The Midwest Structural Sciences Center relies on numerous models to predict aerospace vehicle performance under thermo-mechanical-acoustical loadings.

We are looking for a post-doctorial researcher to investigate error in these models associated with:

1. uncertainties in data such as material properties and loads,
2. modeling simplifications resulting from dimensional reduction, e.g the use of beam rather than continuum theory and
3. discretization error introduced by the numerical schemes that are used to resolve the models, e.g. the finite element method. Our primary focus is directed towards item 2 and to a lesser extent item 1.

Our modeling error problem is concerned with the following:

We have PDEs which are subject to the control b, e.g. loading and material distribution, and resolved to evaluate the true response fields u(b), e.g. displacement. We then process these fields to evaluate our functionals of interest Q(u(b)) such as maximum principle stress at a point. As is often the case, however, we make simplifying assumptions to make our life easier. Using beam theory instead of continuum theory or using homogenized material properties instead of modeling the microstructure heterogeneities are two classic examples of these simplifications. Nonetheless, we still solve PDEs, albeit different ones, from which we obtain the surrogate response fields u'(b) which in turn are used to evaluate the functionals of interest Q(u'(b)). In a related scenario, we can view a detailed finite element model as the PDE which we resolve to obtain the true response u(b) and then Q(u(b)). In this case, a reduced order model serves as the simplified model; from it we obtain the surrogate response u'(b) and Q(u'(b)). Related to this is a parametric study, where we use the detailed finite element analysis to evaluate Q(u(b)) for several choices of our parameter b, e.g. a dimension. Interpolation may then be used to evaluate u'(b) and Q(u'(b)) as in a response surface methodology. And finally, in stochastic sense, b represents the random input and Monte Carlo schemes are used to obtain the statistics on Q(u(b)). Computational limitations, however, require that we replace the costly Q(u(b)) evaluations with economical Q(u'(b)) evaluations. The error we speak of is the difference Q(u(b))-Q(u'(b)) and our goal is to develop tight bounds on and sharp error estimates of Q(u'(b)). Potential collaborations with optimization and large-scale finite element analysis projects will also be available through this project.

Applicants should have a Ph.D. in applied mathematics (or a related field) and experience with the finite element method.

Please apply to Prof. Daniel A. Tortorelli - (dtortore@illinois.edu <mailto:dtortore@illinois.edu>) with a cover letter, detailed CV, copies relevant publications and the names of three referees.
This two year position with annual renewal will be filled immediately.

The University of Illinois is an Affirmative Action Equal Opportunity Employer. Applications from women and under represented minorities are especially welcome.

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Review of applications will continue until positions are filled

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