Trilinos is a community-developed, open-source software framework that facilitates building large-scale, complex, multiscale, multiphysics simulation code bases for scientific and engineering problems. Since the Trilinos framework has undergone substantial changes to support new applications and new hardware architectures, this document is an update to “An Overview of the Trilinos project” by Heroux et al. (ACM Transactions on Mathematical Software, 31(3):397–423, 2005). It describes the design of Trilinos, introduces its new organization in product areas, and highlights established and new features available in Trilinos. Particular focus is put on the modernized software stack based on the Kokkos ecosystem to deliver performance portability across heterogeneous hardware architectures. This article also outlines the organization of the Trilinos community and the contribution model to help onboard interested users and contributors.

The Trilinos Project is an effort to facilitate the design, development, integration, and ongoing support of mathematical software libraries within an object-oriented framework for the solution of large-scale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundamental issues of developing software for these problems: (i) providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software.Trilinos uses a two-level software structure designed around collections of packages . A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common look-and-feel, including configuration, documentation, licensing, and bug-tracking.Here we present the overall Trilinos design, describing our use of abstract interfaces and default concrete implementations. We discuss the services that Trilinos provides to a prospective package and how these services are used by various packages. We also illustrate how packages can be combined to rapidly develop new algorithms. Finally, we discuss how Trilinos facilitates high-quality software engineering practices that are increasingly required from simulation software.

Algebraic multigrid methods offer the hope that multigrid convergence can be achieve (for at least some important applications) without a great deal of effort from engineers an scientists wishing to solve linear systems. In this paper we consider parallelization of the smoothe aggregation multigrid methods. Smoothed aggregation is one of the most promising algebraic multigrid methods. Therefore, eveloping parallel variants with both good convergence an efficiency properties is of great importance. However, parallelization is nontrivial due to the somewhat sequential aggregation (or grid coarsening) phase. In this paper, we discuss three different parallel aggregation algorithms an illustrate the advantages an disadvantages of each variant in terms of parallelism an convergence. Numerical results will be shown on the Intel Teraflop computer for some large problems coming from nontrivial codes: quasi-static electric potential simulation an a fluid flow calculation.

In this paper we describe general software utilities for performing unstructured sparse matrix–vector multiplications on distributed-memory message-passing computers. The matrix–vector multiply comprises an important kernel in the solution of large sparse linear systems by iterative methods. Our focus is to present the data structures and communication parameters required by these utilities for general sparse unstructured matrices with data locality. These types of matrices are commonly produced by finite difference and finite element approximations to systems of partial differential equations. In this discussion we also present representative examples and timings which demonstrate the utility and performance of the software. © 1998 John Wiley & Sons, Ltd.

Abstract The parallelization of sophisticated applications has dramatically increased in recent years. As machine capabilities rise, greater emphasis on modeling complex phenomena can be expected. Many of these applications require the solution of large sparse matrix equations which approximate systems of partial differential equations (PDEs). Therefore we consider parallel iterative solvers for large sparse non‐symmetric systems and issues related to parallel sparse matrix software. We describe a collection of parallel iterative solvers which use a distributed sparse matrix format that facilitates the interface between specific applications and a variety of Krylov subspace techniques and multigrid methods. These methods have been used to solve a number of linear and non‐linear PDE problems on a 1024‐processor NCUBE 2 hypercube. Over 1 Gflop sustained computation rates are achieved with many of these solvers, demonstrating that high performance can be attained even when using sparse matrix data structures.