A KDC-enhanced closest point method for thermal analysis on curved geometries using LS-GFDM

This paper presents a Krylov-deferred correction (KDC)-enhanced closest point method (CPM) integrated with the least-squares generalized finite difference method (LS-GFDM) for thermal analysis on curved geometries. To overcome the inherent limitations of conventional single-step/multi-step temporal schemes in long-time simulations, we systematically unify three advanced components: (i) CPM’s embedding strategy that transforms surface PDEs into extended problems over Cartesian grids, (ii) LS-GFDM’s spatial discretization employing dual point sets to enhance applicability beyond conventional GFDM, and (iii) KDC’s predictor–corrector framework that iteratively refines temporal solutions to achieve high-order accuracy. Building upon our previous work (Tang et al. 2025) where LS-GFDM was integrated with CPM using explicit Euler temporal schemes, this study constitutes a critical advancement by replacing low-order temporal discretization with the KDC methodology. Numerical experiments demonstrate that our KDC-CPM-LSGFDM framework achieves superior numerical performance.