Support Operator Rupture Dynamics on GPU

Abstract

The method of Support Operator (SOM) is a numerical method to simulate seismic wave propagation by solving the three dimension viscoelastic equations. Its implementation, the Support Operator Rupture Dynamics (SORD) has been proved to be highly scalable in large-scale multi-processors calculations. This paper discusses accelerating SORD using on GPU using NVIDIA CUDA C. Compared to its original version on CPU, we have acrhieved a maximum 12.8X speed-up.

Appendix A: Hourglass Control from Node to Cell

This is the CUDA C code of hourglass operator Q $_{k}$. We use a modified form of the hourglass control scheme described by Flanagan & Belytschko. Flanagan and Belytschko (1981) and more recently by Day et al. Day et al (2005). and Ma & Liu. Ma and Liu (2006). As Equations (16), the code is used for transforming the node variables to cell variables.

$$\begin{aligned} {} (Q_1 F)_{000}&=F_{000} +F_{011} -F_{101} -F_{110} +F_{111} +F_{100} -F_{010} -F_{001} \end{aligned}$$

(25.23)

$$\begin{aligned} (Q_2 F)_{000}&=F_{000} +F_{101} -F_{110} -F_{011} +F_{111} +F_{101} -F_{001} -F_{100} \end{aligned}$$

(25.24)

$$\begin{aligned} (Q_3 F)_{000}&=F_{000} +F_{110} -F_{011} -F_{101} +F_{111} +F_{001} -F_{100} -F_{010} \end{aligned}$$

(25.25)

$$\begin{aligned} (Q_4 F)_{000}&=F_{000} +F_{011} +F_{101} +F_{110} -F_{111} -F_{100} -F_{010} -F_{001} \end{aligned}$$

(25.26)