Optimized waveform relaxation methods for RC type circuits

Waveform relaxation (WR) has been widely used in circuit theory for the solution of large systems of ordinary differential equations, and the solution of partial differential equations. In the past, clever partitioning schemes have been used for circuit applications to enhance convergence. However, a drawback of the classical WR algorithm is the nonuniform convergence over the window in time for which the equations are integrated. We propose a new optimized WR algorithm which greatly accelerates the convergence by introducing new transmission conditions. These conditions are responsible for the exchange of information between the subcircuits. We use two RC circuit examples to illustrate the theory, as well as the improved convergence behavior.