Adaptive Multi-Grid in 3-Dimensions using P1-finite elements (AMG3DP1)

Prof. Arup Mukherjee

Department of Mathematics, Rutgers University, New Brunswick

The talk will concentrate on some algorithmic, computational, and theoretical aspects of AMG3DP1--a code for solving elliptic linear (and semi-linear) boundary value problems in 3-dimensions. After a brief summary on the structure of AMG3DP1 and the motivation for its development, I will discuss two interrelated aspects of the code:
(1) An algorithm based on a-posteriori error estimators, which determines the degree of refinement needed for elements in a tetrahedral mesh, and aims to generate a refined mesh adapted to the solution with a geometric increase in the number of nodes, will be presented.
(2) An algorithm based on "bisection of tetrahedra", designed to yield a family of adapted, conforming, tetrahedral meshes starting with an arbitrary coarse conforming mesh will be presented. Two theorems, the first guaranteeing that only a finite number of dissimilar tetrahedra are ever produced, and the second proving that a recursive algorithm involved terminates in a finite number of steps, will be presented.