Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

Abstract

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

<i>Albany/FELIX</i>: a parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

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Block Iterative Methods and Recycling for Improved Scalability of Linear Solvers

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A Numerical Soft Fault Model for Iterative Linear Solvers

“…We implemented our solvers using the Tpetra [1] sparse linear algebra package in the Trilinos framework [7] and validated them against both MATLAB and the solvers in Trilinos' Belos package [2]. Implementing our solvers using Trilinos lets us benefit from the scalability and performance of its sparse matrices and dense vectors.…”