A fast and stable explicit integration method by matrix exponential operator for large scale circuit simulation

In this paper, we present a fast and stable explicit numerical integration method. Our method utilizes matrix exponential operator to compute numerical solution of the ordinary differential equations of circuits to avoid the stability issue. A matrix partition algorithm and a numerical approximation are proposed to reduce the complexity of matrix exponential and matrix inverse operation. Experimental results show that our method is stable and efficient. Our method is over two times faster than backward Euler on average.