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

该项目的第一个目标是有效地实现（顺序）Ruge-Stüben经典AMG算法，并在真实的生命工程应用中进行广泛的测试。第二个目标是研究新的并行方法，适合分布式存储计算机，并实现一个通用的并行代数多重网格算法有限元离散（非重叠）区域分解的想法的基础上。特别是，不同的并行策略的粗化阶段和平滑算子将被检查。至于算法的鲁棒性，将利用自适应过程。虽然AMG算法适用于各种问题，但在某些情况下需要特别注意，例如，在拉伸网格上，获得鲁棒且有效的解决方案仍然是个问题。其原因之一是，有时，插值算子不能充分插值误差的平滑模式。因此，光滑误差的表征将提供，分析和实施沿着线的基于元素的代数多重网格（AMGe），和无元素AMGe。最后，仔细分析和（实施）的兼容松弛算法，将进行，因为它持有的并行计算的希望。该项目将为博士一级的高素质人员提供重要培训。目前的项目的成果将是开发高效和强大的并行代数多重网格算法，可扩展的机器和问题的大小，面向对象的软件，是便携式的，模块化的和基于MPI的。蒙特利尔的航空航天工程业将有兴趣将（成功的）结果融入其业务，并从预期的成果中受益，即算法，并行代码和合格的专业知识。

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.