Related papers: Local Solution Method for Numerical Solving of the…
We propose a novel on-surface radiation condition to approximate the outgoing solution to the Helmholtz equation in the exterior of several impenetrable convex obstacles. Based on a local approximation of the Dirichlet-to-Neumann operator…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while…
Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing…
Consider the elastic scattering of a time-harmonic wave by multiple well separated rigid particles in two dimensions. To avoid using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert…
The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis consisting of solutions of the partial differential equation…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…
In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…
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…
We propose a spectral collocation method to approximate the exact boundary control of the wave equation in a square domain. The idea is to introduce a suitable approximate control problem that we solve in the finite-dimensional space of…
High-frequency wave propagation is often modelled by nonlinear Friedrichs systems where both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, which causes oscillations with wavelengths…
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
We use the work of Milton, Seppecher, and Bouchitt\'{e} on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In…
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…