A novel combined space-time algorithm for transient heat conduction problems with heat sources in complex geometry

Abstract A space-time algorithm, integrated by the localized space-time method of fundamental solutions (LSTMFS) and space-time Chebyshev collocation scheme (STCCS), is developed to resolve heat conduction problems with heat sources. Based on the Chebyshev collocation scheme, a STCCS involving Gauss-Lobatto space-time nodes is constructed to obtain the particular solution of the inhomogeneous problem. The particular solution is then used to convert the inhomogeneous transient heat conduction problem to a classical homogeneous one which can be directly solved via the LSTMFS. Considering that no temporal-difference is employed and the generated matrix is sparse, the STCCS-LSTMFS has promising potential to directly and quickly address inhomogeneous transient heat conduction problems. Numerical experiments are presented to show the accuracy and efficiency of the proposed methodology for the transient heat conduction problems with sophisticated/unknown analytical solution, mixed boundary conditions, and complex computational domain.