An anisotropic adaptation process is applied to a three-dimensional incompressible two-phase flow solver. The solver uses a level set/finite element method on unstructured tetrahedral meshes. We show how the level set function can be used to build an anisotropic mesh with good properties. Some computations with a strong transient character and large densities ratios (1/1000) are presented. We s...

We present a new method for remeshing of triangular and tetrahedral meshes. Relative element sizes are computed from an error estimation. Then their gradient is limited in an optimal way by solving a Hamilton-Jacobi equation numerically. The new mesh is generated using smoothing-based iterations with connectivity updates (changes in topology of the mesh). The boundary nodes are projected using ...

The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismatic and pyramidal elements. Numerical results illustrate the convergence rates and non-oscillatory properties of the schemes for various smooth and discontinuous solutions test cases and the compressible Euler equations on variou...

This paper considers the hp-finite element discretization of an elliptic boundary value problem using tetrahedral elements. The discretization uses a polynomial basis in which the number of nonzero entries per row is bounded independently of the polynomial degree. The authors present an algorithm which computes the nonzero entries of the stiffness matrix in optimal complexity. The algorithm is ...

A systematic and analytic process is conducted to identify natural superconvergence points of high degree polynomial C0 finite elements in a three-dimensional setting. This identification is based upon explicitly constructing an orthogonal decomposition of local finite element spaces. Derivative and function value superconvergence points are investigated for both the Poisson and the Laplace equ...

Several performance improvements for finite-element edge-based sparse matrix–vector multiplication algorithms on unstructured grids are presented and tested. Edge data structures for tetrahedral meshes and triangular interface elements are treated, focusing on nodal and edges renumbering strategies for improving processor and memory hierarchy use. Benchmark computations on Intel Itanium 2 and P...

This paper considers the main algorithmic issues associated with developing parallel mesh adaptivity software for use with tetrahedral-based parallel nite element or nite volume solvers for transient computational mechanics problems in three space dimensions. Issues that are addressed include the use of diierent parallel data structures, the modiication of these data structures when adaptivity ...