### Table 3: Nonlinear solver results for BJT inverter circuit. The entry - indicates that the problem did not converge.

2003

"... In PAGE 39: ...igure 13. Inverter Schematic. The result for a transient simulation of the inverter is shown in Figure 14. Nonlinear solver results are shown in Table3 . For all the results presented here, the nonlinear Poisson solution was used as an initial guess, as without it, none of the methods would have been successful.... In PAGE 41: ... When one is high, the other should be low, and vice-versa. The results presented in Table3 notwithstanding, it is often possible to obtain con- vergence with the full-Newton algorithm for mixed-level problems, even with high- valued voltage sources. However, doing so requires that the user apply a con- tinuation algorithm by hand, either by using the DC sweep capability of Xyce, or, in the case of a transient simulation, gradually ramping up the voltage source(s) over time, and letting the time integrator handle step size control, rather than the continuation algorithm.... ..."

### Table lookup is used to invert the nonlinear function ~i(t) (spec-

### Table 1. Programs with the most nonlinear control

"... In PAGE 12: ... Consider as a measure of linearity the ratio between the control dependence graph size and the number of executable statements in a program. Table1 shows number of storage words required to store the full control dependence graphs for the 20 programs with the largest such ratio. The median procedure required a graph whose size (in words) was 3.... ..."

### Table 2: Number of controller refreshments in nonlinear simulations.

1997

"... In PAGE 11: ...: dotted every 50 deg.: dashdot; no refreshment: dashed The simulations corresponding to di erent refreshment strategies, Table2 , are compared in Figure 3 with the fully-continuous simulations, that are obtained using the original continuous gain-scheduled con- troller. It can be seen that when the discrete controller is refreshed at each sample, the time responses are... In PAGE 12: ...using the trapezoidal method with a sampling frequency of 50 Hz. When the discrete controller is refreshed every 30 degrees of observed deviation the total amount of ops is roughly divided by 120 ( Table2 ) without signi cant performance degradation. With fewer refreshments (every 50 degrees), alterations of the per- formance are more visible in the transient and steady-state zones of the responses.... ..."

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### Table 2: Number of controller refreshments in nonlinear simulations.

1997

"... In PAGE 11: ...: dotted every 50 deg.: dashdot; no refreshment: dashed The simulations corresponding to di erent refreshment strategies, Table2 , are compared in Figure 3 with the fully-continuous simulations, that are obtained using the original continuous gain-scheduled con- troller. It can be seen that when the discrete controller is refreshed at each sample, the time responses are... In PAGE 12: ...using the trapezoidal method with a sampling frequency of 50 Hz. When the discrete controller is refreshed every 30 degrees of observed deviation the total amount of ops is roughly divided by 120 ( Table2 ) without signi cant performance degradation. With fewer refreshments (every 50 degrees), alterations of the per- formance are more visible in the transient and steady-state zones of the responses.... ..."

Cited by 2

### Table 5: A Multilevel Scheme for Engineering Optimization Calculations

"... In PAGE 22: ... Once the location of an optimal value is determined, a high-fidelity model is used to determine its converged value. This methodology resembles the scheme proposed in Section 8 ( Table5 ) in that it provides a way to identify candidate optima ( regions of interest ) followed by local refinement of the candidate optima.... In PAGE 41: ... 8.3 A Multilevel Scheme for Engineering Optimization Calculations We therefore propose the following scheme for performing practical optimization calculations using a mesh-based engineering model (such as a finite-difference or finite- element code) ( Table5 ). The concept of the scheme is to use a coarser mesh to identify candidate optima, and then improve the objective function values at the candidate optima using a finer mesh, followed by a final ranking of the optima based on the converged value of the objective function.... In PAGE 49: ...) One must also be able to find a mesh which is fine enough to give reasonable approximations to the local optima, but coarse enough to run on an available platform in a practical amount of time. Having thus an improved CTH model for the BRL 81-mm shaped charge and an improved scheme for locating the jet tip, we employed the scheme presented in Table5 to find an optimum solution to the Sandia wave-shaper optimization problem.... ..."

### Table 6- Effect of e on multilevel decompostion optimization procedure

1994

"... In PAGE 12: ...ion procedure. Results for three e values (+0.4, -0.2, and -0.4) are presented in Table6 and Figs. 15-16, and 9, respectively.... In PAGE 12: ... Therefore, the upper level opti- mizer makes only small changes and the process converges in three cycles. As shown in Table6 , when e is 0.4, the optimization process is able to improve the performance and dynamics measures over the initial blade values and improve the... In PAGE 13: ... When e is -0.2, the optimization procedure is able to obtain a design that has some improvement over the initial starting point ( Table6 ). The upper level objective function is reduced slightly, but not as much as when e is positive.... In PAGE 13: ...0.4. With this value of e, the optimization procedure is able to obtain improvement on the upper level and find a set of consistent stiffnesses on the lower level. These re- sults (Example 1) are included in Table6 for completeness. The stiffness distributions are shown in Fig.... ..."

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### Table 2. Sequential Multilevel Optimization of a 2D bump.

1998

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