Method of Local Corrections Solver for Manycore Architectures

Microprocessor designs are now changing to reflect the ending of Dennard Scaling. This leads to a reconsideration of design tradeoffs for designing discretization methods for PDEs based on simplified performance models like Roofline.In this work we carry out an end-to-end analysis and implementation study on a Cray XC40 with Intel⃝R XeonTM E5-2698 v3 processors for the Method of Local Corrections (MLC). MLC is a non-iterative method for solving Poisson’s Equation on locally rectangular meshes. The Roofline model predicts that MLC should have faster time to solution than traditional iterative methods such as Geometric Multigrid. We find that Roofline is a useful guide for performance engineering and obtain perfor- mance within a factor of 3 the Roofline performance upper bound. We determine that the algorithm is limited by identified architectural features that are not captured in the Roofline model, are quantifiable, and can be addressed in future implementations