Related papers: A plane wave method based on approximate wave dire…
A two-dimensional water wave model based on conformal mapping is presented. The model is exact in the sense that it does not rely on truncated series expansions, nor suffer any numerical diffusion. Additionally, it is computationally highly…
A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…
Plane waves are regarded as the general solution of the wave equation. However the plane wave expansion of standing waves by means of complex phasors leads to a theory in which the time coordinate does not receive the same treatment as the…
We study numerically the dispersion and dissipation properties of the plane wave virtual element method and the nonconforming Trefftz virtual element method for the Helmholtz problem. Whereas the former method is based on a conforming…
We examine the use of the Dirichlet-to-Neumann coarse space within an additive Schwarz method to solve the Helmholtz equation in 2D. In particular, we focus on the selection of how many eigenfunctions should go into the coarse space. We…
An adapted bubble approach which is a modifiation of the residual-free bubbles (RFB) method, is proposed for the Helmhotz problem in 2D. A new two-level finite element method is introduced for the approximations of the bubble functions.…
This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…
This work introduces a novel Trefftz Continuous Galerkin (TCG) method for 2D Helmholtz problems based on evanescent plane waves (EPWs). We construct a new globally-conforming discrete space, departing from standard discontinuous Trefftz…
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 consider the numerical solution of scalar wave equations in domains which are the union of a bounded domain and a finite number of infinite cylindrical waveguides. The aim of this paper is to provide a new convergence analysis of both…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
Spatial sound field interpolation relies on suitable models to both conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest…
Electronic correlation energies from the random-phase approximation converge slowly with respect to the plane wave basis set size. We study the conditions, under which a short-range local density functional can be used to account for the…
A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained.
The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates…
Boundary element methods for the Helmholtz equation lead to large dense matrices that can only be handled if efficient compression techniques are used. Directional compression techniques can reach good compression rates even for…
We present a simple, robust and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on…
Two concepts of plane waves in anisotropic viscoelastic media are studied. One of these concepts allows for the use of methods based on the theory of complete Bernstein functions. This allows for a deeper study of frequency-domain…
Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…
The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing wave spacetimes and then extracts approximate solutions of the physical problem, with…