PetIGA-MF

PetIGA-MF: a multi-field high-performance toolbox for structure-preserving B-splines 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.


References in zbMATH (referenced in 9 articles , 1 standard article )

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  1. Widlund, O. B.; Zampini, S.; Scacchi, S.; Pavarino, L. F.: Block FETI-DP/BDDC preconditioners for mixed isogeometric discretizations of three-dimensional almost incompressible elasticity (2021)
  2. Eldred, Christopher; Le Roux, Daniel Y.: Dispersion analysis of compatible Galerkin schemes for the 1D shallow water model (2018)
  3. Puzyrev, Vladimir; Deng, Quanling; Calo, Victor: Spectral approximation properties of isogeometric analysis with variable continuity (2018)
  4. A.F. Sarmiento, A.M.A. Cortes, D.A. Garcia, L. Dalcin, N. Collier, V.M. Calo: PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces (2017) not zbMATH
  5. Côrtes, A. M. A.; Dalcin, L.; Sarmiento, A. F.; Collier, N.; Calo, V. M.: A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem (2017)
  6. Espath, L. F. R.; Sarmiento, A. F.; Dalcin, L.; Calo, V. M.: On the thermodynamics of the Swift-Hohenberg theory (2017)
  7. Puzyrev, Vladimir; Deng, Quanling; Calo, Victor: Dispersion-optimized quadrature rules for isogeometric analysis: modified inner products, their dispersion properties, and optimally blended schemes (2017)
  8. Espath, L. F. R.; Sarmiento, A. F.; Vignal, P.; Varga, B. O. N.; Cortes, A. M. A.; Dalcin, L.; Calo, V. M.: Energy exchange analysis in droplet dynamics via the Navier-Stokes-Cahn-Hilliard model (2016)
  9. Vázquez, R.: A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0 (2016)