A direct solver with reutilization of previouslycomputed LU factorizations for hadaptive finite element grids with point singularities
Abstract
This paper describes a direct solver algorithm for a sequence of finite element meshes that are hrefined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of hadaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of hrefined grids from O(N^2) down to O(N). Theoretical estimates are illustrated with numerical results on two and threedimensional model problems exhibiting one or several point singularities.
 Publication:

arXiv eprints
 Pub Date:
 December 2012
 arXiv:
 arXiv:1212.1992
 Bibcode:
 2012arXiv1212.1992P
 Keywords:

 Computer Science  Numerical Analysis;
 Mathematics  Numerical Analysis
 EPrint:
 21 papers, 18 figures