Parallel Computing Procedure for Dynamic Relaxation Method on GPU Using NVIDIA's CUDA

Abstract

This paper introduces a procedure for parallel computing with the Dynamic Relaxation method (DR) on a Graphic Processing Unit (GPU).This method facilitates the consideration of a variety of nonlinearities in an easy and explicit manner.Because of the presence of inertial forces, a static problem leads to a transient dynamic problem where the Central Difference Method is usedas a method for direct integration of equations of motion which arise from the Finite Element model.The natural characteristic of this explicit method is that the scheme can be easily parallelized. The assembly of a global stiffness matrix is not required.Due to slow convergence with this method, the high performance which GPUs provide is strongly suitable for this kind of computation.NVIDIA's CUDA is used for general-purpose computing on graphics processing units (GPGPU) for NVIDIA's GPUs with CUDA capability.

Explicit integration of equations of motion solved on computer cluster

“…This algorithm belongs to the cornerstones of the entire parallel model. The rest of the code related to parallel processing on a single workstation is applied similarly to the algorithm proposed for GPGPU technology [16] for multicore CPU environment [17]. This applies to the integration of respective finite elements and explicit integration of equations of motion applied to all the finite element nodes.…”

Parallel Computation on Multicore Processors Using Explicit Form of the Finite Element Method and C++ Standard Libraries

“…Computational software tools that are already written in C or C++ programming languages are now able to enrich the possibility to use parallelism while maintaining the portability of code. In a field of an explicit form of the Finite Element Method ( [6], [7]) or explicit meshless methods [16] the possibility of usage of parallelism is more than desirable, mainly because of time-consuming calculations, which is caused by the conditional stability of explicit methods used for the direct integration of equations of motion.…”