Element partition trees for h-refined meshes to optimize direct solver performance. Part I: Dynamic programming - Aboueisha, Hassan; Calo, Victor Manuel; Jopek, Konrad; Moshkov, Mikhail; Paszyńska, Anna; Paszyński, Maciej; Skotniczny, Marcin (Zielona Góra: Uniwersytet Zielonogórski)
We consider a class of two- and three-dimensional h-refined meshes generated by an adaptive finite element method. We introduce an element partition tree, which controls the execution of the multi-frontal solver algorithm over these refined grids. We propose and study algorithms with polynomial computational cost for the optimization of these element partition trees. The trees provide an ordering for the elimination of unknowns. The algorithms automatically optimize the element partition trees using extensions of dynamic programming.
Keywords: h-adaptive finite element method; ordering; element partition tree; extensions of dynamic rogramming; multifrontal direct solvers