The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem:standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is us...
We consider the mixed discontinuous Galerkin(DG)finite element approximation of the Stokes equation and provide the analysis for the[P_(k)]^d-P_(k-1)element on the tensor product meshes.Comparing to the previous stabi...
supported by the National Natural Science Foundation of China(Grant Nos.12071045,12201299);the Natural Science Foundation of Jiangsu Province(Grant No.BK20220870);the Youth Foundation of Laboratory of Computational Physics(Grant No.HX02021-37).
In this paper,we present a nonlinear correction technique to modify the nine-point scheme proposed in[SIAM J.Sci.Comput.,30:3(2008),1341-1361]such that the resulted scheme preserves the positivity.We first express the...
This work was performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No.89233218CNA000001.
We explore an intersection-based remap method between meshes consisting of isoparametric elements.We present algorithms for the case of serendipity isoparametric elements(QUAD8 elements)and piece-wise constant(cell-ce...
European Research Council(725555);Fonds Wetenschappelijk Onderzoek(11O0923N,G020421).
Programmable photonic integrated circuits(PPICs)emerge as a novel technology with an enormous potential for ground-breaking innovation.Different architectures are currently being considered that dictate how waveguides...
The numerical manifold method(NMM)is a numerical method pioneered by Genhua Shi in 1991 to approximate continuousdiscontinuous(C-D)fields.C-D fields are widespread and involve complex boundaries,moving discontinuities...
supported by the Fundamental Research Funds for Central Public Welfare Research Institutes in China(Grant Nos.CKSF2010012/CL,CKSF2013031/CL,CKSF2014054/CL,CKSF2015033/CL,and CKSF2016022/CL)。
Aiming to solve mesh generation,computational stability,accuracy control,and other problems encountered with existing numerical methods,such as the finite element method and the finite volume method,a new numerical co...
supported in part by the National Natural Science Foundation of China grants NSFC 12131005 and NSAF U2230402.
We propose two families of nonconforming elements on cubical meshes:one for the -curlΔcurl problem and the other for the Brinkman problem.The element for the -curlΔcurl problem is the first nonconforming element on ...
supported by the National Natural Science Foundation of China(Grant Nos.12062007 and 12072135).
A steady-state thermal hybrid element model is proposed to calculate particle-reinforced composites divided by an improved quadtree mesh.The functional of hybrid flux finite element method(HF-FEM)is constructed using ...
supported by the National Natural Science Foundation of China(Nos.61877056,61972368);the Anhui Provincial Natural Science Foundation,PR China(No.1908085QA11).
Mesh segmentation is a fundamental and critical task in mesh processing,and it has been studied extensively in computer graphics and geometric modeling communities.However,current methods are not well suited for segme...