# Extension of modified power method to two-dimensional problems

## Abstract

In this study, the generalized modified power method was extended to two-dimensional problems. A direct application of the method to two-dimensional problems was shown to be unstable when the number of requested eigenmodes is larger than a certain problem dependent number. The root cause of this instability has been identified as the degeneracy of the transfer matrix. In order to resolve this instability, the number of sub-regions for the transfer matrix was increased to be larger than the number of requested eigenmodes; and a new transfer matrix was introduced accordingly which can be calculated by the least square method. The stability of the new method has been successfully demonstrated with a neutron diffusion eigenvalue problem and the 2D C5G7 benchmark problem. - Graphical abstract:.

- Authors:

- School of Power and Mechanical Engineering, Wuhan University, Bayilu 299, Wuchang Dist., Wuhan, Hubei, 430072 (China)
- (Korea, Republic of)
- Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919 (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 22572344

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 320; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BENCHMARKS; EIGENVALUES; INSTABILITY; LEAST SQUARE FIT; MATRICES; NEUTRON DIFFUSION EQUATION; NEUTRONS; STABILITY; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Zhang, Peng, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Lee, Hyunsuk, and Lee, Deokjung, E-mail: deokjung@unist.ac.kr.
```*Extension of modified power method to two-dimensional problems*. United States: N. p., 2016.
Web. doi:10.1016/J.JCP.2016.05.024.

```
Zhang, Peng, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Lee, Hyunsuk, & Lee, Deokjung, E-mail: deokjung@unist.ac.kr.
```*Extension of modified power method to two-dimensional problems*. United States. doi:10.1016/J.JCP.2016.05.024.

```
Zhang, Peng, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Lee, Hyunsuk, and Lee, Deokjung, E-mail: deokjung@unist.ac.kr. Thu .
"Extension of modified power method to two-dimensional problems". United States.
doi:10.1016/J.JCP.2016.05.024.
```

```
@article{osti_22572344,
```

title = {Extension of modified power method to two-dimensional problems},

author = {Zhang, Peng and Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919 and Lee, Hyunsuk and Lee, Deokjung, E-mail: deokjung@unist.ac.kr},

abstractNote = {In this study, the generalized modified power method was extended to two-dimensional problems. A direct application of the method to two-dimensional problems was shown to be unstable when the number of requested eigenmodes is larger than a certain problem dependent number. The root cause of this instability has been identified as the degeneracy of the transfer matrix. In order to resolve this instability, the number of sub-regions for the transfer matrix was increased to be larger than the number of requested eigenmodes; and a new transfer matrix was introduced accordingly which can be calculated by the least square method. The stability of the new method has been successfully demonstrated with a neutron diffusion eigenvalue problem and the 2D C5G7 benchmark problem. - Graphical abstract:.},

doi = {10.1016/J.JCP.2016.05.024},

journal = {Journal of Computational Physics},

number = ,

volume = 320,

place = {United States},

year = {Thu Sep 01 00:00:00 EDT 2016},

month = {Thu Sep 01 00:00:00 EDT 2016}

}