Large-scale level set topology optimization for elasticity and heat conduction

We present a numerical study of a new large-scale level set topology optimization (LSTO) method for engineering design. Large-scale LSTO suffers from challenges in both slow convergence and high memory consumption. We address these shortcomings by adopting the spatially adaptive and temporally dynamic Volumetric Dynamic B+ (VDB) tree data structure, open sourced as OpenVDB, which is tailored to minimize the computational cost and memory footprint by not carrying high fidelity data outside the narrow band. This enables an efficient level set topology optimization method and it is demonstrated on common types of heat conduction and structural design problems. A domain decomposition-based finite element method is used to compute the sensitivities. We implemented a typical state-of-the-art LSTO algorithm based on a dense grid data structure and used it as the reference for comparison. Our studies demonstrate the level set operations in the VDB algorithm to be up to an order of magnitude faster.