相关论文: A new Lagrange multiplier approach for constructin…
The numerical approximation of incompressible fluid-structure interaction problems with Lagrange multiplier is generally based on strongly coupled schemes. This delivers unconditional stability but at the expense of solving a…
We develop a conservative, positivity-preserving discontinuous Galerkin (DG) method for the population balance equation (PBE), which models the distribution of particle numbers across particle sizes due to growth, nucleation, aggregation,…
This work focuses on the numerical approximation of the Shallow Water Equations (SWE) using a Lagrange-Projection type approach. We propose to extend to this context recent implicit-explicit schemes developed in the framework of…
The use of Lagrange multipliers in the context of quintessence/phantom scalar fields allows to constrain the behavior of the scalar field, which provides a powerful tool, not only for the reconstruction of cosmological solutions but also…
We introduce novel entropy-dissipative numerical schemes for a class of kinetic equations, leveraging the recently introduced scalar auxiliary variable (SAV) approach. Both first and second order schemes are constructed. Since the…
We consider an optimization based limiter for enforcing positivity of internal energy in a semi-implicit scheme for solving gas dynamics equations. With Strang splitting, the compressible Navier-Stokes system is splitted into the…
This paper develops a family of fast, structure-preserving numerical algorithms for the nonlinear Maxwell-Ampere Nernst-Planck equations. For the first-order scheme, the Slotboom transformation rewrites the Nernst-Planck equation to enable…
In this paper, we perform stability analysis for a class of second and third order accurate strong-stability-preserving modified Patankar Runge-Kutta (SSPMPRK) schemes, which were introduced in [4,5] and can be used to solve convection…
As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…
Most numerical methods developed for solving nonlinear programming problems are designed to find points that satisfy certain optimality conditions. While the Karush-Kuhn-Tucker conditions are well-known, they become invalid when constraint…
In this work, we focus on the numerical approximation of the shallow water equations in two space dimensions. Our aim is to propose a well-balanced, all-regime and positive scheme. By well-balanced, it is meant that the scheme is able to…
The paper concerns the study of criticality of Lagrange multipliers in variational systems that has been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
Since almost twenty years, modified Patankar--Runge--Kutta (MPRK) methods have proven to be efficient and robust numerical schemes that preserve positivity and conservativity of the production-destruction system irrespectively of the time…
A lift-and-permute scheme of alternating direction method of multipliers (ADMM) is proposed for linearly constrained convex programming. It contains not only the newly developed balanced augmented Lagrangian method and its dual-primal…
It is possible to introduce external time dependent back ground fields in the formulation of a system as fields whose dynamics can not be deduced from Euler Lagrange equations of motion. This method leads to singular Lagrangians for real…
We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The…
The main objective of this paper is to present an efficient structure-preserving scheme, which is based on the idea of the scalar auxiliary variable approach, for solving the space fractional nonlinear Schr\"{o}dinger equation. First, we…
We propose a semi-discrete scheme for 2D Keller-Segel equations based on a symmetrization reformation, which is equivalent to the convex splitting method and is free of any nonlinear solver. We show that, this new scheme is unconditionally…
A high-order, well-balanced, positivity-preserving quasi-Lagrange moving mesh DG method is presented for the shallow water equations with non-flat bottom topography. The well-balance property is crucial to the ability of a scheme to…