Related papers: A second-order face-centred finite volume method o…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
In this paper, we propose new basis functions defined on curved sides or faces of curvilinear elements (polygons or polyhedrons with curved sides or faces) for the weak Galerkin finite element method. Those basis functions are constructed…
A common approach for generating an anisotropic mesh is the M-uniform mesh approach where an adaptive mesh is generated as a uniform one in the metric specified by a given tensor M. A key component is the determination of an appropriate…
Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…
Industrial 3D face assets creation typically reconstructs topology-consistent face meshes from multi-view images for downstream production. However, high-quality reconstruction usually requires manual processing or specific capture…
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…
In this paper we present a conservative cell-centered Lagrangian finite volume scheme for the solution of the hyper-elasticity equations on unstructured multidimensional grids. The starting point of the new method is the Eucclhyd scheme,…
Gradient reconstruction is a key process for the spatial accuracy and robustness of finite volume method, especially in industrial aerodynamic applications in which grid quality affects reconstruction methods significantly. A novel gradient…
We analyze two types of summation-by-parts finite difference operators for approximating the second derivative with variable coefficient. The first type uses ghost points, while the second type does not use any ghost points. A previously…
This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…
The increasing demand for larger and higher fidelity simulations has made Adaptive Mesh Refinement (AMR) and unstructured mesh techniques essential to focus compute effort and memory cost on just the areas of interest in the simulation…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and…
We propose a high-order FDTD scheme based on the correction function method (CFM) to treat interfaces with complex geometry without increasing the complexity of the numerical approach for constant coefficients. Correction functions are…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
We study a colocated cell centered finite volume method for the approximation of the incompressible Navier-Stokes equations posed on a 2D or 3D finite domain. The discrete unknowns are the components of the velocity and the pressures, all…
We present a method to solve two-stage stochastic problems with fixed recourse when the uncertainty space can have either discrete or continuous distributions. Given a partition of the uncertainty space, the method is addressed to solve a…
This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…
We present a new effective way for performance capture of deforming meshes with fine-scale time-varying surface detail from multi-view video. Our method builds up on coarse 4D surface reconstructions, as obtained with commonly used…
We consider in this work the numerical resolution of a 2D shallow water system with a Coriolis effect and bottom friction stresses on unstructured meshes by a new Finite Volume Characteristics (FVC) scheme, which has been introduced in the…