Substrate resistance extraction with direct boundary element method

It is important to model the substrate coupling for mixed-signal circuit designs today. This paper presents the direct boundary element method (BEM) for substrate resistance calculation, where only the boundary of substrate region is discretized. Firstly, an efficient scheme for non-uniform element partition is proposed. Secondly, a new technique is presented which can reduce the scale of produced linear system and then accelerate the equation solving, especially for the multiple righthand sides problem like substrate resistance extraction. Experiments show that the proposed method has shown high efficiency compared with existing methods while preserving high accuracy.