Analysis And Design of Polygonal Registors By Conformal Mapping
Analysis And Design of Polygonal Registors By Conformal Mapping
Lloyd N Trefethen
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Instead, one can design the wafer so that the resistance is 10% or so too low, and then tune it to the desired value by cutting a slit with a k ~er. The mathematical problem of predicting the appropriate slit length has been -2- attackcd previously by other methods [3, 6]. The Schw: rz-Christoffel approach to L^pkje-rclated calculations en polygons has the virtue that unlike methods based on integral equations, finite differences, finite element:', or the superposition of partieular solutions, ...it preserves the property inherent in the pre'; lem of having only a finite number cf parameters. In particular it automatically obtains the correct singularities at comers. Because cf this, the ScLwarz-Christcffcl method can achieve very high accuracy without much penalty in execution time, as cur examples will shew. (For low accuracy, other methods may be better; see [5] for a description cf a highly effective method based en breaking the domain up into simple subpclygcns. ) Its chief drawback is that it genc^lizea poorly to related problems involving more compli- cates differential equations (e.
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