Evaluation of massively parallel linear sparse solvers on unstructured finite element meshes

• We present a comprehensive comparison of parallel linear sparse solvers in finite element method.
• Solution time, parallel scalability, and robustness are evaluated on test cases with up to 40 million equations.
• WSMP direct multifontal solver offers an additional advantage with its higher robustness.
• ABF-IC with adaptive block factorized preconditioning requires much less memory.

The performance of massively parallel direct and iterative methods for solving large sparse systems of linear equations arising in finite element method on unstructured (free) meshes in solid mechanics is evaluated on a latest high performance computing system. We present a comprehensive comparison of a representative group of direct and iterative sparse solvers. Solution time, parallel scalability, and robustness are evaluated on test cases with up to 40 million degrees of freedoms and 3.3 billion nonzeros. The results show that direct solution methods, such as multifrontal with hybrid parallel implementation, as well as new hybrid adaptive block factorized preconditioning iterative methods can take a full advantage of a modern high performance computing system and provide superior solution time and parallel scalability performance.