Fast Auxiliary Space Preconditioning 2.7.7 Aug/28/2022

Over the last few decades, researchers have expended significant effort on developing efficient iterative methods for solving discretized partial differential equations (PDEs). Though these efforts have yielded many mathematically optimal solvers such as the multigrid method, the unfortunate reality is that multigrid methods have not been much used in practical applications. This marked gap between theory and practice is mainly due to the fragility of traditional multigrid (MG) methodology and the complexity of its implementation. We aim to develop techniques and the corresponding software that will narrow this gap, specifically by developing mathematically optimal solvers that are robust and easy to use in practice.

We believe that there is no one-size-for-all solution method for discrete linear systemsfrom different applications. And, efficient iterative solvers can be constructed by taking the properties of PDEs and discretizations into account. In this project, we plan to construct a pool of discrete problems arising from partial differential equations (PDEs) or PDE systems and efficient linear solvers for these problems. We mainly utilize the methodology of Auxiliary Space Preconditioning (ASP) to construct efficient linear solvers. Due to this reason, this software package is called Fast Auxiliary Space Preconditioning or FASP for short.

The levels of abstraction are designed as follows:

  • Level 0 (Aux*.c): Auxiliary functions (timing, memory, threading, ...)
  • Level 1 (Bla*.c): Basic linear algebra subroutines (SpMV, RAP, ILU, SWZ, ...)
  • Level 2 (Itr*.c): Iterative methods and smoothers (Jacobi, GS, SOR, Poly, ...)
  • Level 3 (Kry*.c): Krylov iterative methods (CG, BiCGstab, MinRes, GMRES, ...)
  • Level 4 (Pre*.c): Preconditioners (GMG, AMG, FAMG, ...)
  • Level 5 (Sol*.c): User interface for FASP solvers (Solvers, wrappers, ...)
  • Level x (Xtr*.c): Interface to external packages (Mumps, Umfpack, ...)

FASP contains the kernel part and several applications (ranging from fluid dynamics
to reservoir simulation). The kernel part is open-source and licensed under GNU Lesser General Public License or LGPL version 3.0 or later. Some of the applications contain contributions from and owned partially by other parties.

For the moment, FASP is under alpha testing. If you wish to obtain a current version of FASP or you have any questions, feel free to contact us at

This software distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.