Issues in adaptive mesh refinement implementation

Abstract

Physical phenomena often involve discontinuities and/or localized high-gradient areas. The numerical simulation of these problems and conventional techniques (Finite Elements, Finite Volumes, Finite Differences, and Spectral Methods) with a uniform grid is inefficient when high accuracy is required. Adaptive Mesh Refinement (AMR) is a technique that allows local refinement of the grid. In this presentation, we describe a typical AMR technique and address implementation and algorithmic issues. Triangular unstructured grids and a regular 1 to 4 refinement are considered.

Keywords

• Adaptive mesh refinement
• data structure
• computational method
• object oriented programming
• conservation laws.