Distributed algebraic multigrid for finite element computations

The Finite Element Method has been successfully applied to a variety of problems in engineering, medicine, biology, and physics. However, this method can be computationally intensive, particularly for problems in which an unstructured mesh of elements is generated. In such situations, the Algebraic Multigrid (AMG) can prove to be a robust method for solving the discretized linear systems that emerge from the problem. Unfortunately, AMG requires a large amount of storage (thus causing swapping on most sequential machines), and typically converges slowly. We show that distributing the algorithm across a cluster of workstations can help alleviate these problems. The distributed algorithm is run on a number of geomechanics problems that are solved using finite elements. The results show that distributed processing is extremely useful in maintaining the performance of the AMG algorithm with increasing problem size, particularly by reducing the amount of disk swapping required.