Related papers: A Fast Summation Method for Oscillatory Lattice Su…
A direct summation method for the Madelung constant calculation is presented where a crystal lattice is constructed from linear arrays of charges or axial multipoles. An array is designed to have vanishing low order electric moments such…
In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…
A spectral method using associated Legendre functions with algebraic mapping is developed for a linear stability analysis of wake vortices. These functions serve as Galerkin basis functions, capturing correct analyticity and boundary…
A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equations. In the proposed method, the exterior domain…
The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the…
We suggest a local wave function based ab initio correlation method for infinite periodic systems, which can describe both the near range as well as the long range correlation effects coherently in the same scheme. Specifically, this work…
This manuscript is the second in a series presenting fast direct solution techniques for solving two-dimensional wave scattering problems from quasi-periodic multilayered structures. The fast direct solvers presented in the series are for…
We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…
We propose a new method to renormalize lattice operators. The method is based on the technique to compute the spectral sum appearing in the Shifman-Vainshtein-Zakharov QCD sum rule from lattice correlators. The application of this technique…
Motivated by research in metamaterials, we consider the challenging problem of acoustic wave scattering by a doubly periodic quadrant of sound-soft scatterers arranged in a square formation, which we have dubbed the quarter lattice. This…
Scattering of a time harmonic anti-plane shear wave due to either a pair of crack tips or a pair of rigid constraint tips on square lattice is considered. The two problems correspond to the so called zero-offset case of scattering due to a…
We present a hybridization technique for summation-by-parts finite difference methods with weak enforcement of interface and boundary conditions for second order, linear elliptic partial differential equations. The method is based on…
We analyse a linear lattice Boltzmann (LB) formulation for simulation of linear acoustic wave propagation in heterogeneous media. We employ the single-relaxation-time Bhatnagar-Gross-Krook (BGK) as well as the general multi-relaxation-time…
This paper is concerned with inverse scattering problems of determining the support of an isotropic and homogeneous penetrable body from knowledge of multi-static far-field patterns in acoustics and in linear elasticity. The normal…
We present a perturbative technique for modeling the scattering of light by a nonlinear material. This approach eliminates the need for an iterative algorithm to solve the fully coupled nonlinear problem. We demonstrate its effectiveness in…
We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen's method of…
Traditionally resonant interactions among short waves, with large real wave-numbers, were described statistically and only a small domain in spectral space with integer wave-numbers, discrete resonances, had to be studied separately in…