K. Mayaram, P. Yang, J. Chem, R. Burch. L. Arledge, and P. Cox, "A parallel block-diagonal preconditioned conjugate-gradient solution algorithm for circmt and devtce simulations" in Proc. lot. Conf on Computer Aided Design, Santa Clara, CA. Nov. 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... transistors) methods suitable for non symmetric matrices must be considered, e.g. CGNR, GCR, GCR(k) ORTHOMIN, CGS [11] 13] The present discussion will be restricted to CGS, presented in [13] since experience has shown that it is the most efficient of the methods ex amined (see also [14] [15]) To demonstrate the effectiveness of the conjugate di rection algorithm, in Table I the CPU time required to compute the transient analysis of the network in Fig. 1 is compared using several different matrix solution algo rithms to solve (6) These results were obtained using the simulation ....

K. Mayaram, P. Yang, J. Chem, R. Burch. L. Arledge, and P. Cox, "A parallel block-diagonal preconditioned conjugate-gradient solution algorithm for circmt and devtce simulations" in Proc. lot. Conf on Computer Aided Design, Santa Clara, CA. Nov. 1990.

....for the waveform relaxation method [16, 61] have been proposed. There are a small number of researches on iterative linear solvers other than the waveform relaxation method. Some preconditioned CG type methods, which are widely used to solve partial differential equations, have been applied [75, 6, 43], but the performance is not satisfactory. Some other researchers use the relaxation method with the incomplete LU (ILU) decomposition [42, 44, 7] Those methods have potential to attain high performance and high stability, though not realized in those researches. Parallel implementation of those ....

....when the number of equations becomes larger than 10,000. However they used the Markowitz method for pivoting of the direct method, and the performance of the direct method will be much improved by a better pivoting algorithm. The number of CGS iterations is more than one hundred. Mayaram et al. [43] restrict the ILU preconditioner on diagonal blocks (Block Diagonal ILU preconditioner) Although the number of CGS iterations is somewhat larger than the ILU, they claimed that the parallelism is much higher than the ILU. 2.3.3. Relaxation Methods with Incomplete LU Decomposition Some ....

K. Mayaram, P. Cox, et al., "A Parallel Block-Diagonal Preconditioned Conjugate-Gradient Solution Algorithm for Circuit and Device Simulations," Proc. ICCAD, pp. 446--449, 1990.

....simulation techniques, including harmonic balance, it is important to consider a variety of previous circuit simulation parallelization efforts. For example, several non harmonic balance analog circuit simulators have been speed up by parallelization of their inherent linear matrix operations [12, 3, 8]. A parallelization of the (linear part of the) harmonic balance method has been demonstrated This work supported in part by the DoD HPCMO Office and ARPA under Order Number F425 (via ONR contract N6600197C8534) 2 [15] While this effort provided 97 processor efficiency this approach as ....

....PEs beyond the number of frequencies for the particular input file causes no additional speed up. Alternatively, methods which parallelize the underlying mathematics as it arises in circuit simulation have not, as of yet, achieved reasonable scalability. For example, the results in [12, 3] show efficiencies that are rapidly falling off even for ten PE computing systems. A peak efficiency of about 38 for 8 processors (about 3 Theta) has been shown, but speed up then decreases beyond 8 processors [8] A different parallel approach which leverages circuit substructure, as we do ....

[Article contains additional citation context not shown here]

K. Mayaram, P. Yang, J. Chern, R. Burch, L. Arledge, and P. Cox. A parallel block-diagonal preconditioned conjugate-gradient solution algorithm for circuit and device simulations. In IEEE Int. Conf. on Computer-Aided Design (ICCAD'90), pages 446--9, 11--15 Nov 1990. Santa Clara, CA.

....simulation techniques, including harmonic balance, it is important to consider a variety of previous circuit simulation parallelization efforts. For example, several non harmonic balance analog circuit simulators have been speed up by parallelization of their inherent linear matrix operations [11, 3, 7]. A parallelization of the (linear part of the) harmonic balance method has been demonstrated [13] While this effort provided 97 processor efficiency this approach as well as the others cited all display limited scalability. Scalability is a measure of the ability of the parallelization ....

....PEs beyond the number of frequencies for the particular input file causes no additional speed up. Alternatively, methods which parallelize the underlying mathematics as it arises in circuit simulation have not, as of yet, achieved reasonable scalabilty. For example, the results in [11, 3] show efficiencies that are rapidly falling off even for ten PE computing systems. A peak efficiency of about 38 for 8 processors (about 3 Theta) has been shown, but speed up then decreases beyond 8 processors [7] A different parallel approach which leverages circuit substructure, as we do ....

[Article contains additional citation context not shown here]

K. Mayaram, P. Yang, J. Chern, R. Burch, L. Arledge, and P. Cox. A parallel block-diagonal preconditioned conjugate-gradient solution algorithm for circuit and device simulations. In IEEE Int. Conf. on Computer-Aided Design (ICCAD'90), pages 446--9, 11--15 Nov 1990. Santa Clara, CA.

....MOS transistors) methods suitable for non symmetric matrices must be considered, e.g. CGNR, GCR, GCR(k) ORTHOMIN, CGS [7, 8] The present discussion will be restricted to CGS, presented in Algorithm 3. 1, since experience has shown that it is the most efficient of the methods examined (see also [9, 10]) One reason for the suitability of conjugate direction methods to the problem under consideration is that the convergence rates of these methods depend on the condition number of J F . By taking timesteps small enough, the capacitive portion of the Jacobian, which tends to be better conditioned ....

K. Mayaram, P. Yang, J. Chern, R. Burch, L. Arledge, and P. Cox, "A parallel block-diagonal preconditioned conjugate-gradient solution algorithm for circuit and device simulations," in International Conference on Computer Aided-Design, (Santa Clara, California), pp. 446--449, November 1990.

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