A family of inexpensive discretization schemes for diffusion problems on unstructured polygonal and polyhedral meshes is introduced. The material properties are described by a full tensor. The theoretical results are confirmed with numerical experiments.

In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element method of arbitrary order. We prove that the proposed Hessian recovery method preserves polynomials of degree k + 1 on general unstructured meshes and superconverges at a rate of O(hk) on mildly structured meshes. In addition, the method is proved to be ultraconvergent (two orders hi...

A three-dimensional unstructured mesh discretization of the rotational from of the incompressible Navier–Stokes is presented. The method uses novel and highly efficient algorithms for interpolating the velocity vector and constructing the convention term. The resulting discretization is shown to conserve mass, kinetic energy, and vorticity to machine precision both locally and globally. The spa...

An algorithm for automatic parallel generation of three-dimensional unstructured computational meshes based on geometrical domain decomposition is proposed in this paper. Software package build upon proposed algorithm is described. Several practical examples of mesh generation on multiprocessor computational systems are given. It is shown that developed parallel algorithm enables us to reduce m...

This paper contains error estimates for covolume discretizations of Maxwell’s equations in three space dimensions. Several estimates are proved. First, an estimate for a semi-discrete scheme is given. Second, the estimate is extended to cover the classical interlaced time marching technique. Third, some of our unstructured mesh results are specialized to rectangular meshes, both uniform and non...

A three-dimensional semi-implicit edge-based unstructured-mesh model is developed that integrates nonhydrostatic anelastic equations, suitable for simulation of small-to-mesoscale atmospheric flows. The model builds on nonoscillatory forwardin-time MPDATA approach using finite-volume discretization and admitting unstructured meshes with arbitrarily shaped cells. The numerical advancements are e...

PETSc’s DMPlex interface for unstructured meshes has been extended to support non-conformal meshes. The topological construct that DMPlex implements—the CW-complex—is by definition conformal, so representing nonconformal meshes in a way that hides complexity requires careful attention to the interface between DMPlex and numerical methods such as the finite element method. Our approach—which com...

In principle, unstructured mesh CFD codes can be parallelised using a mesh decomposition approach similar to structured mesh codes. However, for unstructured codes the mesh structure is problem dependent and algorithms for automatically decomposing the mesh onto the processors are required. An algorithm based upon a recursive clustering technique, for decomposing meshes into an arbitrary number...

The discrete convection-diffusion equations obtained from streamline diffusion finite element discretization are solved on both uniform meshes and adaptive meshes. Estimates of error reduction rates for both geometric multigrid (GMG) and algebraic multigrid (AMG) are established on uniform rectangular meshes for a model problem. Our analysis shows that GMG with line Gauss-Seidel smoothing and b...

Most nite element methods used nowadays utilize unstructured meshes These meshes are often very large and require substantial computational and memory resources Hence they are a reasonable application for par allel supercomputers One of the steps of nite element methods is mesh partitioning In this paper recursive coordinate bisection RCB algorithms for mesh partitioning are studied and a new h...