Iterative solution with AGgregation-based algebraic MultiGrid. AGMG implements an aggregation-based algebraic multigrid method. This method solves algebraic systems of linear equations, and is expected to be efficient for large systems arising from the discretization of scalar second order elliptic PDEs. The method is however purely algebraic and may be tested on any problem. No information has to be supplied besides the system matrix and the right-hand-side. AGMG comes either as a function that may be called from Matlab environment, or as a Fortran 90 subroutine that may be linked with an application program. Both versions have been designed to be easy to use by non experts (in a black box fashion). The Matlab version accepts real and complex matrices, whereas the Fortran version is available in the four standard arithmetics (real, double precision, complex, double complex). A Fortran 90 parallel implementation is also provided.

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  1. Axelsson, Owe: A survey of optimal control problems for PDEs (2021)
  2. Axelsson, Owe; Liang, Zhao-Zheng; Kruzik, Jakub; Horak, David: Inner product free iterative solution and elimination methods for linear systems of a three-by-three block matrix form (2021)
  3. Ku, JaEun; Reichel, Lothar: A novel iterative method for discrete Helmholtz decomposition (2020)
  4. Liang, Zhao-Zheng; Axelsson, Owe; Zhang, Guo-Feng: Efficient iterative solvers for a complex valued two-by-two block linear system with application to parabolic optimal control problems (2020)
  5. Adrian, S. B.; Andriulli, F. P.; Eibert, T. F.: On a refinement-free Calderón multiplicative preconditioner for the electric field integral equation (2019)
  6. Axelsson, Owe; Liang, Zhao-Zheng: A note on preconditioning methods for time-periodic eddy current optimal control problems (2019)
  7. D’Ambra, Pasqua; Vassilevski, Panayot S.: Improving solve time of aggregation-based adaptive AMG. (2019)
  8. Liang, Zhao-Zheng; Zhang, Guo-Feng: Robust additive block triangular preconditioners for block two-by-two linear systems (2019)
  9. Notay, Yvan: Convergence of some iterative methods for symmetric saddle point linear systems (2019)
  10. Perrussel, Artem Napov Ronan: Revisiting aggregation-based multigrid for edge elements (2019)
  11. Ku, Jaeun; Reichel, Lothar: Simple efficient solvers for certain ill-conditioned systems of linear equations, including (H(\operatornamediv)) problems (2018)
  12. McDonald, Eleanor; Pestana, Jennifer; Wathen, Andy: Preconditioning and iterative solution of all-at-once systems for evolutionary partial differential equations (2018)
  13. Adrian, S. B.; Andriulli, F. P.; Eibert, T. F.: A hierarchical preconditioner for the electric field integral equation on unstructured meshes based on primal and dual Haar bases (2017)
  14. Donatelli, Marco; Dorostkar, Ali; Mazza, Mariarosa; Neytcheva, Maya; Serra-Capizzano, Stefano: Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem (2017)
  15. Pearson, John W.; Gondzio, Jacek: Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization (2017)
  16. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)
  17. Napov, Artem; Notay, Yvan: An efficient multigrid method for graph Laplacian systems (2016)
  18. Notay, Yvan: A new algebraic multigrid approach for Stokes problems (2016)
  19. Palitta, Davide; Simoncini, Valeria: Matrix-equation-based strategies for convection-diffusion equations (2016)
  20. Pearson, John W.: Fast iterative solvers for large matrix systems arising from time-dependent Stokes control problems (2016)

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