# Large Scale Non-Linear Programming for PDE Constrained Optimization

## Abstract

Three years of large-scale PDE-constrained optimization research and development are summarized in this report. We have developed an optimization framework for 3 levels of SAND optimization and developed a powerful PDE prototyping tool. The optimization algorithms have been interfaced and tested on CVD problems using a chemically reacting fluid flow simulator resulting in an order of magnitude reduction in compute time over a black box method. Sandia's simulation environment is reviewed by characterizing each discipline and identifying a possible target level of optimization. Because SAND algorithms are difficult to test on actual production codes, a symbolic simulator (Sundance) was developed and interfaced with a reduced-space sequential quadratic programming framework (rSQP++) to provide a PDE prototyping environment. The power of Sundance/rSQP++ is demonstrated by applying optimization to a series of different PDE-based problems. In addition, we show the merits of SAND methods by comparing seven levels of optimization for a source-inversion problem using Sundance and rSQP++. Algorithmic results are discussed for hierarchical control methods. The design of an interior point quadratic programming solver is presented.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 805833

- Report Number(s):
- SAND2002-3198

TRN: US200303%%268

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 1 Oct 2002

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; DESIGN; FLUID FLOW; PROGRAMMING; COMPUTERIZED SIMULATION; SIMULATORS; CHEMICAL VAPOR DEPOSITION

### Citation Formats

```
VAN BLOEMEN WAANDERS, BART G, BARTLETT, ROSCOE A, LONG, KEVIN R, BOGGS, PAUL T, and SALINGER, ANDREW G.
```*Large Scale Non-Linear Programming for PDE Constrained Optimization*. United States: N. p., 2002.
Web. doi:10.2172/805833.

```
VAN BLOEMEN WAANDERS, BART G, BARTLETT, ROSCOE A, LONG, KEVIN R, BOGGS, PAUL T, & SALINGER, ANDREW G.
```*Large Scale Non-Linear Programming for PDE Constrained Optimization*. United States. doi:10.2172/805833.

```
VAN BLOEMEN WAANDERS, BART G, BARTLETT, ROSCOE A, LONG, KEVIN R, BOGGS, PAUL T, and SALINGER, ANDREW G. Tue .
"Large Scale Non-Linear Programming for PDE Constrained Optimization". United States. doi:10.2172/805833. https://www.osti.gov/servlets/purl/805833.
```

```
@article{osti_805833,
```

title = {Large Scale Non-Linear Programming for PDE Constrained Optimization},

author = {VAN BLOEMEN WAANDERS, BART G and BARTLETT, ROSCOE A and LONG, KEVIN R and BOGGS, PAUL T and SALINGER, ANDREW G},

abstractNote = {Three years of large-scale PDE-constrained optimization research and development are summarized in this report. We have developed an optimization framework for 3 levels of SAND optimization and developed a powerful PDE prototyping tool. The optimization algorithms have been interfaced and tested on CVD problems using a chemically reacting fluid flow simulator resulting in an order of magnitude reduction in compute time over a black box method. Sandia's simulation environment is reviewed by characterizing each discipline and identifying a possible target level of optimization. Because SAND algorithms are difficult to test on actual production codes, a symbolic simulator (Sundance) was developed and interfaced with a reduced-space sequential quadratic programming framework (rSQP++) to provide a PDE prototyping environment. The power of Sundance/rSQP++ is demonstrated by applying optimization to a series of different PDE-based problems. In addition, we show the merits of SAND methods by comparing seven levels of optimization for a source-inversion problem using Sundance and rSQP++. Algorithmic results are discussed for hierarchical control methods. The design of an interior point quadratic programming solver is presented.},

doi = {10.2172/805833},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2002},

month = {10}

}