A TPAA-MsSBFEM for solving nonlinear transient heat transfer problems

A new numerical model is presented for two-dimensional transient nonlinear heat transfer problem of heterogeneous material by integrating the advantages of the Multiscale Scale Boundary Finite Element Method (MsSBFEM) and the Temporally Piecewise Adaptive Algorithm (TPAA). Based on the basic framework of TPAA-MsSBFEM, the construction of numerical base function can be conveniently and efficiently performed for the heterogeneous media with complex geometries at the small-scale, and the accuracy in time domain is adaptively maintained under different sizes of time steps. In order to accelerate the updating of numerical base function in the nonlinear multiscale computation, which is a critical issue to influence computational efficiency, a new adaptive judgment criterion is presented based on TPAA in order to save computational cost, and the use of fixed patterns of the scaled boundary elements further accelerate the updates of numerical base function. Numerical examples are provided to prove the effectiveness of proposed approaches, and satisfactory computational accuracy and efficiency are achieved at both the large and small scales.