A bounded aspect-ratio coarsening sequence of an unstructured mesh M 0 is a sequence of meshes M 1 ; : : : ; M k such that: M i is a bounded aspect-ratio mesh, and M i is an approximation of M i?1 that has fewer elements, where a mesh is called a bounded aspect-ratio mesh if all its elements are of bounded aspect-ratio. The sequence is node-nested if the set of the nodes of M i is a subset of t...

A method is outlined for optimising graph partitions which arise in mapping unstructured mesh calculations to parallel computers. The method employs a combination of iterative techniques to both evenly balance theworkload andminimise the number and volume of interprocessor communications. They are designed to work efficiently in parallel as well as sequentially and when combined with a fast dir...

In this paper we describe a parallel h-refinement algorithm for unstructured finite element meshes based on the longest-edge bisection of triangles and tetrahedrons. This algorithm is implemented in PARED, a system that supports the parallel adaptive solution of PDEs. We discuss the design of such an algorithm for distributed memory machines including the problem of propagating refinement acros...

An overview of current multigrid techniques for unstructured meshes is given. The basic principles of the multigrid approach are first outlined. Application of these principles to unstructured mesh problems is then described, illustrating various different approaches, and giving examples of practical applications. Advanced multigrid topics, such as the use of algebraic multigrid methods, and th...

One of the most difficult problems in reverse engineering is the processing of unstructured data. NURBS (Non-uniform Rational B-splines) surfaces are a popular tool for surface modeling. However, they cannot be directly created from unstructured data, as they are defined on a four-sided domain with explicit parametric directions. Therefore, in reverse engineering, it is necessary to process uns...

Two discontinuous Galerkin schemes for linear elastic waves in two and three dimensions with Dirichlet and optional Neumann boundary conditions are formulated: a pure displacement formulation and a mixed formulation with the displacement and a pressure parameter as variables. The schemes are implemented for two dimensions using Concepts with piecewise linear orthogonal basis functions for the d...

Guaranteed-quality unstructured meshing algorithms facilitate the development of automatic meshing tools. However, these algorithms require domains discretized using a set of linear segments, leading to numerical errors in domains with curved boundaries. We introduce an extension of Ruppert’s Delaunay refinement algorithm to domains with curved boundaries and prove that the same quality bounds ...

In this paper, we present a three-dimensional immersed boundary method to simulate the eukaryotic cell growth and cytokinesis. The proposed model and numerical method are a non-trivial three-dimensional extension of the previous work (Li et al., 2012). Unstructured triangular meshes are employed to discretize the cell membrane. The nodes of the surface mesh constitute a set of Lagrangian contro...

We present a new approach towards the construction of a genuinely multidimensional high-resolution scheme for computing steady-state solutions of the Euler equations of gas dynamics. The unique advantage of this approach is that the Gauss-Seidel relaxation is stable when applied directly to the high-resolution discrete equations, thus allowing us to construct a very eecient and simple multigrid...

A moving-grid, shock-fitting, finite element method has been implemented that can achieve high-order accuracy for flow simulations with shocks. In this approach, edges in the computational mesh are fitted to shock front and moved throughout simulation. The Euler or Navier-Stokes equations solved on moving an arbitrary Lagrangian-Eulerian framework. is two-dimensions context of a streamwise upwi...