Symbolic and Numeric Kernel Division for GPU-based FEA Assembly of Regular Meshes with Modified Sparse Storage Formats
Abstract This paper presents an efficient strategy to perform the assembly stage of finite element analysis (FEA) on general-purpose graphics processing units (GPU). This strategy involves dividing the assembly task by using symbolic and numeric kernels, and thereby reducing the complexity of the standard single-kernel assembly approach. Two sparse storage formats based on the proposed strategy are also developed by modifying the existing sparse storage formats with the intention of removing the degrees of freedom-based redundancies in the global matrix. The inherent problem of race condition is resolved through the implementation of coloring and atomics. The proposed strategy is compared with the state-of-the-art GPU-based and CPU-based assembly techniques. These comparisons reveal a significant number of benefits in terms of reducing storage space requirements and execution time and increasing performance (GFLOPS). Moreover, using the proposed strategy, it is found that the coloring method is more effective compared to the atomics-based method for the existing as well as the modified storage formats.