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Communication Hiding for Matrix-Free Finite Element Operators of a Complex PDE: Nonlinear Stokes Flow of Earth’s Mantle

SessionResearch, ACM SRC, and Doctoral Showcase Posters

DescriptionFor large-scale matrix-free finite-element PDE solvers, parallel matrix-vector products typically comprise the dominant computational cost. Synchronization steps for input and output, when degrees of freedom (DOFs) lying on inter-process boundaries are communicated, become the dominant serial portion of the program and the main scalability bottleneck. However, the cost of communication can be mitigated if it can be overlapped with local computations which do not require the values of DOFs on process boundaries. In this research, we study the nonlinear Stokes solver of the mantle convection code Rhea, comparing several different methods for overlapping communication with computation during matrix-vector products, including a new dynamic method which automatically adjusts to measured imbalances in communication waiting times. We observe significant improvements in the waiting times, and in the overall computation times, for the matrix-vector products in Rhea.

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