# Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation

## Abstract

Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF.

- Authors:

- Publication Date:

- Research Org.:
- Idaho National Laboratory (INL)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1120821

- Report Number(s):
- INL/JOU-14-31308

Journal ID: ISSN 0029-5639

- DOE Contract Number:
- DE-AC07-05ID14517

- Resource Type:
- Journal Article

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 175; Journal Issue: 3; Journal ID: ISSN 0029-5639

- Publisher:
- American Nuclear Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS; angular flux form

### Citation Formats

```
Sanchez, Richard, Rabiti, Cristian, and Wang, Yaqi.
```*Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation*. United States: N. p., 2012.
Web. doi:10.13182/NSE12-50.

```
Sanchez, Richard, Rabiti, Cristian, & Wang, Yaqi.
```*Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation*. United States. doi:10.13182/NSE12-50.

```
Sanchez, Richard, Rabiti, Cristian, and Wang, Yaqi. Thu .
"Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation". United States. doi:10.13182/NSE12-50.
```

```
@article{osti_1120821,
```

title = {Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation},

author = {Sanchez, Richard and Rabiti, Cristian and Wang, Yaqi},

abstractNote = {Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF.},

doi = {10.13182/NSE12-50},

journal = {Nuclear Science and Engineering},

issn = {0029-5639},

number = 3,

volume = 175,

place = {United States},

year = {2012},

month = {11}

}

DOI: 10.13182/NSE12-50

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