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Sensitivity analysis and optimal design in charge transport problems
Author(s) -
Shi Fan,
Mukherjee Subrata,
Ramesh Palghat
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620370903
Subject(s) - sensitivity (control systems) , poisson's equation , charge conservation , charge (physics) , partial differential equation , boundary value problem , mathematics , mathematical optimization , optimal design , boundary (topology) , mathematical analysis , computer science , physics , engineering , electronic engineering , statistics , quantum mechanics
The focus of this paper is the accurate and efficient determination of sensitivities of electrostatic potential and charge density in charge transport problems, and the use of these sensitivities to carry out optimal design. Direct differentiations of the boundary integral formulation of Poisson's equation for charge conservation and of the non‐linear partial differential equation for current continuity are carried out to obtain equations satisfied by the sensitivities. Methods for solving the sensitivity equations are discussed. A numerical implementation of the methods is validated through several examples. It is demonstrated that the Design Sensitivity Coefficients (DSCs) of the quantities of interest in charge transport are obtained accurately and that optimal design problems can be solved efficiently using these DSCs.