Abstract
To obtain the optimal shape of a 3D object minimizing the fluid drag, an adjoint variable method based on the variational principle was formulated and applied to the finite element method. The optimality condition of the method consists of the state equation, the adjoint equation, and the sensitivity equation. To overcome technical problems (e.g., heavy computational tasks and large memory requirements), the present 3D optimization system was developed with the data compression technology supplied by the software library HPC-MW. Utilizing HPC-MW in developing the shape optimization software, the number of program lines, the data compression and the parallel computing were reduced by about 60%. The development period was also dramatically shortened. The parallel computing performance was successfully inherited from HPC-MW. Comparing to the initial shape under stokes flow conditions, the fluid drag on the optimized shape can be reduced by about 25%. The optimal shape given in the present study is in good agreement with that of the Pironneau result.
