Related papers: Computational multiscale methods for parabolic wav…
Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations…
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
Efficient and accurate numerical simulation of 3D acoustic wave propagation in heterogeneous media plays an important role in the success of seismic full waveform inversion (FWI) problem. In this work, we employed the combined scheme and…
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…
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop…
We consider the numerical approximation of acoustic wave propagation problems by mixed BDM(k+1)-P(k) finite elements on unstructured meshes. Optimal convergence of the discrete velocity and super-convergence of the pressure by one order are…
A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The…
We study multi-parameter solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation which include oscillating laser beams in a parabolic waveguide, spiral light beams, and other important families of…
We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic…
In this work, we introduce a Variational Multi-Scale (VMS) method for the numerical approximation of parabolic problems, where sub-grid scales are approximated from the eigenpairs of associated elliptic operator. The abstract method is…
Partial Differential Equations (PDEs) models for wave propagation in inhomogeneous media are relevant for many applications. We will discuss numerical methods tailored for tackling problems governed by these variable-coefficient PDEs.…
We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…
Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results…
In this paper we propose a multiscale method for the acoustic wave equation in highly oscillatory media. We use a higher-order extension of the localized orthogonal decomposition method combined with a higher-order time stepping scheme and…
A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential…
We present a new hybrid numerical method for multiscale partial differential equations, which simultaneously captures the global macroscopic information and resolves the local microscopic events over regions of relatively small size. The…
In this paper, we develop a local multiscale model reduction strategy for the elastic wave equation in strongly heterogeneous media, which is achieved by solving the problem in a coarse mesh with multiscale basis functions. We use the…
We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, and typical solutions oscillate with frequency proportional…