Inverse Problems in Aerodynamics, Heat Transfer, Elasticity and Materials Design

Abstract

A number of existing and emerging concepts for formulating solution algorithms applicable to multidisciplinary inverse problems involving aerodynamics, heat conduction, elasticity, and material properties of arbitrary three-dimensional objects are briefly surveyed. Certain unique features of these algorithms and their advantages are sketched for use with boundary element and finite element methods.

A pseudo-compressibility method for solving inverse problems based on the 3D incompressible Euler equations

“…Nevertheless, it offers the main advantage of requiring a fewer number of flow-field evaluations to determine the enquired geometry, and also it allows for an easier imposition of the flow constrains (e.g. no flow separation and adverse pressure gradient control [5,6]). Approaches to the inverse problem solution are based on the potential flow theory and conformal mapping techniques, [4,7,8] on stream-function base formulations, [9][10][11] on boundary elements replacing the body surface [12] and on direct design methods.…”

“…Approaches to the inverse problem solution are based on the potential flow theory and conformal mapping techniques, [4,7,8] on stream-function base formulations, [9][10][11] on boundary elements replacing the body surface [12] and on direct design methods. [13][14][15][16] Several examples of inverse problem solution methodologies are presented in [5,17] and references therein.…”

Calculation of film stress from pitch measurements in LCD panel manufacturing

“…Determination of film stress from deformation measurements falls into the general category of inverse problems, which is a broad field in engineering. 4 In this paper, we describe a model relating film stress to deformation of a coated glass substrate and a method to invert it to obtain film stress from in-plane deformation measurements. In the study by Fu, 5 a similar method is described to obtain film stress from out-of-plane measurements.…”