Publications

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This work, building on previous efforts, develops a suite of new graph neural network machine learning architectures that generate data-driven prolongators for use in Algebraic Multigrid (AMG). Algebraic Multigrid is a powerful and common technique for solving large, sparse linear systems. Its effectiveness is problem dependent and heavily depends on the choice of the prolongation operator, which interpolates the coarse mesh results onto a finer mesh. Previous work has used recent developments in graph neural networks to learn a prolongation operator from a given coefficient matrix. In this paper, we expand on previous work by exploring architectural enhancements of graph neural networks. A new method for generating a training set is developed which more closely aligns to the test set. Asymptotic error reduction factors are compared on a test suite of 3-dimensional Poisson problems with varying degrees of element stretching. Results show modest improvements in asymptotic error factor over both commonly chosen baselines and learning methods from previous work.

As the number of supported platforms for SNL software increases, so do the testing requirements. This increases the total time spent between when a developer submits code for testing, and when tests are completed. This in turn leads developers to hold off submitting code for testing, meaning that when code is ready for testing there's a lot more of it. This increases the likelihood of merge conflicts which the developer must resolve by hand -- because someone else touched the files near the lines the developer touched. Current text-based diff tools often have trouble resolving conflicts in these cases. Work in Europe and Japan has demonstrated that, using programming language aware diff tools (e.g., using the abstract syntax tree (AST) a compiler might generate) can reduce the manual labor necessary to resolve merge conflicts. These techniques can detect code blocks which have moved, as opposed than current text-based diff tools, which only detect insertions / deletions of text blocks. In this study, we evaluate one such tool, GumTree, and see how effective it is as a replacement for traditional text-based diff approaches.

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Sparse matrix-matrix multiplication is a critical kernel for several scientific computing applications, especially the setup phase of algebraic multigrid. The MPI+X programming model, which is growing in popularity, requires that such kernels be implemented in a way that exploits on-node parallelism. We present a single-pass OpenMP variant of Gustavson's sparse matrix matrix multiplication algorithm designed for architectures (e.g. CPU or Intel Xeon Phi) with reasonably large memory and modest thread counts (tens of threads, not thousands). These assumptions allow us to exploit perfect hashing and dynamic memory allocation to achieve performance improvements of up to 2x over third-party kernels for matrices derived from algebraic multigrid setup.

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This is the official user guide for MUELU multigrid library in Trilinos version 12.13 (Dev). This guide provides an overview of MUELU, its capabilities, and instructions for new users who want to start using MUELU with a minimum of effort. Detailed information is given on how to drive MUELU through its XML interface. Links to more advanced use cases are given. This guide gives information on how to achieve good parallel performance, as well as how to introduce new algorithms Finally, readers will find a comprehensive listing of available MUELU options. Any options not documented in this manual should be considered strictly experimental.

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