Lawrence Livermore National Laboratory

Computational science is facing several major challenges with rapidly changing highly complex heterogeneous computer architectures. To meet these challenges and yield fast and efficient performance, solvers need to be easily portable. Algebraic multigrid (AMG) methods have great potential to achieve good performance, since they have shown excellent numerical scalability for a variety of problems. However, their implementation on emerging computer architectures, which favor structure, presents new challenges. To face these difficulties, we have considered modularization of AMG, that is breaking AMG components into smaller kernels to improve portability as well as the development of new algorithms to replace components that are not suitable for GPUs. Another way to achieve performance on accelerators is to increase structure in algorithms. This talk will discuss new algorithmic developments, including a new class of interpolation operators that consists of simple matrix operations for unstructured AMG and efforts to develop a semi-structured AMG method.

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