Recent Advances of the ADER-DG Finite Element Method for Seismic Simulations

Alexander N. Breuer, Alexander Heinecke, & Yifeng Cui

Published August 15, 2016, SCEC Contribution #6779, 2016 SCEC Annual Meeting Poster #342

In this poster we present a novel local time stepping (LTS) scheme for ADER-DG finite element method and a holistic optimization targeting seismic simulations on the Intel Xeon Phi x200 processor, codenamed Knights Landing (KNL).

The ADER-DG method’s flexibility has proven to be highly valuable when simulating multi-physics earthquake simulations coupling seismic wave propagation and the rupture process. While LTS offers great opportunity to reduce the computational footprint of ADER-DG, complex update-dependencies of the elements might occur if implemented naively. Our LTS-scheme summarizes elements with similar time steps and thus aims for optimal large-scale throughput by trading some of the algorithmic optimality.

Our results include petascale performance when using local time stepping for the computationally heavy seismic wave propagation. Further, our performance comparisons demonstrate that KNL is able to outperform its previous generation, the Intel Xeon Phi coprocessor x100 family, by more than 2.6× in time-to-solution when running LTS-workloads. Additionally, our results show a 2.9× speedup compared to latest Intel Xeon E5v3 CPUs.

We conclude our poster by presenting recent work, aiming at even higher machine utilization by fusing multiple earthquake simulations into one single execution of the ADER-DG solver. This approach greatly reduces the memory requirements over sequential execution, since a significant fraction of the data is shared among the fused simulations. In addition, our approach does not require zero-operations to fulfill hardware requirements in the micro-kernels. Our performance benchmarks (4th order, matrix Fm2, M=9, N=20, K=20, 16% non-zero, hot L2) underline the potential of the approach and show that we are able reduce time-to-solution by more than 3.5x on the Intel Xeon Phi processor if compared to the fastest non-fused implementation.

Breuer, A. N., Heinecke, A., & Cui, Y. (2016, 08). Recent Advances of the ADER-DG Finite Element Method for Seismic Simulations. Poster Presentation at 2016 SCEC Annual Meeting.

Related Projects & Working Groups
Computational Science (CS)