Efficient Design of Thermoelastic Structures Using a Krylov Subspace Preconditioner and Parallel Sensitivity Computation

The repeated updating of parametric designs is computationally challenging, especially for large-scale multi-physics models. This work is focused on proposing an efficient modal modification method for gradient-based topology optimization of thermoelastic structures, which is essential when dealing with their complex eigenproblems and global sensitivity analysis for a huge number of design parameters. The degrees of freedom of the governing equation of thermoelastic structures is very huge when its parametric partial differential equation is discretized using the numerical technique. A Krylov subspace preconditioner is constructed based on the Neumann series expansion series so that the thermoelastic eigenproblem can be solved in an efficient low-dimension solver, rather than its original high-fidelity solver. In the construction of Krylov reduced-basis vectors, the computational cost of the systemic matrix inverse becomes a critical issue, which is solved efficiently by means of constructing a diagonal systemic matrix with the lumped mass and heat generation submatrices. Then, the reduced-basis preconditioner can provide an efficient optimal solver for both the thermoelastic eigenproblem and its eigen sensitivity. Furthermore, a master-slave pattern parallel method is developed to reduce the computational time of computing the global sensitivity numbers, and therefore, the global sensitivity problem can be efficiently discretized into element-scale problems in a parallel way. The sensitivity numbers can thus be solved at the element scale and aggregated to the global sensitivity number. Finally, two case studies of the iterative topology optimization process, in which the proposed modal modification method and the traditional method are implemented, are used to illustrate the effectiveness of the proposed method. Numerical examples show that the proposed method can reduce the computational cost remarkably with acceptable accuracy.