Components

AMGCL provides the following components:

• Backends – classes that define matrix and vector types and operations necessary during the solution phase of the algorithm. When an AMG hierarchy is constructed, it is moved to the specified backend. The approach enables transparent acceleration of the solution phase with OpenMP, OpenCL, or CUDA technologies, and also makes tight integration with user-defined data structures possible.
• Value types – enable transparent solution of complex or non-scalar systems. Most often, a value type is simply a double, but it is possible to use small statically-sized matrices as value type, which may increase cache-locality, or convergence ratio, or both, when the system matrix has a block structure.
• Matrix adapters – allow AMGCL to construct a solver from some common matrix formats. Internally, the CRS format is used, but it is easy to adapt any matrix format that allows row-wise iteration over its non-zero elements.
• Coarsening strategies – various options for creating coarse systems in the AMG hierarchy. A coarsening strategy takes the system matrix \(A\) at the current level, and returns prolongation operator \(P\) and the corresponding restriction operator \(R\).
• Relaxation methods – or smoothers, that are used on each level of the AMG hierarchy during solution phase.
• Preconditioners – aside from the AMG, AMGCL implements preconditioners for some common problem types. For example, there is a Schur complement pressure correction preconditioner for Navie-Stokes type problems, or CPR preconditioner for reservoir simulations. Also, it is possible to use single level relaxation method as a preconditioner.
• Iterative solvers – Krylov subspace methods that may be combined with the AMG (or other) preconditioners in order to solve the linear system.