Massive efficiencies to be realized through GPU computations in finite element optimization: The promises and observations

In finite element optimization, the computational load limits the size of problem that can be solved. Finite element computation involves the solution of large matrix equations. Then optimization requires several such equations to be solved. Parallelization has been the preferred route to overcome this problem but was again limited by the cost of computers and the number of processors available. The graphics processing unit (GPU) on a PC provides a means of implementing the massive computations on numerous parallel threads cheaply on PCs. The purpose of this is to review finite element matrix equation solution on the GPU and point out areas where further investigation is warranted. Our intention is to direct computational research and computer architecture development so that we may use the GPU better for more effective computational parallelization in finite element field computation.