# Novel Parallel Numerical Methods for Radiation& Neutron Transport

## Abstract

In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation tomore »

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 15005562

- Report Number(s):
- UCRL-ID-142830

TRN: US0305546

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

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 6 Mar 2001

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; BOLTZMANN EQUATION; DIFFUSION; IMPLEMENTATION; ION TEMPERATURE; ITERATIVE METHODS; LTE; MONTE CARLO METHOD; NEUTRON TRANSPORT; NEUTRONS; PHOTONS; SIMULATION; TRANSPORT

### Citation Formats

```
Brown, P N.
```*Novel Parallel Numerical Methods for Radiation& Neutron Transport*. United States: N. p., 2001.
Web. doi:10.2172/15005562.

```
Brown, P N.
```*Novel Parallel Numerical Methods for Radiation& Neutron Transport*. United States. doi:10.2172/15005562.

```
Brown, P N. Tue .
"Novel Parallel Numerical Methods for Radiation& Neutron Transport". United States. doi:10.2172/15005562. https://www.osti.gov/servlets/purl/15005562.
```

```
@article{osti_15005562,
```

title = {Novel Parallel Numerical Methods for Radiation& Neutron Transport},

author = {Brown, P N},

abstractNote = {In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both.},

doi = {10.2172/15005562},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2001},

month = {3}

}