# Efficient solutions to the NDA-NCA low-order eigenvalue problem

## Abstract

Recent algorithmic advances combine moment-based acceleration and Jacobian-Free Newton-Krylov (JFNK) methods to accelerate the computation of the dominant eigenvalue in a k-eigenvalue calculation. In particular, NDA-NCA [1], builds a sequence of low-order (LO) diffusion-based eigenvalue problems in which the solution converges to the true eigenvalue solution. Within NDA-NCA, the solution to the LO k-eigenvalue problem is computed by solving a system of nonlinear equation using some variant of Newton's method. We show that we can speed up the solution to the LO problem dramatically by abandoning the JFNK method and exploiting the structure of the Jacobian matrix. (authors)

- Authors:

- North Carolina State University, Raleigh, NC 27606 (United States)
- Department of Mathematics, North Carolina State University, Raleigh, NC 27606 (United States)

- Publication Date:

- Research Org.:
- American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)

- OSTI Identifier:
- 22212911

- Resource Type:
- Conference

- Resource Relation:
- Conference: M and C 2013: 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Sun Valley, ID (United States), 5-9 May 2013; Other Information: Country of input: France; 8 refs.; Related Information: In: Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M and C 2013| 3016 p.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ACCELERATION; EIGENFUNCTIONS; EIGENVALUES; EQUATIONS; MATHEMATICAL SOLUTIONS; MATRICES; NEWTON METHOD; NONLINEAR PROBLEMS; VELOCITY

### Citation Formats

```
Willert, J. A., and Kelley, C. T.
```*Efficient solutions to the NDA-NCA low-order eigenvalue problem*. United States: N. p., 2013.
Web.

```
Willert, J. A., & Kelley, C. T.
```*Efficient solutions to the NDA-NCA low-order eigenvalue problem*. United States.

```
Willert, J. A., and Kelley, C. T. Mon .
"Efficient solutions to the NDA-NCA low-order eigenvalue problem". United States.
```

```
@article{osti_22212911,
```

title = {Efficient solutions to the NDA-NCA low-order eigenvalue problem},

author = {Willert, J. A. and Kelley, C. T.},

abstractNote = {Recent algorithmic advances combine moment-based acceleration and Jacobian-Free Newton-Krylov (JFNK) methods to accelerate the computation of the dominant eigenvalue in a k-eigenvalue calculation. In particular, NDA-NCA [1], builds a sequence of low-order (LO) diffusion-based eigenvalue problems in which the solution converges to the true eigenvalue solution. Within NDA-NCA, the solution to the LO k-eigenvalue problem is computed by solving a system of nonlinear equation using some variant of Newton's method. We show that we can speed up the solution to the LO problem dramatically by abandoning the JFNK method and exploiting the structure of the Jacobian matrix. (authors)},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2013},

month = {7}

}

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