Related papers: A "Trefftz Machine" for Absorbing Boundary Conditi…
We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral equation techniques that allow for the efficient and accurate evaluation of quantities needed in…
In this paper a generalized fundamental solution using the boundary element method to solve the Helmholtz equation is proposed. It is observed that the commonly used fundamental solution is only valid for good conductors since the…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
The time-dependent form of Tappert's range refraction parabolic equation is derived using Daletskiy-Krein formula form noncommutative analysis and proposed as an artificial boundary condition for the wave equation in a waveguide. The…
Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…
We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for bound states in a basis set of finite size. We obtain two classes of solutions written as finite series of square integrable functions…
Single-ended circuit topologies, and a theorem for the development thereof, are presented with which one may realize constant-resistance (or reflectionless) filters, having ideally zero reflection coefficient at all frequencies and from all…
In this paper, we consider initial-boundary value problems for two-component nonlinear systems of time-fractional diffusion equations with the homogeneous Neumann boundary condition and non-negative initial values. The main results are the…
Time reflection and refraction are temporal analogies of the spatial boundary effects derived from Fermat's principle. They occur when classical waves strike a time boundary where an abrupt change in the properties of the medium is…
We consider the high frequency Helmholtz equation with a variable refraction index $n^2(x)$ ($x \in \R^d$), supplemented with a given high frequency source term supported near the origin $x=0$. A small absorption parameter…
This paper investigates the Knudsen layer equation in half-space, arising from the hydrodynamic limit of the Boltzmann equation to fluid dynamics. We consider the Maxwell reflection boundary condition with accommodation coefficient…
This paper is concerned with fast and accurate computation of exterior wave equations truncated via exact circular or spherical nonreflecting boundary conditions (NRBCs, which are known to be nonlocal in both time and space). We first…
The recent results presented in arXiv:2202.05608 have led to significant developments in achieving stable approximations of Helmholtz solutions by plane wave superposition. The study shows that the numerical instability and ill-conditioning…
In finite-volume-based flow-simulations with free-surface waves, wave reflections at the domain boundaries can cause substantial errors in the results and must therefore be minimized. This can be achieved via `implicit relaxation zones',…
Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two and three dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a…
A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…
Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from…
We propose a novel approach to simulate the solution of the time-dependent Schr\"odinger equation with a general variable potential. The key idea is to approximate the Titchmarsh-Weyl m-function (exact Dirichlet-to-Neumann operator) by a…
Solar oscillations can be modeled by Galbrun's equation which describes Lagrangian wave displacement in a self-gravitating stratified medium. For spherically symmetric backgrounds, we construct an algorithm to compute efficiently and…
The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary value problems. Its main drawback is that it often leads to ill-conditioned systems of equations. In this paper we investigate for the…