Space-time method for analyzing transient heat conduction in functionally graded materials

In this study, a novel approach is presented for simulating transient heat conduction in functionally graded materials (FGM) with varying material properties only in the z direction. The proposed collocation method employs a meshless localized space-time radial basis function (LSTRBF), which yields a linear sparse matrix system, offering advantages over the global method in terms of scalability and suitability for multidimensional problems. Additionally, a novel shape parameter strategy, known as variable leave-one-out cross-validation (LOOCV), is introduced to enhance accuracy while overcoming conventional LOOCV limitations. Four benchmark numerical examples are utilized to demonstrate the simplicity, efficiency, accuracy, and stability of the method. Overall, the proposed LSTRBF method presents a promising alternative for efficiently and accurately simulating transient heat conduction in FGMs.