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KDRSolvers: Scalable, Flexible, Task-Oriented Krylov Solvers
DescriptionWe present KDRSolvers, a novel framework for representing sparse linear systems and implementing Krylov subspace methods on modern heterogeneous supercomputers. KDRSolvers uses dependent partitioning to uniformly represent sparse matrix storage formats as abstract maps between a matrix's domain, range, and set of nonzero entries. This enables KDRSolvers to define universal co-partitioning operators for matrices and vectors independent of underlying storage formats, allowing changes in data partitioning strategies to automatically propagate through an application with no code modification. KDRSolvers also introduces multi-operator systems in which matrix and vector data can be ingested and processed in multiple non-contiguous pieces without data movement. Our implementation of KDRSolvers, targeting the Legion runtime system, achieves greater flexibility and competitive performance compared to PETSc and Trilinos. In experiments with up to 1,024 GPUs on the Lassen supercomputer, our implementation achieves up to a 9.6% reduction in execution time per iteration.