Parallel algebraic multigrid methods on distributed memory computers for industrial CFD problems

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(PLEASE READ DETAILED ABSTRACT) The first aim of the proposed project is to efficiently implement the (sequential) Ruge-Stüben classical AMG algorithm, and extensively test it on real life engineering applications. The second aim is to investigate new parallel approaches suitable for distributed memory computers, and implement a general parallel algebraic multigrid algorithm for finite element discretizations based on (non-overlapping) domain decomposition ideas. In particular, different parallel strategies for the coarsening phase and the smoothing operator will be examined. As for the robustness of the algorithm, an adaptive process will be utilized. While the AMG algorithm works well for a wide range of problems, there are situations in which it requires special care, e.g., on stretched grids where obtaining a robust and efficient solution still remains problematic. One reason for this is that, sometimes, the interpolation operator does not interpolate adequately the smooth modes of the error. Hence, a characterization of the smooth error will be provided, analyzed and implemented along the lines of element-based algebraic multigrids (AMGe), and element-free AMGe. Lastly, a careful analysis and (implementation) of the compatible relaxation algorithm, will be undertaken, as it holds much promise for parallel computation. The project will provide significant training of highly qualified personnel at the PhD level. The outcome of the current project will be the development of efficient and robust parallel algebraic multigrid algorithms which scale both with machine and problem size, and an object-oriented software that is portable, modular and MPI-based. The aerospace engineering industry in Montreal would be interested in integrating the (successful) results into their operations, and benefiting from the anticipated outcomes, namely the algorithms, the parallel code, and the qualified expertise.