Reduced order multirate schemes in industrial circuit simulation

Abstract

Abstract In this paper the industrial application of Reduced Order Multirate (ROMR) schemes is presented. This paper contains the mathematical foundations of the ROMR schemes and elaborates on the construction of these schemes using specific Model Order Reduction (MOR) techniques. Especially the Maximum Entropy Snapshot Sampling method for generating a reduced basis and reduction by Gauß–Newton with Approximated Tensors (GNAT). This basis generation method is also used for generating the basis for the gappy hyper-reduction method used for nonlinear function evaluation. For the multirate integration part, a Backward Differentation Formula approach to integration is used in conjunction with a coupled-slowest-first multirate approach. After introducing the numerical approach to industrial circuit simulation validation experiments are performed. First a simple academic model is used, and then an industrial test case is simulated as presented by STMicroelectronics. A significant speedup in simulation time is achieved whilst accuracy and convergence is kept.

Keywords

• Mulitrate
• Model order reduction
• Differential-algebraic equations
• Snapshot sampling