PCPATCH. Software for the topological construction of multigrid relaxation methods. Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß-Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms or saddle point structure. In this article, we present a unifying software abstraction, PCPATCH, for the topological construction of space decompositions for multigrid relaxation methods. Space decompositions are specified by collecting topological entities in a mesh (such as all vertices or faces) and applying a construction rule (such as taking all degrees of freedom in the cells around each entity). The software is implemented in PETSc and facilitates the elegant expression of a wide range of schemes merely by varying solver options at runtime. In turn, this allows for the very rapid development of fast solvers for difficult problems.

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

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  1. Fabien, Maurice; Guzmán, Johnny; Neilan, Michael; Zytoon, Ahmed: Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits (2022)
  2. Farrell, Patrick; Orozco, Pablo Alexei Gazca; Süli, Endre: Finite element approximation and preconditioning for anisothermal flow of implicitly-constituted non-Newtonian fluids (2022)
  3. Adler, James H.; Benson, Thomas R.; Cyr, Eric C.; Farrell, Patrick E.; MacLachlan, Scott P.; Tuminaro, Ray S.: Monolithic multigrid methods for magnetohydrodynamics (2021)
  4. Boon, Wietse M.; Kuchta, Miroslav; Mardal, Kent-Andre; Ruiz-Baier, Ricardo: Robust preconditioners for perturbed saddle-point problems and conservative discretizations of Biot’S equations utilizing total pressure (2021)
  5. Farrell, Patrick E.; Knepley, Matthew G.; Mitchell, Lawrence; Wechsung, Florian: PCPATCH. Software for the topological construction of multigrid relaxation methods (2021)
  6. Farrell, Patrick E.; Mitchell, Lawrence; Scott, L. Ridgway; Wechsung, Florian: A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations (2021)
  7. Kirby, Robert C.; Kernell, Tate: Preconditioning mixed finite elements for tide models (2021)
  8. Xia, Jingmin; Farrell, Patrick E.; Wechsung, Florian: Augmented Lagrangian preconditioners for the Oseen-Frank model of nematic and cholesteric liquid crystals (2021)
  9. Farrell, P. E.; Gazca-Orozco, P. A.: An augmented Lagrangian preconditioner for implicitly constituted non-Newtonian incompressible flow (2020)