E.J.W. ter Maten

Trajectory piecewise linear approach for nonlinear differential-algebraic equations in circuit simulation

In this paper we extend the Trajectory Piecewise Linear (TPWL) model order reduction (MOR) method for nonlinear differential algebraic equations (DAE). The TPWL method is based on combining several linear reduced models at different time points, which are created along a typical trajectory, to approximate the full nonlinear model. We discuss how to select the linearization tuples for linearization and the choice of linear MOR method. Then we study how to combine the local linearized reduced systems to create a global TPWL model. Finally, we show a numerical result.

Adjoint transient sensitivity analysis in circuit simulation

Sensitivity analysis is an important tool that can be used to assess and improve the design and accuracy of a model describing an electronic circuit. Given a model description in the form of a set of differential-algebraic equations it is possible to observe how a circuits output reacts to varying input parameters, which are introduced at the requirements stage of design. In this paper we consider the adjoint method more closely. This method is efficient when the number of parameters is large.We extend the transient sensitivity work of Petzold et al., in particular we take into account the parameter dependency of the dynamic term.We also compare the complexity of the direct and adjoint sensitivity and derive some error estimates. Finally we sketch out how Model Order Reduction techniques could be used to improve the efficiency of adjoint sensitivity analysis.

Automatic partitioning for multirate methods

The (nonlinear) transient analysis of electrical circuit models plays an important role in circuit design. Multirate time integration can be able to achieve the same accuracy for much lower costs. An essential assumption is the existence of a good partition of the circuit in a slow and fast part. This paper describes how this can be done automatically.

Importance sampling for determining SRAM yield and optimization with statistical constraint

Importance Sampling allows for efficient Monte Carlo sampling that also properly covers tails of distributions. From Large Deviation Theory we derive an optimal upper bound for the number of samples to efficiently sample for an accurate fail probability Pfail ≤ 10− 10. We apply this to accurately and efficiently minimize the access time of Static Random Access Memory (SRAM), while guaranteeing a statistical constraint on the yield target.

Time Domain Simulation of Power Systems with Different Time Scales

The time evolution of power systems is modeled by a system of differential and algebraic equations. The variables involved in the system may exhibit different time scales. In standard numerical time integration methods the most active variables impose the time step for the whole system. We present a strategy, which allows the use of different, local time steps over the variables. The partitioning of the components of the system in different classes of activity is performed automatically and is based on the topology of the power system.

Terminal current interpolation for multirate time integration of hierarchical IC models

Multirate time-integration methods [3–5] appear to be attractive for initial value problems for DAEs with latency or multirate behaviour. Latency means that parts of the circuit are constant or slowly time-varying during a certain time interval, while multirate behaviour means that some variables are slowly time-varying compared to other variables. In both cases, it would be attractive to integrate these slow parts with a larger timestep than the other parts. This saves the computational workload while the accuracy is preserved. A nice property of multirate is that it does not use any linear structure, in contrast to MOR, but only a relaxation concept. If the coupling is sufficiently monitored and the partitioning is well chosen, multirate can be very efficient.