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# Algorithm for Detection and Correction of Transient Singular Matrices

IP.com Disclosure Number: IPCOM000043300D
Original Publication Date: 1984-Aug-01
Included in the Prior Art Database: 2005-Feb-04
Document File: 1 page(s) / 11K

IBM

## Related People

Hsieh, HY: AUTHOR [+2]

## Abstract

During network analysis computations, it has been occasionally noted that the Jacobian matrix in the circuit simulation program has become singular during transient simulations. Since the expected quadratic convergence of the Newton iteration will degenerate to linear convergence when its Jacobian matrix is nearly singular, the transient singular phenomenon may not only cause a non-convergence problem but waste large amounts of computer time during Newton iteration on the non- linearities. The basic cause of the transient singularity problem has been identified with sudden growth of a non-linear function such as; If = Is (eqV/kT-1) due to a value of V predicted during the Newton iteration.

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Algorithm for Detection and Correction of Transient Singular Matrices

During network analysis computations, it has been occasionally noted that the Jacobian matrix in the circuit simulation program has become singular during transient simulations. Since the expected quadratic convergence of the Newton iteration will degenerate to linear convergence when its Jacobian matrix is nearly singular, the transient singular phenomenon may not only cause a non-convergence problem but waste large amounts of computer time during Newton iteration on the non- linearities. The basic cause of the transient singularity problem has been identified with sudden growth of a non-linear function such as; If = Is (eqV/kT-1) due to a value of V predicted during the Newton iteration. Having located the cause of the transient matrix singularity, the problem has been determined to be rectifiable by application of either of the following means: 1. monitoring the predicted growth of If and reducing the time step whenever If tends to increase by more

than some factor, or 2. monitoring the predicted change in V (forward) and reducing the time step whenever that change exceeds

some absolute voltage. The addition of the monitoring and correction algorithm, here outlined, to existing network analysis computation programs has eliminated any further occurrence of transient matrix singularities and has improved the computational efficiency of the simulation.

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