Ying et al. [L. Y...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 12 January 2021Accepted: 07 June 2021Published online: 28 September 2021Keywordsmultiple scattering, multipole expansion, layer potential, error analysis, truncation errorAMS Subject Headings31A10, 42B10, 65N12, 65N15, 65R20, 70F10, 78M15, 78M16Publication DataISSN (print...

~assuming the simulation box is cubic!, where qi and ri are the charge and position of particle i, L is the size of the simulation box, n5(n1 ,n2 ,n3), and the prime indicates that the i5 j terms are omitted when n50. The Ewald summation method has been widely used to handle the lattice sum in Eq. ~1!. In the method, the above-mentioned conditionally convergent series is written as a sum of a c...

The evaluation of sums (matrix-vector products) of the solutions of the three-dimensional biharmonic equation can be accelerated using the fast multipole method, while memory requirements can also be significantly reduced. We develop a complete translation theory for these equations. It is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering ...

In this paper we present an implementation of the well known “fast multipole” method for the efficient calculation of dipole fields, that uses polynomials in the Cartesian coordinates rather than spherical harmonics. This has considerable efficiency and simplicity advantages. We have implemented it in the context of an arbitrary hierarchical system of cells – no periodic mesh is required. The i...