XAMG: A library for solving linear systems with multiple right-hand side vectors
| Autor: | Alexey V. Medvedev, Boris I. Krasnopolsky |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Algebraic multigrid method
FOS: Computer and information sciences Speedup Discretization Iterative method Computer science MathematicsofComputing_NUMERICALANALYSIS Parallel computing 01 natural sciences Multiple right-hand sides 03 medical and health sciences QA76.75-76.765 Multigrid method Krylov subspace iterative methods 0103 physical sciences FOS: Mathematics Computer software Mathematics - Numerical Analysis 010306 general physics 030304 developmental biology 0303 health sciences Numerical analysis Linear system Krylov subspace Numerical Analysis (math.NA) Computer Science::Numerical Analysis Computer Science Applications MPI+POSIX shared memory Hybrid programming model Shared memory Systems of linear algebraic equations Computer Science - Distributed Parallel and Cluster Computing Computer Science - Mathematical Software Distributed Parallel and Cluster Computing (cs.DC) Mathematical Software (cs.MS) Software |
| Zdroj: | SoftwareX, Vol 14, Iss, Pp 100695-(2021) |
| Popis: | This paper presents the XAMG library for solving large sparse systems of linear algebraic equations with multiple right-hand side vectors. The library specializes, but is not limited, to the solution of linear systems obtained from the discretization of elliptic differential equations. A corresponding set of numerical methods includes Krylov subspace, algebraic multigrid, Jacobi, Gauss–Seidel, and Chebyshev iterative methods. The parallelization is implemented with MPI+POSIX shared memory hybrid programming model, which introduces a three-level hierarchical decomposition using the corresponding per-level synchronization and communication primitives. The code contains a number of optimizations, including the multilevel data segmentation, compression of indices, mixed-precision floating-point calculations, vector status flags, and others. The XAMG library uses the program code of the well-known hypre library to construct the multigrid matrix hierarchy. The XAMG’s own implementation for the solve phase of the iterative methods provides up to a twofold speedup compared to hypre for the tests performed. Additionally, XAMG provides extended functionality to solve systems with multiple right-hand side vectors. |
| Databáze: | OpenAIRE |
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