Leveraging Workflows and Clouds for a Multi-frontal Solver for Finite Element Meshes

Scientific workflows in clouds have been successfully used for automation of large-scale computations, but so far they were applied to the loosely-coupled problems, where most workflow tasks can be processed independently in parallel and do not require high volume of communication. The multi-frontal solver algorithm for finite element meshes can be represented as a workflow, but the fine granularity of resulting tasks and the large communication to computation ratio makes it hard to execute it efficiently in loosely-coupled environments such as the Infrastructure-as-a-Service clouds. In this paper, we hypothesize that there exists a class of meshes that can be effectively decomposed into a workflow and mapped onto a cloud infrastructure. To show that, we have developed a workflow-based multi-frontal solver using the HyperFlow workflow engine, which comprises workflow generation from the elimination tree, analysis of the workflow structure, task aggregation based on estimated computation costs, and distributed execution using a dedicated worker service that can be deployed in clouds or clusters. The results of our experiments using the workflows of over 10,000 tasks indicate that after task aggregation the resulting workflows of over 100 tasks can be efficiently executed, and the overheads are not prohibitive. These results lead us to conclusions that our approach is feasible and gives prospects for providing a generic workflow-based solution using clouds for problems typically considered as requiring HPC infrastructure.