Multisplitting waveform relaxation for systems of linear integral-differential-algebraic equations in circuit simulation

The multisplitting technique introduced by D. P. O'Leary and R. E. White is applied to treat the waveform relaxation solutions for systems of linear integral-difierential-algebraic equations in circuit simulation. The convergence condition of the multisplitting waveform relaxation method which can contain overlapping is established for the continuous-time case. The convergence rates of the relaxation-based method for different multisplittings are compared from the view-point of spectral radii of splitting matrices in systems. Numerical experiments are provided to confirm the new theoretical results.