# Advantages of Analytical Transformations in Monte Carlo Methods for Radiation Transport

## Abstract

Monte Carlo methods for radiation transport typically attempt to solve an integral by directly sampling analog or weighted particles, which are treated as physical entities. Improvements to the methods involve better sampling, probability games or physical intuition about the problem. We show that significant improvements can be achieved by recasting the equations with an analytical transform to solve for new, non-physical entities or fields. This paper looks at one such transform, the difference formulation for thermal photon transport, showing a significant advantage for Monte Carlo solution of the equations for time dependent transport. Other related areas are discussed that may also realize significant benefits from similar analytical transformations.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab., Livermore, CA (US)

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

- OSTI Identifier:
- 15015946

- Report Number(s):
- UCRL-CONF-208593

TRN: US0501674

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Conference

- Resource Relation:
- Conference: Presented at: The Monte Carlo Method: Versatility Unbounded In A Dynamic Computing World, Chattanooga, TN (US), 04/17/2005--04/21/2005; Other Information: PBD: 13 Dec 2004

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; MONTE CARLO METHOD; PHOTON TRANSPORT; PROBABILITY; RADIATION TRANSPORT; SAMPLING; TRANSFORMATIONS; TRANSPORT

### Citation Formats

```
McKinley, M S, Brooks, III, E D, and Daffin, F.
```*Advantages of Analytical Transformations in Monte Carlo Methods for Radiation Transport*. United States: N. p., 2004.
Web.

```
McKinley, M S, Brooks, III, E D, & Daffin, F.
```*Advantages of Analytical Transformations in Monte Carlo Methods for Radiation Transport*. United States.

```
McKinley, M S, Brooks, III, E D, and Daffin, F. Mon .
"Advantages of Analytical Transformations in Monte Carlo Methods for Radiation Transport". United States. https://www.osti.gov/servlets/purl/15015946.
```

```
@article{osti_15015946,
```

title = {Advantages of Analytical Transformations in Monte Carlo Methods for Radiation Transport},

author = {McKinley, M S and Brooks, III, E D and Daffin, F},

abstractNote = {Monte Carlo methods for radiation transport typically attempt to solve an integral by directly sampling analog or weighted particles, which are treated as physical entities. Improvements to the methods involve better sampling, probability games or physical intuition about the problem. We show that significant improvements can be achieved by recasting the equations with an analytical transform to solve for new, non-physical entities or fields. This paper looks at one such transform, the difference formulation for thermal photon transport, showing a significant advantage for Monte Carlo solution of the equations for time dependent transport. Other related areas are discussed that may also realize significant benefits from similar analytical transformations.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2004},

month = {12}

}