Abstract: According to the Langevin Green's function theory, the key to calculating heat flux in a harmonic lattices is to calculate the phonon transmission coefficient. Traditionally, people use the method based on decomposing the determinant of the tridiagonal matrix to transform the process of solving the transmission coefficient into solving the product of the transfer matrix to reduce the time complexity, which is called the transfer matrix method. However, the parallel effect of the transfer matrix method is poor and this method cannot be used for systems with long-range interactions. An efficient algorithm based on solving linear equations to calculate the phonon transmission coefficient in harmonic lattices is proposed to improve the parallel efficiency of computation and reduce the time complexity of solving the phonon transmission coefficient with arbitrary neighbor coupling to O(N), providing algorithmic assistance for research in related fields.

Key words: heat conduction, Langevin green's function theory, transmission, efficient algorithm