Symbolic and Numeric Kernel Division for Graphics Processing Unit-Based Finite Element Analysis Assembly of Regular Meshes With Modified Sparse Storage Formats

This paper presents an efficient strategy to perform the assembly stage of finite element analysis (FEA) on general purpose graphics processing units (GPUs). This strategy involves dividing the assembly task 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 central processing unit (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.