Related papers: Mimetic Spectral Element advection
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…
We derive and analyze a fully computable discrete scheme for fractional partial differential equations posed on the full space $\mathbb{R}^d$ . Based on a reformulation using the well-known Caffarelli-Silvestre extension, we study a…
In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…
We consider the two-dimensional advection-diffusion equation on a bounded domain subject to either Dirichlet or von Neumann boundary conditions and study both time-independent and time-periodic cases involving Liouville integrable…
Discretization is a fundamental step in numerical analysis for the problems described by differential equations, and the difference between the continuous model and discrete model is one of the most important problems. In this paper, we…
We consider $n\times n$ non-Hermitian random matrices with independent entries and a variance profile, as well as an additive deterministic diagonal deformation. We show that their empirical eigenvalue distribution converges to a limiting…
We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…
This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an…
We present a finite element variational integrator for compressible flows. The numerical scheme is derived by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the…
An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…
Recently, the numerical solution of multi-frequency, highly-oscillatory Hamiltonian problems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs) as spectral methods in time. When the problem derives from the space semi-…
In this paper, we consider the initial boundary value problem of the two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations. An alternating direction implicit (ADI) spectral method is developed based on…
We develop a structure-preserving computational framework for acoustic wave scattering by moving objects, comprising a new PML-domain-embedding model and a compatible numerical approximation. The model couples a perfectly matched layer…
An abstract framework is developed that enables the analysis of algebraically stabilized discretizations in a unified way. This framework is applied to a discretization of this kind for convection-diffusion-reaction equations. The…
In the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest.…
Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is…
In this paper, we introduce an alternative representation of the electromagnetic field scattered from a homogeneous sphere coated with a homogeneous layer of uniform thickness. Specifically, we expand the scattered field using a set of…
We propose a compressive spectral collocation method for the numerical approximation of Partial Differential Equations (PDEs). The approach is based on a spectral Sturm-Liouville approximation of the solution and on the collocation of the…
We consider an advection-diffusion equation that is advection-dominated and posed on a perforated domain. On the boundary of the perforations, we set either homogeneous Dirichlet or homogeneous Neumann conditions. The purpose of this work…
We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…