A novel time-spectral BEM for efficient 2D dynamic analysis

This study presents a new boundary element method (BEM) framework for the numerical solution of general time-dependent or transient problems. By reformulating the time derivative as a domain integral, the framework effectively decouples the treatment of spatial and temporal variables, allowing for the independent application of specialized discretization methods. For the temporal domain, we introduce an innovative time-spectral integration technique, which is based on Gaussian-quadrature-based orthogonal polynomial expansions. This method not only achieves arbitrary orders of accuracy but also significantly enhances computational efficiency and stability, particularly for simulations involving rapid transients or long-time dynamic simulations. The domain integrals in the spatial domain are calculated using the scaled coordinate transformation BEM (SCT-BEM), a mathematically rigorous technique that converts domain integrals into equivalent boundary integrals, preserving the boundary-only discretization advantage inherent in BEM. Numerical experiments on transient heat conduction and dynamic wave propagation further demonstrate the framework’s performance and capabilities. These experiments show that the proposed framework outperforms traditional time-stepping BEM methods, particularly in terms of stability, convergence rates, and computational cost, making it a highly promising tool for practical engineering applications.