Minisymposia Abstracts
Speaker:  Luther White University of Oklahoma 
Title:  Modeling, data, validation, and inversion for a girder 
Abstract:  A beam model with shearing having spatially dependent elastic properties is determined
for the purpose of modeling a prestressed concrete mended girder. Data has been obtained
from a collection of experiments in which the girder is loaded and the displacements
at points along the girder are observed. This data is used for a validation procedure. Different
elastic parameterizations are considered. Numerical studies and presented. Finally,
issues involving the inversion of data and applications for health monitoring are discussed.

Speaker:  Kurt M. Bryan RoseHulman Institute of Technology 
Title:  Efficient computational methods for thermal imaging of small cracks in plates 
Abstract:  We present some fast computational methods for identifying cracks in a twodimensional
plate using input flux and temperature measurements, based on the “small volume”
asymptotic expansions of Ammari, Moskow, Vogelius, et. al. For a given input heat
flux the temperature of the plate is measured using an infrared image of the entire surface of
the plate (so unlike problems in which measurements are restricted to the onedimensional
boundary of the object, we have access to the “interior”of the object.) The novelty here
is that the cracks we seek to image are very small, below the singlepixel resolution of the
infrared camera.

Speaker:  Herb Kunze University of Guelph 
Title:  Using the ideas and philosophy of fractalbased analysis to solve differential equations inverse problems 
Abstract: 
In fractal imaging, one seeks to approximate a target image by the fixed point of a
fractal transform, but the true error in terms of parameters is not available to be minimized.
One instead shifts to a different minimization problem via the Collage Theorem. Broadly
speaking, a similar situation occurs when considering inverse problems for differential equations:
the true error in terms of parameters is not available. Motivated by a fractalbased
approach, in this talk, we shift to a different minimization problem. We develop and discuss
the theoretical machinery for treating both ODEs and PDEs inverse problems, in deterministic
and random settings, with applications. 
Speaker:  Assad Oberai Rensselaer Polytechnic Institute 
Title:  Direct computation of inverse problems of incompressible elasticity 
Abstract:  Solving inverse problems for the distribution of mechanical properties is typically
based on constrained optimization procedures, requiring numerous forward solutions. Current
image processing techniques often provide fullfield kinematic measurements. In such
cases, the inverse problem may be approached directly. For linear elasticity this leads to
system of advectiontype equations for the sought moduli, with coefficients that depend on
the known strains. A novel variational formulation related to the adjoint operator (AWE)
leads to a boundary value problem that is well posed under mild conditions, allowing for
the presence of measurement error, and lends itself well to Galerkin discretization. In this
talk we consider the application of this formulation to different problems in linear elasticity
imaging including, those of qausistatic plane stress and strain and timeharmonic plane
stress.

Speaker:  Paul Barbone Boston University 
Title:  Improved inverse problem solutions using improved forward solvers 
Abstract: 
A large class of inverse problems may be described as trying to infer medium
properties in a domain based upon measurement of a field within or on the
boundary of that domain. The ability to do this depends upon the measured
field being sensitive to changes in the material properties. This sensitivity may
be expressed in terms of an inequality which may be derived directly from the
governing partial differential equations. More precisely, there exists a constant
C ≤ 1 such that:

Speaker:  Ian Knowles University of Alabama at Birmingham 
Title:  Wellposedness for the inverse groundwater problem 
Abstract:  The inverse problem of determining subsurface parameters, such as hydraulic
conductivity, storativity, and recharge from well measurements in an aquifer system has a
long history. W n this problem showing that the recovered parameters depend continuously
on the well data. We also discuss the related problem of practical error estimation in aquifer
modelling.

Speaker:  Fabio Raciti University of Catania 
Title:  On an inverse problem related to the Lamé system 
Abstract:  We consider an inverse problem for an elastic body occupying a bounded domain
A. Let B be a subdomain of A such that the Lamé parameters have different constant values
in B and A\B. We study the problem of localizing B with boundary measurements under
the assumption that B has the shape of a polyhedron.

Speaker:  Akhtar A. Khan Rochester Institute of Technology 
Title:  Parameter identification in variational and quasivariational inequalities 
Abstract:  In recent years new optimality conditions, by means of multiplier rules, were obtained
for abstract optimization problems in function spaces where the associated ordering
cone of has a nonempty interior. However, it turns out that the multipliers for these problems
belong to nonregular spaces of measures. One of the essential requirement of these
studies is the validity of a Slater’s type constraint qualification. It is known that Slater’s
type constraint qualification is a stringent condition and it does not hold for many important
cases of interest. In this talk, we will discuss a new conical regularization technique that
gives optimality conditions without requiring any Slater’s type constraint qualification. The
Henig dilating cones is the basic technical tool for this study. Finite element discretization
of the dilating cone will be discussed and numerical examples will be presented.

Please address administrative questions to aipc@math.tamu.edu. Scientific questions should be addressed to the chair of the Scientific Program Committee: rundell AT math.tamu.edu