Transient thermal analysis of integrated systems by discontinuous galerkin time domain (DGTD) method

A discontinuous Galerkin time-domain (DGTD) algorithm is proposed in this paper for transient thermal simulation of system integration. In order to reduce the complexity in the modeling of package structures, the equivalent thermal parameters of TSV interposer and bump layers are extracted properly. Then, by introducing the heat flux as an intermediate variable, the Laplace operator in the heat conduction equation is degraded to be a divergence operator. By this means, the resulting equations are written in the form of conservation and solved by the standard DGTD method. Due to the local operation of DGTD, the finalized matrix equations can be solved in the element-level form with the explicit time-marching scheme, which is rather suitable for large-scale problems. To validate the proposed method, a representative example on the thermal analysis of system integration is illustrated.