Quadrature solutions for 3D capacitance extraction
US6314545A · kind A · utility
Assignee
Inventors
Key dates
| Filing date | Nov 6, 1998 |
| Grant date | Nov 6, 2001 |
| Priority date | — |
| Expiry date | Nov 6, 2018 |
Classification
- Technology area (CPC G)Physics
- CPC primaryG06F30/23
- WIPO fieldComputer technology
- WIPO sectorElectrical engineering
Abstract
The element to be simulated is divided into regions, and each region is further divided into a plurality of quadrature nodes. Pairs are formed for all the quadrature nodes. Green's functions are computed and stored for the pairs. Each of the pairs is allocated to either the far field or the near field for purposes of simulation in accordance with a criterion. A Gaussian quadrature is computed for the pairs allocated to the far field while a high order quadrature is computed for those allocated in the near field. The component simulation is arrived after combining information derived from the Gaussian quadrature and the high order quadrature into a matrix which is then solved to obtain the charge distribution. Summation of the charges thus obtained yields the capacitance of the element. The high order quadrature is computed using a plurality of basis functions. The basis functions, denoted .psi..sub.i.sup.k (r'), are 1,x,y,x.sup.2,xy,y.sup.2. The basis functions are used to compute a set of weights v.sub.j.sup.k. The weights are computed by solving ##EQU1## PA1 where .psi..sub.i.sup.k (r') are the basis functions, G(r,r') are the Green's functions for each of the pairs allocated to …
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