Element Partition Trees for H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming
MetadataShow full item record
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. The construction of the trees by the dynami c programming approach is expensive. These generated trees cannot be used in practice, but rather utilized as a learning tool to propose fast heuristic algorithms. In this first part of our paper we focus on the dynamic programming approach, and draw a sketch of the heuristic algorithm. The second part will be devoted to a more detailed analysis of the heuristic algorithm extended for the case of hp-adaptive grids. © 2017 H. AbouEisha et al.
Showing items related by title, author, creator and subject.
Paszynska, A.; Paszynski, M.; Jopek, K.; Wofniak, M.; Goik, D.; Gurgul, P.; Aboueisha, H.; Moshkov, M.; Calo, Victor; Lenharth, A.; Nguyen, D.; Pingali, K. (2015)We construct quasi-optimal elimination trees for 2D finite element meshes with singularities.These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination ...
Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive GridsAbouEisha, H.; Calo, Victor; Jopek, K.; Moshkov, M.; Paszynska, A.; Paszynski, M. (2018)The hp-adaptive Finite Element Method (hp-FEM) generates a sequence of adaptive grids with different polynomial orders of approximation and element sizes. The hp-FEM delivers exponential convergence of the numerical error ...
Lam, Bee K. (1999)A network is a system that involves movement or flow of some commodities such as goods and services. In fact any structure that is in the form of a system of components some of which interact can be considered as a network. ...