Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures Part II. Single-processor implementation Original Research Article

An efficient single-processor implementation of the Adaptive Dynamic Relaxation (ADR) algorithm is developed. It is designed to exploit data locality and can exploit vectorization of the finite element computations. The ADR algorithm is used to solve for the non-linear static response of two- and three-dimensional hyperelastic systems involving frictionless contact. Performance is compared with an existing finite element code which utilizes a direct solution method. ADR is found to be reliable and highly vectorizable, and it outperforms the direct solution method for the highly non-linear problems considered. In addition, it permits the use of a very simple and efficient contact algorithm. In contrast to direct solution methods, ADR has minimal memory requirements and is easily parallelizable and scalable to more processors. For the class of problems addressed, it represents a very promising approach for parallel-vector processing.