相关论文: A new Lagrange multiplier approach for constructin…

We propose two numerical algorithms in the fully nonconvex setting for the minimization of the sum of a smooth function and the composition of a nonsmooth function with a linear operator. The iterative schemes are formulated in the spirit…

We develop a positivity-preserving finite difference WENO scheme for the Ten-Moment equations with body forces acting as a source in the momentum and energy equations. A positive forward Euler scheme under a CFL condition is first…

A rezoning-type adaptive moving mesh discontinuous Galerkin method is proposed for the numerical solution of the shallow water equations with non-flat bottom topography. The well-balance property is crucial to the simulation of perturbation…

We introduce a new method for building higher-degree sum-of-squares lower bounds over the hypercube $\mathbf{x} \in \{\pm 1\}^N$ from a given degree 2 lower bound. Our method constructs pseudoexpectations that are positive semidefinite by…

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…

We present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. Given a system of differential equations possessing conservation laws, our approach is based on…

We consider a smooth pessimistic bilevel optimization problem, where the lower-level problem is convex and satisfies the Slater constraint qualification. These assumptions ensure that the Karush-Kuhn-Tucker (KKT) reformulation of our…

A second order accurate numerical scheme is proposed and analyzed for the periodic three-component Macromolecular Microsphere Composite(MMC) hydrogels system, a ternary Cahn-Hilliard system with a Flory-Huggins-deGennes free energy…

We formulate a novel numerical method suitable for the solution of topology optimization problems in solid mechanics. The most salient feature of the new approach is that the space and time discrete equations of the numerical method can be…

We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard…

Two primary scalar auxiliary variable (SAV) approaches are widely applied for simulating gradient flow systems, i.e., the nonlinear energy-based approach and the Lagrange multiplier approach. The former guarantees unconditional energy…

This paper presents a novel Fourier spectral method that utilizes optimization techniques to ensure the positivity and conservation of moments in the space of trigonometric polynomials. We rigorously analyze the accuracy of the new method…

In this paper we propose and investigate a general approach to constructing local energy-preserving algorithms which can be of arbitrarily high order in time for solving Hamiltonian PDEs. This approach is based on the temporal…

This paper presents two kinds of strategies to construct structure-preserving algorithms with homogeneous Neumann boundary conditions for the sine-Gordon equation, while most existing structure-preserving algorithms are only valid for zero…

This paper seeks to derive the modified KdV (mKdV) equation using a novel approach from systems generated from abstract Lagrangians that possess a two-parameter symmetry group. The method to do uses a modified modulation approach, which…

In this paper, we develop a fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme for simulating the chemically reacting, compressible Euler equations with complex thermodynamics. The proposed…

In this study, we present a novel approach to mimetic gravity incorporating a non-zero nonmetricity tensor with vanishing torsion and curvature, establishing a generalized mimetic-$f(Q)$ gravity framework. Using the Lagrange multiplier…

In this work, we aim at constructing numerical schemes, that are as efficient as possible in terms of cost and conservation of invariants, for the Vlasov--Fokker--Planck system coupled with Poisson or Amp\`ere equation. Splitting methods…

Anti-selfdual Lagrangians on a state space lift to path space provided one adds a suitable selfdual boundary Lagrangian. This process can be iterated by considering the path space as a new state space for the newly obtained anti-selfdual…

In this paper, we propose and analyse a reconstruction technique which enables one to design high-order conservative semi-Lagrangian schemes for kinetic equations. The proposed reconstruction can be obtained by taking the sliding average of…