Enhancing the stability of asymptotic waveform evaluation for digital interconnect circuit applications

Fast transient thermal analysis of Fourier and non-Fourier heat conduction

“…Solutions from AWE and also Crank-Nicolson (conventional iterative solver) agree well for all the nodes, except for nodes 6, 7, 14 and 15. This is because Padé approximation is known for producing unstable response even for stable system [15,16].…”

“…In addition, partial Padé approximation [15,16] is also introduced to stabilize the AWE solutions for the case Z T = 0.0001. In this stability scheme, the set of poles at an arbitrarily chosen node is used to approximate the responses of other nodes.…”

Transient analysis of transmission line circuits based on the semidiscretization of telegraph equations

“…Of course, after getting a rational approximation of the transmission lines, the discrete model can also be derived by transforming it into an ordinary differential equations [4]. The numerical instability in moment-matching has been a disturbing problem in the application of this method [5], However, the Krylov subspace techniques such as PVL(Pade Via Lanczos) introduced in recent years improves this significantly Is], and some algorithms that can preserve passivity in the approximation and so guarantee the stability of the reduced order model finally gotten have been developed [z's]. An alternative in this class of methods is the characteristic method [9'I°], which obtains the discrete model by the discretization of the ordinary differential equations along the characteristic line of the telegraph equations.…”

Model Order Reduction for Peec Modeling Based on Moment Matching

“…One of the important properties of Padé approximation is that poles of horizontal sequences (fixed M , increasing L) in the table converge to the actual poles [18,19]. This is as (23) indicates, where p j 's are the actual poles of transfer function.…”

“…We take a unit ramp input r(t) as an example. The Laplace transform of the input is L {r(t)} = 1/s 2 ; therefore, the corresponding transient response obtained by (19) can be written as where u(t) is a unit step function. This approach of the time-domain response calculation can be extended to general inputs by applying superposition of elementary responses.…”