This article deals with an adaptive-grid finite difference solver for time-dependent two-dimensional systems of partial differential equations. It describes the ANSI Fortran 77 code, VLUGR2, autovectorizable on the Cray Y-MP, that is based on this method. The robustness and the efficiency of the solver, both for vector and scalar processors, are illustrated by the application of the code to two example problems arising from a groundwater-flow model. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Moyles, I.; Tse, W. H.; Ward, M. J.: Explicitly solvable nonlocal eigenvalue problems and the stability of localized stripes in reaction-diffusion systems (2016)
  2. Rasheed, A.; Belmiloudi, A.: An analysis of a phase-field model for isothermal binary alloy solidification with convection under the influence of magnetic field (2012)
  3. Chen, W.; Ward, M. J.: The stability and dynamics of localized spot patterns in the two-dimensional Gray-Scott model (2011)
  4. Fazio, Riccardo; Jannelli, Alessandra: Second order positive schemes by means of flux limiters for the advection equation (2009)
  5. Kolokolnikov, T.; Ward, M. J.; Wei, J.: Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain (2009)
  6. Kolokolnikov, T.; Ward, M. J.; Wei, J.: Zigzag and breakup instabilities of stripes and rings in the two-dimensional Gray-Scott model (2006)
  7. Montijn, C.; Hundsdorfer, W.; Ebert, U.: An adaptive grid refinement strategy for the simulation of negative streamers (2006)
  8. Pernice, Michael; Philip, Bobby: Solution of equilibrium radiation diffusion problems using implicit adaptive mesh refinement (2006)
  9. Magar, Vanesa; Pedley, T. J.: Average nutrient uptake by a self-propelled unsteady squirmer (2005)
  10. Morgan, David S.; Kaper, Tasso J.: Axisymmetric ring solutions of the 2D Gray-Scott model and their destabilization into spots (2004)
  11. Zegeling, P. A.: Tensor-product adaptive grids based on coordinate transformations. (2004)
  12. Balmforth, N. J.; Craster, R. V.; Sassi, R.: Shallow viscoplastic flow on an inclined plane (2002)
  13. Warner, M. R. E.; Craster, R. V.; Matar, O. K.: Unstable Van der waals driven line rupture in marangoni driven thin viscous films (2002)
  14. Trefry, M. G.; Öhman, J.; Davis, G. B.: A simple numerical approach for assessing coupled transport processes in partitioning systems (2001)
  15. de Sturler, Eric: Truncation strategies for optimal Krylov subspace methods (1998)
  16. Blom, J. G.; Trompert, R. A.; Verwer, J. G.: Algorithm 758. VLUGR2: a vectorizable adaptive-grid solver for PDEs in 2D. (1996) ioport
  17. Blom, J. G.; Trompert, R. A.; Verwer, J. G.: Algorithm 758: VLUGR2: A vectorizable adaptive-grid solver for PDEs in 2D (1996)