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Algorithmic and architecture-oriented optimizations are essential forachieving performance worthy of anticipated energy-austere exascale systems. Inthis paper, we present an extreme scale FMM-accelerated boundary integralequation solver for wave scattering, which uses FMM as a matrix-vectormultiplication inside the GMRES iterative method. Our FMM Helmholtz kernelstreat nontrivial singular and near-field integration points. We implementhighly optimized kernels for both shared and distributed memory, targetingemerging Intel extreme performance HPC architectures. We extract the potentialthread- and data-level parallelism of the key Helmholtz kernels of FMM. Ourapplication code is well optimized to exploit the AVX-512 SIMD units of IntelSkylake and Knights Landing architectures. We provide different performancemodels for tuning the task-based tree traversal implementation of FMM, anddevelop optimal architecture-specific and algorithm aware partitioning, loadbalancing, and communication reducing mechanisms to scale up to 6,144 computenodes of a Cray XC40 with 196,608 hardware cores. With shared memoryoptimizations, we achieve roughly 77% of peak single precision floating pointperformance of a 56-core Skylake processor, and on average 60% of peak singleprecision floating point performance of a 72-core KNL. These numbers representnearly 5.4x and 10x speedup on Skylake and KNL, respectively, compared to thebaseline scalar code. With distributed memory optimizations, on the other hand,we report near-optimal efficiency in the weak scalability study with respect toboth the logarithmic communication complexity as well as the theoreticalscaling complexity of FMM. In addition, we exhibit up to 85% efficiency instrong scaling. We compute in excess of 2 billion DoF on the full-scale of theCray XC40 supercomputer.

Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering