A novel time-domain SCT-BEM for transient heat conduction analysis

Accurate and efficient treatment of domain integrals is critical for obtaining reliable and precise boundary element method (BEM) solutions in dynamic or time-dependent problems. Despite the success of existing techniques for handling domain integrals, significant challenges still remain, especially in time-dependent BEM analyses where time-dependent fundamental solutions often result in integrands with oscillations or near-singularities, particularly when small time steps are used. To address these issues, this study introduces an improved scaled coordinate transformation BEM (SCT-BEM), combined with a non-linear coordinate transformation, to enhance the robustness of domain integral evaluations in transient time-domain BEM. The proposed method is straightforward to implement, requiring minimal modifications to existing BEM frameworks, and significantly improves both the robustness and accuracy of domain integral evaluations in transient time-domain BEM.