# PDE Constrained Optimization for Digital Image Correlation.

## Abstract

The purpose of this report is to investigate a partial differential equation (PDE) constrained optimiza- tion approach for estimating the velocity field given image data for use within digital image correlation (DIC). We first introduce the problem and the standard DIC approach and then demonstrate why the DIC problem is ill-posed and introduce a standard regularization of the problem. We also demonstrate that the functional used is sensitive and robust via a sequence of experiments given by a stochastic model inducing the PDE constraint.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1494349

- Report Number(s):
- SAND2015-8515

672305

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Turner, Daniel Z., Lehoucq, Richard B., and Garavito-Garzon, Carlos A.
```*PDE Constrained Optimization for Digital Image Correlation.*. United States: N. p., 2015.
Web. doi:10.2172/1494349.

```
Turner, Daniel Z., Lehoucq, Richard B., & Garavito-Garzon, Carlos A.
```*PDE Constrained Optimization for Digital Image Correlation.*. United States. doi:10.2172/1494349.

```
Turner, Daniel Z., Lehoucq, Richard B., and Garavito-Garzon, Carlos A. Thu .
"PDE Constrained Optimization for Digital Image Correlation.". United States. doi:10.2172/1494349. https://www.osti.gov/servlets/purl/1494349.
```

```
@article{osti_1494349,
```

title = {PDE Constrained Optimization for Digital Image Correlation.},

author = {Turner, Daniel Z. and Lehoucq, Richard B. and Garavito-Garzon, Carlos A.},

abstractNote = {The purpose of this report is to investigate a partial differential equation (PDE) constrained optimiza- tion approach for estimating the velocity field given image data for use within digital image correlation (DIC). We first introduce the problem and the standard DIC approach and then demonstrate why the DIC problem is ill-posed and introduce a standard regularization of the problem. We also demonstrate that the functional used is sensitive and robust via a sequence of experiments given by a stochastic model inducing the PDE constraint.},

doi = {10.2172/1494349},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {10}

}

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