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Chebyshev tauQZ Algorithm Methods for Calculating Spectra of Hydrodynamic Stability Problems
, 1996
"... The Chebyshev tau method is examined in detail for a variety of eigenvalue problems arising in hydrodynamic stability studies, particularly those of OrrSommerfeld type. We concentrate on determining the whole of the top end of the spectrum in parameter ranges beyond those often explored. The method ..."
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The Chebyshev tau method is examined in detail for a variety of eigenvalue problems arising in hydrodynamic stability studies, particularly those of OrrSommerfeld type. We concentrate on determining the whole of the top end of the spectrum in parameter ranges beyond those often explored. The method employing a Chebyshev representation of the fourth derivative operator, D 4 ; is compared with those involving the second and first derivative operators, D 2 ; D, respectively. The latter two representations require use of the QZ algorithm in the resolution of the singular generalised matrix eigenvalue problem which arises. Physical problems explored are those of Poiseuille flow, Couette flow, pressure gradient driven circular pipe flow, and Couette and Poiseuille problems for two viscous, immiscible fluids, one overlying the other. Keywords: Eigenvalue problems, OrrSommerfeld equations, Multilayer flows, Chebyshev polynomials, QZ algorithm. * This work was supported in part by the Of...
The Design and Implementation of the ScaLAPACK LU, QR, and Cholesky Factorization Routines
, 1994
"... This paper discusses the core factorization routines included in the ScaLAPACK library. These routines allow the factorization and solution of a dense system of linear equations via LU, QR, and Cholesky. They are implemented using a block cyclic data distribution, and are built using de facto standa ..."
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This paper discusses the core factorization routines included in the ScaLAPACK library. These routines allow the factorization and solution of a dense system of linear equations via LU, QR, and Cholesky. They are implemented using a block cyclic data distribution, and are built using de facto standard kernels for matrix and vector operations (BLAS and its parallel counterpart PBLAS) and message passing communication (BLACS). In implementing the ScaLAPACK routines, a major objective was to parallelize the corresponding sequential LAPACK using the BLAS, BLACS, and PBLAS as building blocks, leading to straightforward parallel implementations without a significant loss in performance. We present the details of the implementation of the ScaLAPACK factorization routines, as well as performance and scalability results on the Intel iPSC/860, Intel Touchstone Delta, and Intel Paragon systems.
Integrating Library Modules into Special Purpose Parallel Algorithms
 PROC. 2ND INT. WORKSHOP ON SOFTWARE ENGINEERING FOR PARALLEL AND DISTRIBUTED SYSTEMS (PDSE'97
, 1997
"... Most programs from scientific computing can benefit from the use of numerical libraries which provide efficient implementations for standard solution methods that often occur in numerical simulations. This is especially true for parallel scientific computing. A methodology that allows the integratio ..."
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Most programs from scientific computing can benefit from the use of numerical libraries which provide efficient implementations for standard solution methods that often occur in numerical simulations. This is especially true for parallel scientific computing. A methodology that allows the integration of library functions without any additional programming effort would ease this programming style. In this paper, we address the question how to integrate library procedures into hierarchically organized parallel programs. The hierarchical structure of a specific algorithms results from a topdown decomposition into submethods which can be realized by library functions. The integration of library functions not only requires a correct specification of data dependencies between different modules but has also to take into account a possible distribution of data among the processors. We present algorithms for the adaptation of library modules such that their functional type and underlying data ...
of hydrodynamic stability problems
"... Chebyshev tauQZ algorithm methods for calculating spectra ..."
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