Related papers: A vertex-weighted-Least-Squares gradient reconstru…

This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries in the finite volume approach. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by…

We propose a family of gradient reconstruction schemes based on the solution of over-determined systems by orthogonal or oblique projections. In the case of orthogonal projections, we retrieve familiar weighted least-squares gradients, but…

This work primarily focuses on the study of three gradient reconstruction techniques applied to the calculation of viscous terms in a cell-centered, finite volume formulation for general unstructured grids. The work also addresses different…

This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative…

In the context of the cell centered finite volume approach, care must be taken when performing the reconstruction of property gradients at cell interfaces. The present work analyzes three different gradient reconstruction procedures, using…

This paper extends the gradient-based reconstruction approach of Chamarthi \cite{chamarthi2023gradient} to genuine high-order accuracy for inviscid test cases involving smooth flows. A seventh-order accurate scheme is derived using the same…

A new discretisation scheme for the gradient operator, suitable for use in second-order accurate Finite Volume Methods (FVMs), is proposed. The derivation of this scheme, which we call the Taylor-Gauss (TG) gradient, is similar to that of…

We propose a level-set-based semi-Lagrangian method on graded adaptive Cartesian grids to address the problem of surface reconstruction from point clouds. The goal is to obtain an implicit, high-quality representation of real shapes that…

Vertex-centroid schemes are cell-centered finite volume schemes for conservation laws which make use of vertex values to construct high resolution schemes. The vertex values must be obtained through a consistent averaging (interpolation)…

We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted-residual error estimator. We prove that the adaptive…

We present a generic framework for gradient reconstruction schemes on unstructured meshes using the notion of a dyadic sum-vector product. The proposed formulation reconstructs centroidal gradients of a scalar from its directional…

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…

High order reconstruction in the finite volume (FV) approach is achieved by a more fundamental form of the fifth order WENO reconstruction in the framework of orthogonally-curvilinear coordinates, for solving the hyperbolic conservation…

Neural networks are typically optimized with variants of stochastic gradient descent. Under a squared loss, however, the optimal solution to the linear last layer weights is known in closed-form. We propose to leverage this during…

Currently, the area of geometric modeling and the construction of 3D models based on point clouds from laser sensors is actively developing. One of the basic tasks of geometric modeling is the reconstruction of a surface from a cloud of…

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…

In this paper, the compact gas-kinetic scheme for compressible flow is extended to hybrid unstructured mesh. Based on both cell-averaged flow variables and their gradients updated from time accurate gas evolution model at cell interfaces, a…

We propose a level set method to reconstruct unknown surfaces from point clouds, without assuming that the connections between points are known. We consider a variational formulation with a curvature constraint that minimizes the surface…

This is the second paper on the study of gradient recovery for elliptic interface problem. In our previous work [H. Guo and X. Yang, 2016, arXiv:1607.05898], we developed gradient recovery finite element method based on body-fitted mesh. In…