Operator Splittings on GPUs
Advisor
Event Type
Doctoral Showcase
Posters
In-Person Only
TP
XO / EX
TimeWednesday, 17 November 20218:30am - 5pm CST
LocationSecond Floor Atrium
DescriptionOperator splittings are a successful method for the solution of parabolic partial differential equations. In this thesis, the same ideas are applied for general sparse linear equation systems. For general graphs, which are induced by the sparse matrix of the equation system, a parallel segmentation algorithm is used to extract one-dimensional segments, and create appropriate renumberings, such that the permuted subgraph has a tridiagonal form. With these tridiagonal factors, multiplicative and alternating operator splittings are created and applied as preconditioners in iterative solvers. The presented experiments with matrices from the Sparse Matrix Collection show that the proposed preconditioners can achieve better convergence rate and performance than state-of-the art preconditioners, like the ILU-ISAI implemented in the Magma library. The tridiagonal factors are solved with the Recursive Partitioned Tridiagonal Schur Complement Algorithm (RPTS), which was developed and implemented within the scope of this thesis. RPTS is a hierarchically tridiagonal GPU solver with scaled partial pivoting, which runs at maximum GPU memory bandwidth, and outperforms the numerically stable tridiagonal solver of cuSPARSE by approximately factor 5 for large problem sizes.
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