Related papers: Numerical treatment of interfaces for second-order…
In this paper a new Runge-Kutta type scheme is introduced for nonlinear stochastic partial differential equations (SPDEs) with multiplicative trace class noise. The proposed scheme converges with respect to the computational effort with a…
In this article we present a novel and general methodology for building second order finite volume implicit-explicit (IMEX) numerical schemes for solving two dimensional financial parabolic PDEs with mixed derivatives. In particular,…
In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by vertical and horizontal straight lines, piecewise constant…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
We present a novel and general methodology for building second-order finite volume implicit-explicit Runge-Kutta numerical schemes for solving two-dimensional financial parabolic PDEs with mixed derivatives. The methods achieve second-order…
In this paper, we present a block-oriented scheme for adaptive mesh refinement based on summation-by-parts (SBP) finite difference methods and simultaneous-approximation-term (SAT) interface treatment. Since the order of accuracy at SBP-SAT…
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…
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…
We analyze two types of summation-by-parts finite difference operators for approximating the second derivative with variable coefficient. The first type uses ghost points, while the second type does not use any ghost points. A previously…
In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogeneous media. We concentrate on the wave equation and distinguish between two classes of…
The scalar, one-dimensional advection equation and heat equation are considered. These equations are discretized in space, using a finite difference method satisfying summation-by-parts (SBP) properties. To impose the boundary conditions,…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
A semi-implicit-explicit (semi-IMEX) Runge-Kutta (RK) method is proposed for the numerical integration of ordinary differential equations (ODEs) of the form $\mathbf{u}' = \mathbf{f}(t,\mathbf{u}) + G(t,\mathbf{u}) \mathbf{u}$, where…
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…
This paper deals with the construction and analysis of two integrators for (semi-linear) second-order partial differential-algebraic equations of semi-explicit type. More precisely, we consider an implicit-explicit Crank-Nicolson scheme as…
We study the numerical solutions of time-dependent systems of partial differential equations, focusing on the implementation of boundary conditions. The numerical method considered is a finite difference scheme constructed by high order…
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
This paper presents a novel implicit scheme for the constraint resolution in real-time finite element simulations in the presence of contact and friction. Instead of using the standard motion correction scheme, we propose an iterative…