Improved procedure for interconnecting piece-wise solutions

✍ Scribed by Gabriel Kron

• Publisher: Elsevier Science
• Year: 1956
• Tongue: English
• Weight: 500 KB
• Volume: 262
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(56)90079-5

✦ Synopsis

When a physical system, or its topological model, is torn apart into n independent parts, a factorized form of the true inverse matrix Z may be established by finding the inverse of n + 1 much smaller matrices. No additional matrix multiplications are needed. The first n matrices Zr represent the n subdivisions, while the (n + 1)-th matrix Z, represents a newly created physical system, to be called "intersection" system. The latter matrix is constructed out of the fragments of the inverted subdivisions. This paper shows that it is not necessary to establish the Zr and Zo matrices that couple Z4 of the intersection system with Zr of the n subdivisions. The role of the coupling matrices can be taken over by the already established connection matrix C. Thus the amount of storage and the clerical work are greatly decreased from that shown previously. Moreover the number of multiplications needed to evaluate the unknown E for a given I is reduced.

A simple numerical example is also worked out by the improved procedure.