# A geometric multigrid preconditioning strategy for DPG system matrices

## Abstract

Here, the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan (2010, 2011) guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has not yet been answered in general – though there are some results for Poisson, e.g.– is how best to precondition the DPG system matrix, so that iterative solvers may be used to allow solution of large-scale problems.

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Rice Univ., Houston, TX (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); Argonne National Laboratory - Argonne Leadership Computing Facility

- OSTI Identifier:
- 1399559

- Alternate Identifier(s):
- OSTI ID: 1429686

- Report Number(s):
- SAND-2017-7727J

Journal ID: ISSN 0898-1221; PII: S0898122117304133

- Grant/Contract Number:
- AC04-94AL85000; AC02-06CH11357; NA0003525

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Computers and Mathematics with Applications (Oxford)

- Additional Journal Information:
- Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 74; Journal Issue: 8; Journal ID: ISSN 0898-1221

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Discontinuous Petrov–Galerkin; Adaptive finite elements; Iterative solvers; Geometric multigrid; Discontinuous Petrov Galerkin; adaptive finite elements; geometric multigrid; iterative solvers

### Citation Formats

```
Roberts, Nathan V., and Chan, Jesse.
```*A geometric multigrid preconditioning strategy for DPG system matrices*. United States: N. p., 2017.
Web. doi:10.1016/j.camwa.2017.06.055.

```
Roberts, Nathan V., & Chan, Jesse.
```*A geometric multigrid preconditioning strategy for DPG system matrices*. United States. doi:10.1016/j.camwa.2017.06.055.

```
Roberts, Nathan V., and Chan, Jesse. Wed .
"A geometric multigrid preconditioning strategy for DPG system matrices". United States.
doi:10.1016/j.camwa.2017.06.055.
```

```
@article{osti_1399559,
```

title = {A geometric multigrid preconditioning strategy for DPG system matrices},

author = {Roberts, Nathan V. and Chan, Jesse},

abstractNote = {Here, the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan (2010, 2011) guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has not yet been answered in general – though there are some results for Poisson, e.g.– is how best to precondition the DPG system matrix, so that iterative solvers may be used to allow solution of large-scale problems.},

doi = {10.1016/j.camwa.2017.06.055},

journal = {Computers and Mathematics with Applications (Oxford)},

number = 8,

volume = 74,

place = {United States},

year = {Wed Aug 23 00:00:00 EDT 2017},

month = {Wed Aug 23 00:00:00 EDT 2017}

}

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