Related papers: Generalized Kirchhoff approximation for Helmholtz …
The sparse approximation of high-frequency Helmholtz-type integral operators has many important physical applications such as problems in wave propagation and wave scattering. The discrete system matrices are huge and densely populated;…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
For elliptic in the half-space and parabolic degenerating on the boundary equation of Keldysh type we construct by similarity method the self-similar solution, which is the approximation to the identity in the class of integrable functions.…
We propose an algorithm for computing the proximity operator of a sum of composite convex functions in Hilbert spaces and investigate its asymptotic behavior. Applications to best approximation and image recovery are described.
Three problems for a discrete analogue of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: 1) the problem with a point source on an entire plane; 2) the…
The nonlinear Helmholtz equation (NLH) models the propagation of electromagnetic waves in Kerr media, and describes a range of important phenomena in nonlinear optics and in other areas. In our previous work, we developed a fourth order…
We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with logarithmic Kirchhoff function. We establish the precise asymptotic formulas for the solution $u_\lambda(x)$ as $\lambda \to \infty$. Here, $\lambda > 0$ is the…
We consider the Dirichlet problem for two types of degenerate elliptic Hessian equations . New results about solvability of the equations in the $C^{1,1}$ space are provided.
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
We introduce some generalizations of the Hermitian-Einstein equation for diagonal harmonic metrics on cyclic Higgs bundles, including a generalization using subharmonic functions. When the coefficients are all smooth, we prove the…
In this paper, based on the overlapping domain decomposition method (DDM) proposed in \cite{Leng2015}, an one step preconditioner is proposed to solve 2D high frequency Helmholtz equation. The computation domain is decomposed in both $x$…
The Helmholtz equation arises in the study of electromagnetic radiation, optics, acoustics, etc. In spherical coordinates, its general solution can be written as a spherical harmonic series which satisfies the radiation condition at…
A known first order method to find a feasible solution to a conic problem is an adapted von Neumann algorithm. We improve the distance reduction step there by projecting onto the convex hull of previously generated points using a primal…
We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…
In these lectures three different methods of computing the asymptotic expansion of a Hermitian matrix integral is presented. The first one is a combinatorial method using Feynman diagrams. This leads us to the generating function of the…
The joint approximate diagonalization of non-commuting symmetric matrices is an important process in independent component analysis. This problem can be formulated as an optimization problem on the Stiefel manifold that can be solved using…
Consider a Urysohn integral equation $x - \mathcal{K} (x) = f$, where $f$ and the integral operator $\mathcal{K}$ with kernel of the type of Green's function are given. In the computation of approximate solutions of the given integral…
We study the periodic homogenization for convex Hamilton-Jacobi equations on perforated domains under the Neumann type boundary conditions. We consider two types of conditions, the oblique derivative boundary condition and the prescribed…
This paper deals with the Cauchy-Dirichlet problem for the fractional Cahn-Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…