### Table 1: Simulation run times for the adjoint and direct

"... In PAGE 3: ... One adjoint analysis was performed for each circuit. Table1 summarizes the run times of the ACES simulation and the associated adjoint simulation as well as direct simulation. Column 1 of the table lists the circuit names.... ..."

### Table 2: Computational cost breakdown of CPOS adjoint

"... In PAGE 6: ... The main advantage of the CPOS method is clear: the computational time was only 3% of the time required by finite-differences. To better understand the computational costs involved in the CPOS adjoint, a breakdown of the cost of computing each partial derivative term is shown in Table2 . In this study, both the number of panels and the number of finite elements was increased to 50.... In PAGE 8: ... For the new architecture, the additional structural variables do not change the system-level problem. From Table2 , it is apparent that the constraint gradients are the main cause for the delay in the structural subspace optimization. This is because the computational time of the complex-step method scales with the number of design variables.... ..."

### Table 4. Running time analysis of exhaustive matroid generation based on Algo- rithm 3.2 (Section 4) in Macek (in seconds per matroid, normalized to 1GHz CPU).

2004

"... In PAGE 17: ...Secondly, Table4 summarizes average time needed to exhaustively generate a small matroid representation in Macek, according to the ideas presented in Section 4 (i.e.... In PAGE 17: ... The last two lines exhibit a somehow di erent behavior, probably related to the existence of many inequivalent repre- sentations of matroids over larger elds. Note the di erence between the numbers of generated matroids in Table 2, and here in the last two lines of Table4 where the GF (q)-representable matroids for q = 4, resp. q = 4; 5; 7, are not excluded.... ..."

### Table 1. The numbers of small 3-connected matroids repre- sented over small elds.

"... In PAGE 4: ... A special feature of our generation routine is that it allows to generate exclusively 3-connected matroids, and thus signi cantly speeding up the process in many cases. For an illustration we present (see also [6]) our exhaustive enumeration results of small representable 3-connected matroids in Table1 . (It is hardly imaginable generating those amounts of matroids without the 3-connectivity restriction.... ..."

### Table 5: Number of synchronization operations for adjoint convolution N = 75.

1994

"... In PAGE 24: ... On machines where access to a local work queue is much cheaper than access to a remote work queue (either due to the cost of non-local access or the cost of non-local synchronization primitives), this property of a nity scheduling could have enormous performance advantages. Table5 presents the total number of synchronization operations for the adjoint convolution application under the various scheduling algorithms. TRAPEZOID again has the smallest number of synchronization operations.... ..."

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### Table 5: Example of an adjoint m-stage R-K algorithm, where the true adjoint is guaranteed by placing the update statement before the adjoint flux calculations

### Table 1. Adjoint boundary conditions for various cost functions

"... In PAGE 4: ... The form of the adjoint boundary conditions depends on the cost function. Table1 summarizes some of the commonly used cost functions. Table 1.... ..."

### Table 2: ADjoint computational cost breakdown (times in seconds)

2007

"... In PAGE 10: ... This expectation is based on the results of a previous comparison done with a single block version of the ADjoint implemented on the SUmb flow solver [18]. The timing results for the oblique wing and X-43 test cases are shown in Table2 . As can be seen for both cases, the ADjoint solution is less expensive than the flow solution, varying from 2/3 to 1/50 of the flow solution time, depending on the test case.... ..."

### Table 1. Expected load imbalance and relative load imbalance for adjoint convolution.

1997

"... In PAGE 4: ... Expected load imbalance and relative load imbalance for adjoint convolution. statement of the loop body, and the corresponding relative load imbalance, a27a63a62 , for N a24a162a159 a8a117a8a121a8 ; the results are shown in Table1 . The performance of the partitioned programs on the KSR1, for the same value of N, is shown in Figure 7; the ideal line corresponds to linear speed-up.... ..."

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### Table 1. Expected load imbalance and relative load imbalance for adjoint convolution.

1997

"... In PAGE 4: ... Expected load imbalance and relative load imbalance for adjoint convolution. statement of the loop body, and the corresponding relative load imbalance, LR, for N = 8000; the results are shown in Table1 . The performance of the partitioned programs on the KSR1, for the same value of N, is shown in Figure 7; the ideal line corresponds to linear speed-up.... ..."

Cited by 3