A GPU-accelerated non-periodic spectral boundary integral method for three-dimensional earthquake-cycle simulations

Federico Ciardo, Anubhav Roy, & Pierre Romanet

Submitted August 30, 2026, SCEC Contribution #15418, 2026 SCEC Annual Meeting Poster #208

Spectral boundary integral equation methods efficiently simulate fault slip, but their Fourier representation introduces artificial periodic replicas of the modeled fault. Cochard and Rice (1997) developed a theoretical formulation that eliminates these replicas using exact finite-support elasto-dynamic kernels. Here, we present, to our knowledge, its first implementation for three-dimensional dynamic rupture and earthquake-cycle simulations. A central challenge is the stable and accurate evaluation of the mode-II and mode-III kernels, whose piecewise structure involves wavefront transitions, removable singularities, and rapidly vary- ing contributions. We develop a robust kernel precomputation procedure that enables accurate evaluation across the retained spectral domain. Once the shear wave has traversed the diagonal of the finite integration domain, the transient kernels vanish exactly and the response reaches its static limit. The resulting temporal convolutions therefore have an exact finite memory and are independent for each Fourier mode, making them particularly well suited to massively parallel GPU evaluation. The numerical framework reproduces the theoretical linear and nonlinear stability transitions of a circular velocity-weakening asperity loaded by steady creep (Viesca and Garagash, 2026) and agrees closely with independent solutions of the SCEC SEAS BP7-FD-A benchmark. Excluding the one-time pre-integration of the elastodynamic kernels, the complete time-marching simulation requires approximately 1 hour and 15 minutes with GPU-accelerated convolutions, compared with approximately 2.2 days for the CPU implementation, corresponding to a wall-clock speedup of about 42×.

Citation
Ciardo, F., Roy, A., & Romanet, P. (2026, 08). A GPU-accelerated non-periodic spectral boundary integral method for three-dimensional earthquake-cycle simulations. Poster Presentation at 2026 SCEC Annual Meeting.

Related Projects & Working Groups
Research Computing (RC)