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，并在实际工程应用中对其进行广泛的测试。第二个目标是研究适合于分布式存储计算机的新的并行方法，并基于(非重叠)区域分解的思想实现有限元离散的通用并行代数多重网格算法。特别是，粗化阶段和平滑算子的不同并行策略将被研究。对于算法的稳健性，将采用自适应过程。虽然AMG算法适用于广泛的问题，但在某些情况下，它需要特别注意，例如，在拉伸的网格上，获得稳健和高效的解决方案仍然是个问题。这其中的一个原因是，有时，内插算子不能充分地内插误差的平滑模式。因此，将沿着基于单元的代数多重网格(AMGE)和无单元的AMGE的路线提供、分析和实现平滑误差的特征。最后，将对兼容松弛算法进行仔细的分析和实现，因为它为并行计算带来了很大的希望。该项目将为博士级别的高素质人员提供大量培训。目前项目的成果将是开发高效和健壮的并行代数多重网格算法，该算法可随机器和问题的大小而扩展，并开发一个可移植、模块化和基于MPI的面向对象的软件。蒙特利尔的航空航天工程行业将有兴趣将(成功的)成果纳入其业务，并受益于预期的成果，即算法、并行代码和合格的专门知识。

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.