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Pedro Bello-Maldonado
- Advisor:
- Paul F. Fischer
- Departments:
- Areas of Expertise:
- Numerical Methods
- High-Performance Computing
- Scientific Computing
- Thesis Title:
- Polynomial Reductiong with Full Domain Decomposition Preconditioner for Spectral Element Poisson Solvers
- Thesis abstract:
- Minimizing communication is central to realizing high performance for scalable execution of parallel algorithms. On GPU-based systems, iterative solvers can be prohibitively expensive without an algorithm that concentrates most of the work on the GPU devices and lightens the load on the network. This work focuses on increased local work per iteration to reduce iteration counts and thus internode communication. We present a polynomial reduction with full domain decomposition (PR+FDD) preconditioner that targets the solution of spectral-element-based Poisson problems discretized by high-order spectral elements on GPU-based exascale architectures. The algorithm constructs local composite grids by first reducing the polynomial order of the elements adjacent to the GPU-local partition, followed by progressive geometric coarsening all the way to the domain boundary. During the preconditioning step of the iterative solver, the residual is restricted to the different levels of the coarsening tree and communicated so that each processor can solve its local problem independently. Once completed, the local solutions are stitched together and the global iterative solver continues. This class of algorithms are known to achieve fast convergence at the cost of more expensive preconditioner evaluations. Our results demonstrate a faster reduction of the relative residual compared to other well known preconditioners like low-order preconditioning and hybrid-Schwarz-multigrid preconditioning.
- Downloads:
Contact information:
belloma2@illinois.edu