# A Method for Treating Discretization Error in Nondeterministic Analysis

## Abstract

A response surface methodology-based technique is presented for treating discretization error in non-deterministic analysis. The response surface, or metamodel, is estimated from computer experiments which vary both uncertain physical parameters and the fidelity of the computational mesh. The resultant metamodel is then used to propagate the variabilities in the continuous input parameters, while the mesh size is taken to zero, its asymptotic limit. With respect to mesh size, the metamodel is equivalent to Richardson extrapolation, in which solutions on coarser and finer meshes are used to estimate discretization error. The method is demonstrated on a one dimensional prismatic bar, in which uncertainty in the third vibration frequency is estimated by propagating variations in material modulus, density, and bar length. The results demonstrate the efficiency of the method for combining non-deterministic analysis with error estimation to obtain estimates of total simulation uncertainty. The results also show the relative sensitivity of failure estimates to solution bias errors in a reliability analysis, particularly when the physical variability of the system is low.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Laboratories, Albuquerque, NM, and Livermore, CA

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 3300

- Report Number(s):
- SAND99-0224C

ON: DE00003300

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Conference

- Resource Relation:
- Conference: 1999 AIAA/ASME Forum on Non-Deferministic Appoaches; St.Louis, MO; 04/12-15/1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; Algorithms; Mathematical Models; Differential Equations

### Citation Formats

```
Alvin, K.F.
```*A Method for Treating Discretization Error in Nondeterministic Analysis*. United States: N. p., 1999.
Web.

```
Alvin, K.F.
```*A Method for Treating Discretization Error in Nondeterministic Analysis*. United States.

```
Alvin, K.F. Wed .
"A Method for Treating Discretization Error in Nondeterministic Analysis". United States. https://www.osti.gov/servlets/purl/3300.
```

```
@article{osti_3300,
```

title = {A Method for Treating Discretization Error in Nondeterministic Analysis},

author = {Alvin, K.F.},

abstractNote = {A response surface methodology-based technique is presented for treating discretization error in non-deterministic analysis. The response surface, or metamodel, is estimated from computer experiments which vary both uncertain physical parameters and the fidelity of the computational mesh. The resultant metamodel is then used to propagate the variabilities in the continuous input parameters, while the mesh size is taken to zero, its asymptotic limit. With respect to mesh size, the metamodel is equivalent to Richardson extrapolation, in which solutions on coarser and finer meshes are used to estimate discretization error. The method is demonstrated on a one dimensional prismatic bar, in which uncertainty in the third vibration frequency is estimated by propagating variations in material modulus, density, and bar length. The results demonstrate the efficiency of the method for combining non-deterministic analysis with error estimation to obtain estimates of total simulation uncertainty. The results also show the relative sensitivity of failure estimates to solution bias errors in a reliability analysis, particularly when the physical variability of the system is low.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {1}

}