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# Latent Graph Theory of Transient Analysis

IP.com Disclosure Number: IPCOM000087726D
Original Publication Date: 1977-Mar-01
Included in the Prior Art Database: 2005-Mar-03
Document File: 6 page(s) / 90K

IBM

## Related People

Hsieh, HY: AUTHOR [+2]

## Abstract

1. General Introduction There is provided a new theory in the transient analysis of large networks. The latent graph theory represents the numerical computation of large networks in graph form.

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Latent Graph Theory of Transient Analysis

1. General Introduction There is provided a new theory in the transient analysis of large networks. The latent graph theory represents the numerical computation of large networks in graph form.

The latent graph theory may be applied to circuit analysis. It could, however, be extended to logic simulation as well as to any type of simulation which involves analyzing differential equations in the time domain.

This theory describes the identification and monitoring of connected paths in a network such that when the network variables within the path are not changing, the subnetworks in the path are not analyzed. The main objective of this disclosure is to reduce storage and time required to simulate networks. 2. Introduction

In previous work the latent principle was applied to a single macro-modular network in a mixed approach. In the present approach, we extend the latent principle to very large networks. A whole section of a large network could be latent, and, therefore, no updating and evaluating of up to 80% of the large network are sometimes possible.

In conventional circuit programs, the step size delta t is usually controlled by deltat = eta.deltat, where eta is related to the truncation error, to the history of the solution vector x(-i), and to a predicted vector x(-1), deltat is the current time step, and deltat is the next time step. Though a great number of partial derivatives in the Jacobian need not be updated since some of them are latent, delta t is still controlled by the nonlatent portion of x(-i). When an MM was combined in a host circuit-analysis program, delta t was controlled by the host program, i.e., by the nonlatent portion of the solution vector, and though no updating was required in the preprocessor program, which computes the solution of the MM, unnecessary calls to the preprocessor program were made.

In the latent graph theory, the updating is directly proportional to the actual physical dynamic behavior of the large network. While delta t is stepped up or down according to the nonlatent portion of the large network, it does not affect the latent portions of the large network, since no updating, accessing, or monitoring is required for whole sections of the network with the latent graph theory, which fully utilizes latency by defining latent-directed paths. 3. Identification of Connected Paths

Let us consider the directed graph of Fig. 1. Each torn subnetwork is represented by F(1) and F(2), with one external stimulus, I(psi1), and a requested output port Q. Edge S(1) represents the external port of F(1), which is also the internal stimulus to F(2). The internal stimulus of the F subnetworks, which are illustrated by the S edges in Fig. 1, represents the effect due to tearing (iXi3). If F(2) becomes latent, its stimulus S(1) needs only to be monitored as described by the latent principle. Once F(1) becomes latent, monitoring I(psi1) is sufficient for both F(1) and F...