  We propose a new hybrid topology optimization algorithm based on multigrid
approach that combines the parallelization strategy of CPU using OpenMP and
heavily multithreading capabilities of modern Graphics Processing Units (GPU).
In addition to that significant computational efficiency in memory requirement
has been achieved using homogenization strategy. The algorithm has been
integrated with versitile computing platform of MATLAB for ease of use and
customization. The bottlenecking repetitive solution of the state equation has
been solved using an optimized geometric multigrid approach along with CUDA
parallelization enabling an order of magnitude faster in computational time
than current state of the art implementations. On-the-fly computation of
auxiliary matrices in the multigrid scheme and modification in interpolation
schemes using homogenization strategy removes memory limitation of GPUs. Memory
hierarchy of GPU has also been exploited for further optimized implementations.
All these enable solution of structures involving hundred millions of three
dimensional brick elements to be accomplished in a standard desktop computer or
a workstation. Performance of the proposed algorithm is illustrated using
several examples including design dependent loads and multimaterial.Results
obtained indicate the excellent performance and scalability of the proposed
approach.
