Multigrid approach for efficient integrated multiscale analysis and design optimization

As an effort to carry out the design optimization without preset design or analysis resolution, an integrated multiscale analysis and optimization for topology optimization problems has been recently proposed¹. Since the multiscale paradigm facilitates multiresolution analysis, an efficient adaptive strategy can be formulated for numerical analysis. Furthermore, design optimization can be carried out progressively in multiscales yielding topologically-simple designs having good manufacturability. Though the potential of the multiscale paradigm in its integrated form was suggested, solution efficiency, especially in numerical analysis, still needs to be improved. The main objective of this investigation is to incorporate a multigrid strategy into the multiscale numerical method to improve the numerical efficiency. The motivation behind this incorporation is that the multiscale and the multigrid concepts are closely related in their nature of a multigrid method. The essential ingredients of the multiscale method will be also presented. We consider a few analysis examples and design optimization problems to illustrate the potential of the multiscale and the multigrid method.