Related papers: A high order finite difference method for the elas…
We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) for the $n$-dimensional non-homogeneous wave equation, $n\geq 1$. Their construction is accomplished by both the…
A new finite difference method on irregular, locally perturbed rectangular grids has been developed for solving electromagnetic waves around curved perfect electric conductors (PEC). This method incorporates the back and forth error…
In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…
A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
A high order finite difference method is proposed for unstructured meshes to simulate compressible inviscid/viscous flows with/without discontinuities. In this method, based on the strong form equation, the divergence of the flux on each…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on…
For elliptic interface problems with discontinuous coefficients, the maximum accuracy order for compact 9-point finite difference scheme in irregular points is three [7]. The discontinuous coefficients usually have abrupt jumps across the…
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…
We consider wave propagation in a coupled fluid-solid region, separated by a static but possibly curved interface. The wave propagation is modeled by the acoustic wave equation in terms of a velocity potential in the fluid, and the elastic…
In this work, we propose and develop efficient and accurate numerical methods for solving the Kirchhoff-Love plate model in domains with complex geometries. The algorithms proposed here employ curvilinear finite-difference methods for…
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…
The application of suitable numerical boundary conditions for hyperbolic conservation laws on domains with complex geometry has become a problem with certain difficulty that has been tackled in different ways according to the nature of the…
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods…
Effective interface conditions for a periodically voided thin layer separating two homogeneous bulk regions are derived for the elastic wave equation by taking the simultaneous limit of vanishing layer periodicity and layer thickness. The…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
We study non-conforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a…
We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…
In this paper, a class of finite difference numerical techniques is presented to solve the second-order linear inhomogeneous damped wave equation. The consistency, stability, and convergences of these numerical schemes are discussed. The…