相关论文: A High Order Multi-Dimensional Characteristic Trac…

The Vlasov-Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{-3}$ at late times. In this…

This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov--Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution…

The classical Dynamic Programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. The DP scheme for the numerical…

Accurate modeling of sea ice dynamics is critical for predicting environmental variables and is important in applications such as navigating ice breaker ships. Research for both modeling and simulating sea ice dynamics is ongoing, with the…

Fusion energy offers the potential for the generation of clean, safe, and nearly inexhaustible energy. While notable progress has been made in recent years, significant challenges persist in achieving net energy gain. Improving plasma…

We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge…

We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…

In this paper, we introduce a fourth-order accurate finite element method for incompressible variable density flow. The method is implicit in time and constructed with the Taylor series technique, and uses standard high-order Lagrange basis…

For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach to the s(trong)-consistency analysis of their finite difference approximations on Cartesian grids. First we apply the…

In this study, we introduce a tensor-train (TT) finite difference WENO method for solving compressible Euler equations. In a step-by-step manner, the tensorization of the governing equations is demonstrated. We also introduce…

In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…

In this paper, we propose a high-order energy-conserving semi-Lagrangian discontinuous Galerkin(ECSLDG) method for the Vlasov-Ampere system. The method employs a semi-Lagrangian discontinuous Galerkin scheme for spatial discretization of…

Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm…

Quasi-periodic solutions with multiple base frequencies exhibit the feature of $2\pi$-periodicity with respect to each of the hyper-time variables. However, it remains a challenge work, due to the lack of effective solution methods, to…

We propose a WENO finite difference scheme to approximate anelastic flows, and scalars advected by them, on staggered grids. In contrast to existing WENO schemes on staggered grids, the proposed scheme is designed to be arbitrarily…

We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a…

This paper presents an innovative approach to dimensionality reduction and feature extraction in high-dimensional datasets, with a specific application focus on wood surface defect detection. The proposed framework integrates sparse…

In this paper, we propose several new stochastic second-order algorithms for policy optimization that only require gradient and Hessian-vector product in each iteration, making them computationally efficient and comparable to policy…

We introduce novel dynamical low-rank methods for solving large-scale matrix differential equations, motivated by algorithms from randomized numerical linear algebra. In terms of performance (cost and accuracy), our methods overperform…

We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented…