# Incremental Volumetric Remapping Method: Analysis and Error Evaluation

## Abstract

In this paper the error associated with the remapping problem is analyzed. A range of numerical results that assess the performance of three different remapping strategies, applied to FE meshes that typically are used in sheet metal forming simulation, are evaluated. One of the selected strategies is the previously presented Incremental Volumetric Remapping method (IVR), which was implemented in the in-house code DD3TRIM. The IVR method fundaments consists on the premise that state variables in all points associated to a Gauss volume of a given element are equal to the state variable quantities placed in the correspondent Gauss point. Hence, given a typical remapping procedure between a donor and a target mesh, the variables to be associated to a target Gauss volume (and point) are determined by a weighted average. The weight function is the Gauss volume percentage of each donor element that is located inside the target Gauss volume. The calculus of the intersecting volumes between the donor and target Gauss volumes is attained incrementally, for each target Gauss volume, by means of a discrete approach. The other two remapping strategies selected are based in the interpolation/extrapolation of variables by using the finite element shape functions or moving leastmore »

- Authors:

- CEMUC, Department of Mechanical Engineering, University of Coimbra, Polo II, Rua Luis Reis Santos, Pinhal de Marrocos, 3030-788 Coimbra (Portugal)
- Department of Mechanical Engineering, University of Minho, Campus de Azurem, 4800-058 Guimaraes (Portugal)

- Publication Date:

- OSTI Identifier:
- 21061765

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 908; Journal Issue: 1; Conference: NUMIFORM 2007: 9. international conference on numerical methods in industrial forming processes, Porto (Portugal), 17-21 Jun 2007; Other Information: DOI: 10.1063/1.2740914; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALLOYS; COMPUTERIZED SIMULATION; D CODES; ERRORS; EVALUATION; EXTRAPOLATION; FINITE ELEMENT METHOD; INTERPOLATION; LEAST SQUARE FIT; MESH GENERATION; METALS; PERFORMANCE; SHEETS; WEIGHTING FUNCTIONS

### Citation Formats

```
Baptista, A. J., Oliveira, M. C., Rodrigues, D. M., Menezes, L. F., and Alves, J. L.
```*Incremental Volumetric Remapping Method: Analysis and Error Evaluation*. United States: N. p., 2007.
Web. doi:10.1063/1.2740914.

```
Baptista, A. J., Oliveira, M. C., Rodrigues, D. M., Menezes, L. F., & Alves, J. L.
```*Incremental Volumetric Remapping Method: Analysis and Error Evaluation*. United States. doi:10.1063/1.2740914.

```
Baptista, A. J., Oliveira, M. C., Rodrigues, D. M., Menezes, L. F., and Alves, J. L. Thu .
"Incremental Volumetric Remapping Method: Analysis and Error Evaluation". United States.
doi:10.1063/1.2740914.
```

```
@article{osti_21061765,
```

title = {Incremental Volumetric Remapping Method: Analysis and Error Evaluation},

author = {Baptista, A. J. and Oliveira, M. C. and Rodrigues, D. M. and Menezes, L. F. and Alves, J. L.},

abstractNote = {In this paper the error associated with the remapping problem is analyzed. A range of numerical results that assess the performance of three different remapping strategies, applied to FE meshes that typically are used in sheet metal forming simulation, are evaluated. One of the selected strategies is the previously presented Incremental Volumetric Remapping method (IVR), which was implemented in the in-house code DD3TRIM. The IVR method fundaments consists on the premise that state variables in all points associated to a Gauss volume of a given element are equal to the state variable quantities placed in the correspondent Gauss point. Hence, given a typical remapping procedure between a donor and a target mesh, the variables to be associated to a target Gauss volume (and point) are determined by a weighted average. The weight function is the Gauss volume percentage of each donor element that is located inside the target Gauss volume. The calculus of the intersecting volumes between the donor and target Gauss volumes is attained incrementally, for each target Gauss volume, by means of a discrete approach. The other two remapping strategies selected are based in the interpolation/extrapolation of variables by using the finite element shape functions or moving least square interpolants. The performance of the three different remapping strategies is address with two tests. The first remapping test was taken from a literature work. The test consists in remapping successively a rotating symmetrical mesh, throughout N increments, in an angular span of 90 deg. The second remapping error evaluation test consists of remapping an irregular element shape target mesh from a given regular element shape donor mesh and proceed with the inverse operation. In this second test the computation effort is also measured. The results showed that the error level associated to IVR can be very low and with a stable evolution along the number of remapping procedures when compared with the other two methods. Besides, the method proved to be very robust even in critical remapping situations such as poor geometrical definition of the mesh domain boundaries.},

doi = {10.1063/1.2740914},

journal = {AIP Conference Proceedings},

number = 1,

volume = 908,

place = {United States},

year = {Thu May 17 00:00:00 EDT 2007},

month = {Thu May 17 00:00:00 EDT 2007}

}