# LDRD Report: Topological Design Optimization of Convolutes in Next Generation Pulsed Power Devices.

## Abstract

This LDRD project was developed around the ambitious goal of applying PDE-constrained opti- mization approaches to design Z-machine components whose performance is governed by elec- tromagnetic and plasma models. This report documents the results of this LDRD project. Our differentiating approach was to use topology optimization methods developed for structural design and extend them for application to electromagnetic systems pertinent to the Z-machine. To achieve this objective a suite of optimization algorithms were implemented in the ROL library part of the Trilinos framework. These methods were applied to standalone demonstration problems and the Drekar multi-physics research application. Out of this exploration a new augmented Lagrangian approach to structural design problems was developed. We demonstrate that this approach has favorable mesh-independent performance. Both the final design and the algorithmic performance were independent of the size of the mesh. In addition, topology optimization formulations for the design of conducting networks were developed and demonstrated. Of note, this formulation was used to develop a design for the inner magnetically insulated transmission line on the Z-machine. The resulting electromagnetic device is compared with theoretically postulated designs.

- Authors:

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

- Publication Date:

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

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

- OSTI Identifier:
- 1413648

- Report Number(s):
- SAND-2017-13410

659455

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING

### Citation Formats

```
Cyr, Eric C., von Winckel, Gregory John, Kouri, Drew Philip, Gardiner, Thomas Anthony, Ridzal, Denis, Shadid, John N., and Miller, Sean.
```*LDRD Report: Topological Design Optimization of Convolutes in Next Generation Pulsed Power Devices.*. United States: N. p., 2017.
Web. doi:10.2172/1413648.

```
Cyr, Eric C., von Winckel, Gregory John, Kouri, Drew Philip, Gardiner, Thomas Anthony, Ridzal, Denis, Shadid, John N., & Miller, Sean.
```*LDRD Report: Topological Design Optimization of Convolutes in Next Generation Pulsed Power Devices.*. United States. doi:10.2172/1413648.

```
Cyr, Eric C., von Winckel, Gregory John, Kouri, Drew Philip, Gardiner, Thomas Anthony, Ridzal, Denis, Shadid, John N., and Miller, Sean. Fri .
"LDRD Report: Topological Design Optimization of Convolutes in Next Generation Pulsed Power Devices.". United States. doi:10.2172/1413648. https://www.osti.gov/servlets/purl/1413648.
```

```
@article{osti_1413648,
```

title = {LDRD Report: Topological Design Optimization of Convolutes in Next Generation Pulsed Power Devices.},

author = {Cyr, Eric C. and von Winckel, Gregory John and Kouri, Drew Philip and Gardiner, Thomas Anthony and Ridzal, Denis and Shadid, John N. and Miller, Sean},

abstractNote = {This LDRD project was developed around the ambitious goal of applying PDE-constrained opti- mization approaches to design Z-machine components whose performance is governed by elec- tromagnetic and plasma models. This report documents the results of this LDRD project. Our differentiating approach was to use topology optimization methods developed for structural design and extend them for application to electromagnetic systems pertinent to the Z-machine. To achieve this objective a suite of optimization algorithms were implemented in the ROL library part of the Trilinos framework. These methods were applied to standalone demonstration problems and the Drekar multi-physics research application. Out of this exploration a new augmented Lagrangian approach to structural design problems was developed. We demonstrate that this approach has favorable mesh-independent performance. Both the final design and the algorithmic performance were independent of the size of the mesh. In addition, topology optimization formulations for the design of conducting networks were developed and demonstrated. Of note, this formulation was used to develop a design for the inner magnetically insulated transmission line on the Z-machine. The resulting electromagnetic device is compared with theoretically postulated designs.},

doi = {10.2172/1413648},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2017},

month = {9}

}