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

- PetIGA-MF is a framework that uses discrete differential forms based on B-splines.
- We solve viscous flows such as Darcy, Stokes, Brinkman, and Navier-Stokes equations.
- Several convergence benchmarks show an exact agreement with a priori error estimates.
- Benchmark tests show no superconvergence for pressure when using distorted meshes.
- Promising results for reduced quadrature schemes on divergence conforming spaces.

We describe a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, an open-source library we have built and developed over the last decade, 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.