Related papers: Approximation of the Scattering Amplitude using No…
We present and numerically implement a computational method to construct relativistic scattering amplitudes that obey analyticity, crossing, elastic and inelastic unitarity in three and four spacetime dimensions. The algorithm is based on…
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…
An iterative algorithm is adopted to construct approximate representations of matrices describing the scattering properties of arbitrary objects. The method is based on the implicit evaluation of scattering responses from iteratively…
A new method to compute the incoherent scattering function of harmonic lattices is introduced. It is based in a saddle point approximation for each term of the phonon expansion, and is simple enough to be used in practice. The method gives…
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…
A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very…
We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions $d=2$ and $3$. This requires to approximate first the scattering field, for some incident…
In this paper, we study the inverse scattering problem for a class of signals that have a compactly supported reflection coefficient. The problem boils down to the solution of the Gelfand-Levitan-Marchenko (GLM) integral equations with a…
We proposed an iterate scheme for solving convex-concave saddle-point problems associated with general convex-concave functions. We demonstrated that when our iterate scheme is applied to a special class of convex-concave functions, which…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…
This is a continuation of our previous work entitled \enquote{Alternating Proximity Mapping Method for Convex-Concave Saddle-Point Problems}, in which we proposed the alternating proximal mapping method and showed convergence results on the…
A numerical method for solving the equations modeling acoustic scattering 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…
In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation…
We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss-Seidel iterative solution of linear equations in the precision matrix. Specifically, the…
In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem. Deterministic first-order schemes, such as Nesterov's…
We obtain a nonperturbative, analytical solution to integral equation of scattering theory by assuming the field within the scattering object is a spherical wave with a scattering amplitude equal to that of the far field. This approximation…