Grammar Based Multi-Frontal Solver For Isogeometric Analysis In 1d

Abstract

In this paper we present multi-frontal direct solver for one dimensional isogeometric finiteelement method. The solver implementation is based on graph-grammar (GG) model. TheGG model allows to express the entire solver algorithm, including generation of frontalmatrices, maerging and eliminations, as a set of basic undividable tasks called graph grammarproductions. Having the solver algorithm expressed as GG productions we can find thepartial order of execution, and create the dependency graph allowing for scheduling of tasksinto shared memory parallel machine. We focus on the implementation of the solver withNVIDIA CUDA on the graphic processing unit (GPU). The solver has been tested for linear,quadratic, cubic and higher ordere B-splines, resulting in logarithmic scalability.