AMGCL documentation

AMGCL is a header-only C++ library for solving large sparse linear systems with algebraic multigrid (AMG) method. AMG is one of the most effective iterative methods for solution of equation systems arising, for example, from discretizing PDEs on unstructured grids [BrMH85], [Stue99], [TrOS01]. The method can be used as a black-box solver for various computational problems, since it does not require any information about the underlying geometry. AMG is often used not as a standalone solver but as a preconditioner within an iterative solver (e.g. Conjugate Gradients, BiCGStab, or GMRES).

The library has minimal dependencies, and provides both shared-memory and distributed memory (MPI) versions of the algorithms. The AMG hierarchy is constructed on a CPU and then is transferred into one of the provided backends. This allows for transparent acceleration of the solution phase with help of OpenCL, CUDA, or OpenMP technologies. Users may provide their own backends which enables tight integration between AMGCL and the user code.

The source code is available under liberal MIT license at


[Demi19]Demidov, Denis. AMGCL: An efficient, flexible, and extensible algebraic multigrid implementation. Lobachevskii Journal of Mathematics 40.5 (2019): 535-546. pdf, bib
[Demi20]Demidov, Denis. AMGCL – A C++ library for efficient solution of large sparse linear systems. Software Impacts, 6:100037, November 2020. bib
[DeMW20]Demidov, Denis, Lin Mu, and Bin Wang. Accelerating linear solvers for Stokes problems with C++ metaprogramming. Journal of Computational Science (2020): 101285. arxiv, bib