We present Tpetra, a Trilinos package for parallel linear algebra primitives implementing the Petra object model. We describe Tpetra's design, based on generic programming via C++ templated types and template meta...
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We present Tpetra, a Trilinos package for parallel linear algebra primitives implementing the Petra object model. We describe Tpetra's design, based on generic programming via C++ templated types and template metaprogramming. We discuss some benefits of this approach in the context of scientific computing, with illustrations consisting of code and notable empirical results.
This paper presents several new variants of the single-vector Arnoldi algorithm for computing approximations to eigenvalues and eigenvectors of a non-symmetric matrix. The context of this work is the efficient impleme...
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This paper presents several new variants of the single-vector Arnoldi algorithm for computing approximations to eigenvalues and eigenvectors of a non-symmetric matrix. The context of this work is the efficient implementation of industrial-strength, parallel, sparse eigensolvers, in which robustness is of paramount importance, as well as efficiency. For this reason, Arnoldi variants that employ Gram-Schmidt with iterative reorthogonalization are considered. The proposed algorithms aim at improving the scalability when running in massively parallel platforms with many processors. The main goal is to reduce the performance penalty induced by global communications required in vector inner products and norms. In the proposed algorithms, this is achieved by reorganizing the stages that involve these operations, particularly the orthogonalization and normalization of vectors, in such a way that several global communications are grouped together while Guaranteeing that the numerical stability of the process is maintained. The numerical properties of the new algorithms are assessed by means of a large set of test matrices. Also, scalability analyses show a significant improvement in parallel performance. (c) 2007 Elsevier B.V.. All rights reserved.
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