Related papers: An efficient filtered scheme for some first order …
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the discrete energy conservation for the undamped model theoretically. Due to the semi-implicit treatment for the…
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…
We propose a novel class of temporal high-order parametric finite element methods for solving a wide range of geometric flows of curves and surfaces. By incorporating the backward differentiation formulae (BDF) for time discretization into…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
We study nonlocal first-order equations arising in the theory of dislocations. We prove the existence and uniqueness of the solutions of these equations in the case of positive and negative velocities, under suitable regularity assumptions…
Staggered grid finite difference scheme is widely used for the first order elastic wave equation, which constitutes the basis for least-squares reverse time migration and full waveform inversion. It is of great importance to improve the…
This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…
In this article, we propose high-order finite-difference entropy stable schemes for the two-fluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux…
In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three…
Multidimensional population balance models (PBMs) describe chemical and biological processes having a distribution over two or more intrinsic properties (such as size and age, or two independent spatial variables). The incorporation of…
A numerical scheme for approximating the nonlinear filtering density is introduced and its convergence rate is established, theoretically under a parabolic H\"{o}rmander condition, and empirically in numerical examples. In a prediction…
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…
In this paper, we introduce a framework for the discretization of a class of constrained Hamilton-Jacobi equations, a system coupling a Hamilton-Jacobi equation with a Lagrange multiplier determined by the constraint. The equation is…
This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…
The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
This paper is concerned with the construction of high order schemes on irregular grids for balance laws, including a discussion of an a-posteriori error indicator based on the numerical entropy production. We also impose well-balancing on…