Efficient transient thermal topology optimization through modal-wavelet integrated framework

The computational intensity of transient heat conduction topology optimization poses a significant challenge for practical engineering applications requiring large temporal domains and fine spatial discretization. This study introduces the parametric level set method-modal coupling optimization (PLSM-MCO) framework, which integrates the modal superposition method (MSM) and discrete wavelet transform (DWT) to achieve system-level efficiency improvements superior to those from individual components. MSM decouples multi-degree-of-freedom governing equations to enable efficient transient thermal analysis, while DWT enhances level-set function evolution through sparsity optimization. Numerical validation shows efficiency improvements of 83% for 2D configurations and 82% for 3D geometries compared to conventional methods. In multi-material optimization, a 49% computational efficiency gain is achieved despite increased design variables. The optimized topologies exhibit clear boundaries and excellent structural integrity, demonstrating the framework’s computational superiority and practical viability for complex thermal design applications.