Explicit spectral element collocation method for nonlinear transient heat transfer

In this paper, we proposed a novel collocation method to solve nonlinear transient heat transfer problems in typical intelligent materials. The new method is derived from the weighted residual method in which the weight of Jacobian is proven to be the best choice. In the paper, the physical variables and their fluxes are respectively approximated by two series of Lagrange interpolation polynomials at Chebyshev-Gauss-Lobatto nodes. In the proposed method, the mass matrices of the final linear system of equations are diagonal and the explicit time discretization method can be employed. Using the proposed method, we solved the heat transfer in intelligent materials and it is proven to be quite efficient and accurate, which benefits from that no large sparse matrix is generated and solved. By the proposed method, one can easily solve the problems with complex geometries.