Abstract
This paper describes a parallel implementation of the Jacobi-Davidson method to compute eigenpairs of large unsymmetric matrices. Taking advantage of the capabilities of the PETSc library —Portable Extensible Toolkit for Scientific Computation—, we build an efficient and robust code adapted either for traditional serial computation or parallel computing environments. Particular emphasis is given to the description of some implementation details of the so-called correction equation, responsible for the subspace expansion, and crucial in the Jacobi-Davidson algorithm. Numerical results are given and the performance of the code is analyzed in terms of serial and parallel efficiency. The developments achieved in the context of this work will be incorporated in future releases of SLEPc —Scalable Library for Eigenvalue Problem Computations—, thus serving the scientific community and guaranteeing dissemination.
This work was partially supported by Fundação para a Ciência e a Tecnologia - FCT, through Centro de Matemática da Universidade do Porto - CMUP, and by the Spanish Ministerio de Ciencia e Innovación under project TIN2009-07519.
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Romero, E., Cruz, M.B., Roman, J.E., Vasconcelos, P.B. (2011). A Parallel Implementation of the Jacobi-Davidson Eigensolver for Unsymmetric Matrices. In: Palma, J.M.L.M., Daydé, M., Marques, O., Lopes, J.C. (eds) High Performance Computing for Computational Science – VECPAR 2010. VECPAR 2010. Lecture Notes in Computer Science, vol 6449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19328-6_35
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DOI: https://doi.org/10.1007/978-3-642-19328-6_35
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