TY - EJOU
AU - Liu, Chihyu
AU - Ku, Chengyu
AU - Xiao, Jingen
AU - Yeih, Weichung
TI - A Novel Spacetime Collocation Meshless Method for Solving Two-Dimensional Backward Heat Conduction Problems
T2 - Computer Modeling in Engineering \& Sciences
PY - 2019
VL - 118
IS - 1
SN - 1526-1506
AB - In this article, a meshless method using the spacetime collocation for solving the two-dimensional backward heat conduction problem (BHCP) is proposed. The spacetime collocation meshless method (SCMM) is to derive the general solutions as the basis functions for the two-dimensional transient heat equation using the separation of variables. Numerical solutions of the heat conduction problem are expressed as a series using the addition theorem. Because the basis functions are the general solutions of the governing equation, the boundary points may be collocated on the spacetime boundary of the domain. The proposed method is verified by conducting several heat conduction problems. We also carry out numerical applications to compare the SCMM with other meshless methods. The results show that the SCMM is accurate and efficient. Furthermore, it is found that the recovered boundary data on inaccessible boundary can be obtained with high accuracy even though the over specified data are provided only at a 1/6 portion of the spacetime boundary.
KW - Spacetime
KW - collocation
KW - meshless method
KW - backward heat conduction problem
KW - basis functions
DO - 10.31614/cmes.2019.04376