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.

Many applications, such as PDE based simulations and machine learning, apply blas/lapack routines to large groups of small matrices. While existing batched blas APIs provide meaningful speedup for this problem type, a non-canonical data layout enabling cross-matrix vectorization may provide further significant speedup. In this paper, we propose a new compact data layout that interleaves matrices in blocks according to the SIMD vector length. We combine this compact data layout with a new interface to blas/lapack routines that can be used within a hierarchical parallel application. Our layout provides up to 14X, 45X, and 27X speedup against OpenMP loops around optimized dgemm, dtrsm and dgetrf kernels, respectively, on the Intel Knights Landing architecture. We discuss the compact batched blas/lapack implementations in two libraries, KokkosKernels and Intel® Math Kernel Library. We demonstrate the APIs in a line solver for coupled PDEs. Finally, we present detailed performance analysis of our kernels.

We present a parallel sparse direct solver for multicore architectures based on Directed Acyclic Graph (DAG) scheduling. Recently, DAG scheduling has become popular in advanced Dense Linear Algebra libraries due to its efficient asynchronous parallel execution of tasks. However, its application to sparse matrix problems is more challenging as it has to deal with an enormous number of highly irregular tasks. This typically results in substantial scheduling overhead both in time and space, which causes overall parallel performance to be suboptimal. We describe a parallel solver based on two-level task parallelism: tasks are first generated from a parallel tree traversal on the assembly tree; next, those tasks are further refined by using algorithms - by - blocks to gain fine-grained parallelism. The resulting fine-grained tasks are asynchronously executed after their dependencies are analyzed. Our approach is distinct from others in that we adopt two-level task scheduling to mirror the two-level parallelism. As a result, we reduce scheduling overhead, and increase efficiency and flexibility. The proposed parallel sparse direct solver is evaluated for the particular problems arising from the hp -Finite Element Method where conventional sparse direct solvers do not scale well.