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We show that even though the Discontinuous Galerkin Spectral Element Method is stable for hyperbolic boundary-value problems, and the overset domain problem is well-posed in an appropriate norm, the energy of the approximation of the latter…
We consider spectral discretizations of hyperbolic problems on unbounded domains using Laguerre basis functions. Taking as model problem the scalar advection equation, we perform a comprehensive stability analysis that includes strong…
Miniaturized optical resonators with spatial dimensions of the order of the wavelength of the trapped light offer prospects for a variety of new applications like quantum processing or construction of meta-materials. Light propagation in…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
In this paper, we propose and test a novel diagonal sweeping domain decomposition method (DDM) with source transfer for solving the high-frequency Helmholtz equation in $\mathbb{R}^n$. In the method the computational domain is partitioned…
The aim of this work is to perform numerical simulations of the propagation of a laser in a plasma. At each time step, one has to solve a Helmholtz equation in a domain which consists in some hundreds of millions of cells. To solve this…
In this paper, phase correction and amplitude compensation are introduced to a previously developed mixed domain method (MDM), which is only accurate for modeling wave propagation in weakly heterogeneous media. Multiple reflections are also…
We consider a parameter dependent family of damped hyperbolic equations with interesting limit behavior: the system approaches steady states exponentially fast and for parameter to zero the solutions converge to that of a parabolic limit…
This paper is concerned with three-dimensional acoustic wave scattering in two-layer media, where the two homogeneous layers are separated by a locally perturbed plane featuring an axially symmetric perturbation. A fast novel boundary…
Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with…
Linear models for the radiative transfer equation have been well developed, while nonlinear models are seldom investigated even for slab geometry due to some essential difficulties. We have proposed a moment model in MPN for slab geometry…
To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the…
Estimating symmetric properties of a distribution, e.g. support size, coverage, entropy, distance to uniformity, are among the most fundamental problems in algorithmic statistics. While each of these properties have been studied extensively…
We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Boltzmann equations. The equations are discretized with Hermite polynomials in velocity space yielding a first order…
We examine stability of summation by parts (SBP) numerical schemes that use hyperboloidal slices to include future null infinity in the computational domain. This inclusion serves to mitigate outer boundary effects and, in the future, will…
We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…
We study and implement a simple method, based on the Perfectly Matched Layer approach, to treat non reflecting boundary conditions with the Smoothed Particles Hydrodynamics numerical algorithm. The method is based on the concept of physical…
We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary…
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…
We present a new Lattice Boltzmann (LB) formulation to solve the Maxwell equations for electromagnetic (EM) waves propagating in a heterogeneous medium. By using a pseudo-vector discrete Boltzmann distribution, the scheme is shown to…