Highly efficient density-based topology optimization using DCT-based digital image compression

Abstract

In this brief note we show that the number of design variables in density-based topology optimization can be phenomenally reduced using discrete cosine transform (DCT), which is one of the most frequently used transforms in digital image compression. Only quite a few nonzero DCT coefficients corresponding to low frequency components are needed to generate optimized topology with high resolution. Through two examples, one for compliance minimization and the other for heat conduction, we show that the density method can be surprisingly efficient than people have thought. Moreover, there is no need to use additional density filter or sensitivity filter since high frequency components are inherently filtered by the DCT-based compression.