### Applicant

Prof. Dr. Thomas Richter

Department of Mathematics

FAU Erlangen-Nürnberg

### Project Summary

Gascoigne 3D is a general purpose finite element library with a focus on fluid dynamics and complex fluid-structure interactions. Base components are a geometric multigrid solver and unstructured 2d and 3d meshes featuring adaptive refinement based on a posteriori error estimators. Goal of this project was to identify possibilities for multicore parallelism. Two steps were undertaken in this project: the analysis of the matrix vector product and to exploit possible preconditioners for accelerating the linear systems that offer better possibilities for parallelization as compared to the incomplete lower upper decomposition which is standard in Gascoigne 3D. Regarding the matrix vector product we identified the memory bandwidth as limiting factor. This is well-known for unstructured finite elements and multicore parallelization can only be efficiently exploited by using matrix free approaches, which however are not robust for the large class of complex problems in the focus of Gascoigne 3D. In the process of optimization we could however speedup the matrix vector product by 30% by a block-restructuring of the matrix entries. This holds for the sequential and parallel performance. As alternative to the ILU preconditioner we investigated the Sparse Approximate Inverse method. Its assembly is easy to parallelize and we observed nearly optimal parallel efficiency. Its application is less costly than the ILU. However, we could not find the same robustness for complex multiphysics problems as compared to the ILU. Further research is required. The immediate outcome of the KONWIHR project is a performance gain in the matrix vector product which is of value to all users of Gascoigne 3D. In addition we identified several possibilities and also limitations with respect to the parallelization of Gascoigne 3D.