Dynamic analysis of power delivery network with nonlinear components using matrix exponential method

In this work, we propose a matrix exponential-based time-integration algorithm for dynamic analysis of power delivery network (PDN) with nonlinear components. The presented method is an explicit method and is very competitive for applications compared to traditional low order approximation methods, such as backward Euler method with Newton-Raphson iterations (BE). The proposed method takes comparable number of time steps to complete the whole simulation. Second, the method takes only one LU decomposition per time step while BE requires at least two LU decompositions for the convergence check of solutions of nonlnear system. Moreover, our method does not need to repeat expensive LU decomposition operations when the length of time steps are adjusted for error controls. The experimental results validate our method´s efficiency. We observe the reductions of total LU operation number and the simulation runtime.