# PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces

## Abstract

We describe the development of a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, PetIGA-MF is a general multi-field discretization tool. To test the capabilities of our implementation, we solve different viscous flow problems such as Darcy, Stokes, Brinkman, and Navier-Stokes equations. Several convergence benchmarks based on manufactured solutions are presented assuring optimal convergence rates of the approximations, showing the accuracy and robustness of our solver.

- Authors:

- King Abdullah Univ. of Science and Technology (KAUST), Thuwal, (Saudi Arabia)
- Federal Univ. of the State of Rio de Janeiro (Brazil)
- Basque Center for Applied Mathematics, Bilbao (Spain)
- King Abdullah Univ. of Science and Technology (KAUST), Thuwal, (Saudi Arabia); Univ. Nacional del Litoral, Santa Fe (Argentina)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Curtin Univ., Perth, WA (Australia); Commonwealth Scientific and Industrial Research Organization (CSIRO), Kensington WA (Australia)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1429197

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Science

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: C; Journal ID: ISSN 1877-7503

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; isogeometric analysis; discrete differential forms; structure-preserving discrete spaces; multi-field discretizations; PetIGA; high-performance computing

### Citation Formats

```
Sarmiento, Adel, Cortes, Adriano, Garcia, Daniel, Dalcin, Lisandro, Collier, Nathaniel O., and Calo, Victor. PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces. United States: N. p., 2016.
Web. doi:10.1016/j.jocs.2016.09.010.
```

```
Sarmiento, Adel, Cortes, Adriano, Garcia, Daniel, Dalcin, Lisandro, Collier, Nathaniel O., & Calo, Victor. PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces. United States. doi:10.1016/j.jocs.2016.09.010.
```

```
Sarmiento, Adel, Cortes, Adriano, Garcia, Daniel, Dalcin, Lisandro, Collier, Nathaniel O., and Calo, Victor. Fri .
"PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces". United States. doi:10.1016/j.jocs.2016.09.010. https://www.osti.gov/servlets/purl/1429197.
```

```
@article{osti_1429197,
```

title = {PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces},

author = {Sarmiento, Adel and Cortes, Adriano and Garcia, Daniel and Dalcin, Lisandro and Collier, Nathaniel O. and Calo, Victor},

abstractNote = {We describe the development of a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, PetIGA-MF is a general multi-field discretization tool. To test the capabilities of our implementation, we solve different viscous flow problems such as Darcy, Stokes, Brinkman, and Navier-Stokes equations. Several convergence benchmarks based on manufactured solutions are presented assuring optimal convergence rates of the approximations, showing the accuracy and robustness of our solver.},

doi = {10.1016/j.jocs.2016.09.010},

journal = {Journal of Computational Science},

number = C,

volume = 18,

place = {United States},

year = {2016},

month = {10}

}

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Cited by: 15 works

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