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Algorithm Which Saves Time and Storage in a Capacitance Computation Program

IP.com Disclosure Number: IPCOM000083077D
Original Publication Date: 1975-Mar-01
Included in the Prior Art Database: 2005-Feb-28
Document File: 2 page(s) / 38K

Publishing Venue

IBM

Related People

Brennan, PA: AUTHOR [+2]

Abstract

A method for capacitance computation has been previously described in a paper by the present authors. [1] The important aspect described in the present publication is that the following matrix can be set up for a number of conductors; Phis = ps Qs (1) where Phi s is the potential vector on the cells, ps is a symmetric matrix of coefficients and Qs is the vector of cell charges. The matrix ps can be put in a specific form with the clustering step which is the 1st step in the algorithm.

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Algorithm Which Saves Time and Storage in a Capacitance Computation Program

A method for capacitance computation has been previously described in a paper by the present authors. [1] The important aspect described in the present publication is that the following matrix can be set up for a number of conductors; Phis = ps Qs (1) where Phi s is the potential vector on the cells, ps is a symmetric matrix of coefficients and Qs is the vector of cell charges. The matrix ps can be put in a specific form with the clustering step which is the 1st step in the algorithm.

As is shown in Fig. 1, seven conductors are clustered into groups C1, C2 and C3, whereby close objects (conductors) are put in the same clusters and distance to any other cluster is maximized. Then the ps-matrix is as shown in Fig.
2.

It can be seen from Fig. 1 how the portions of the matrix and the submatrices are related. Fig. 3 in Reference 1 shows that if max lij over (di,dj) > 3 a 1% error results, if the particular coefficients the matrix are approximated as being independent of the actual shape of the conductor within the cluster. However, much saving is obtained if all the coefficients due to coupling, for example between clusters C1 and C2 are represented by a single coefficient A. For each submatrix marked A, B, C only a single coefficient must be stored, resulting in more than a factor 2 timesaving in setting up the matrix and in storage which is Very significant for actual problems.

Several metho...