5412565 Electronic synapse circuit for artificial neural network : Boser Bernhard; Sackinger Eduard Locust, NJ, UNITED STATES Assigned to AT&T Corp

Abstract

The domain deformation method has been applied successfully to steady state free surface flows where the volume of the flow domain is unknown [V.F. de Almeida, Gas–liquid counterflow through constricted passages, Ph.D. thesis, University of Minnesota, Minneapolis, MN 1995; P.A. Sackinger, P.R. Schunk, R.R. Rao, A Newton–Raphson pseudo-solid domain mapping technique for free and moving boundary problems: a finite element implementation, J. Comput. Phys. 125 (1996) 83–103; L.C. Musson, Two-layer slot coating, Ph.D. thesis, University of Minnesota, Minneapolis, MN 2001]; however, this method does not handle effectively problems where the volume of the flow domain is known a priori. This work extends the original domain deformation method to a new isochoric domain deformation method to account for the volume conservation. Like in the original domain deformation method, the unknown shape of the flow domain is mapped onto a reference domain by using the equations of an elastic pseudo-solid; the difference with the original method is that this pseudo-solid is considered incompressible. Because of the incompressibility, the pseudo-pressure of the mapping appears as a Lagrange multiplier in the equations, and it is determined only up to an arbitrary uniform datum. By analyzing the coupled fluid flow-mapping problem, we show that, in the finite-element setting, such pressure datum can be specified by replacing one continuity equation in the fluid domain.