Guide to available mathematical software

Monahan, John F.; Boisvert, Ronald F.; Howe, Sally E.; Kahaner, David K.; Chatterjee, Samprit

doi:10.6028/nist.ir.90-4237

Cited by 33 publications

(17 citation statements)

References 3 publications

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“…Consider now the case of correcting or updating the mass matrix of the system using the mass updating algorithm developed in Section 2.1 to solve solve Equation (13). This method requires a modal survey of the mass-modiÿed system to be performed.…”

Section: E Ects Of Locations Magnitudes and The Number Of Added Elementioning

confidence: 99%

“…For systems in which there is no special sparsity pattern to be maintained, the least-squares system will always have dimension N 2 e × N 2 [see Equations (13) and (25)]. If the measured modes are incomplete (for N e ¡N ), the problem will always be underdetermined.…”

Section: Relating Accuracy To N E and Nmentioning

confidence: 99%

“…Initially, it may appear that one must solve two underdetermined least-squares problems of size N 2 e × N 2 (assuming N e ¡N ) in order to update the system matrices [see Equations (13) and (25)]. However, the optimal matrix storage scheme commonly used in ÿnite elements [10] can be applied to pass along the available sparsity information of the analytical system and to impose the condition that all zero elements in the analytical system matrices remain zeros in the adjusted system matrices.…”

Section: Solution Techniquementioning

confidence: 99%

“…For solving a least squares problem, we used the CMLIB [13] routine sglss, which is specialized to handle both underdetermined and overdetermined systems of the form is less than min(m,n), then again the minimum norm least squares solution is computed.…”

Section: Numerical Experimentsmentioning

confidence: 99%

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Model updating by adding known masses

Pillis

2001

Numerical Meth Engineering

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SUMMARYNew approaches are developed that use measured data to adjust the analytical mass and sti ness matrices of a system so that the agreement between the analytical modes of vibration and the modal survey is improved. By adding known masses to the structure of interest, measuring the modes of vibration of this mass-modiÿed system, and ÿnally using this set of new data in conjunction with the initial modal survey, the analytical mass matrix of the structure can be corrected, after which the analytical sti ness matrix can be readily updated. By manipulating the correction matrices into vector forms, the connectivity information can be enforced, thereby preserving the physical conÿguration of the system and reducing the sizes of the least-squares problems that need to be solved. Solution techniques for updating the system matrices are introduced, and the numerical issues associated with solving overdetermined and underdetermined least squares problems are investigated. The e ects of round-o errors are also studied, and heuristic criteria are given for determining the minimum number of modes that need to be measured in order to ensure su ciently accurate updated mass and sti ness matrices. Numerical experiments are presented to validate the proposed model-updating techniques, to illustrate the e ects of the number of measured modes on the quality of the updated model, to show how the magnitudes and locations of the added masses in uence the updated matrices, and to highlight the numerical issues discussed in this paper.

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Section: E Ects Of Locations Magnitudes and The Number Of Added Elementioning

confidence: 99%

Section: Relating Accuracy To N E and Nmentioning

confidence: 99%

Section: Solution Techniquementioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

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Model updating by adding known masses

Pillis

2001

Numerical Meth Engineering

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“…For this testcase of MyPYTHIA, we have utilized 124 routines from the GAMS cross-index [35], where the category H2a is for the evaluation of one-dimensional integrals. A collection of 286 test problems and 124 methods were identified.…”

Section: Numerical Quadraturementioning

confidence: 99%

MyPYTHIA: a recommendation portal for scientific software and services

Houstis

Catlin

Dhanjani

et al. 2002

Concurrency and Computation

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SUMMARYWe outline the design of a recommendation system (MyPYTHIA) implemented as a Web portal. MyPYTHIA's design objectives include evaluating the quality and performance of scientific software on Grid platforms, creating knowledge about which software and computational services should be selected for solving particular problems, selecting parameters of software (or of computational services) based on user-specified computational objectives, providing access to performance data and knowledge bases over the Web and enabling recommendations for targeted application domains. MyPYTHIA uses a combination of statistical analysis, pattern extraction techniques and a database of software performance to map featurebased representations of problem instances to appropriate software. MyPYTHIA's open architecture allows the user to customize it for conducting individual case studies. We describe the architecture as well as several scientific domains of knowledge enabled by such case studies.

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Natural Frequencies of a Linear Elastica Carrying Any Number of Sprung Masses

Cha

2001

Journal of Sound and Vibration

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Guide to available mathematical software

Cited by 33 publications

References 3 publications

Model updating by adding known masses

Model updating by adding known masses

MyPYTHIA: a recommendation portal for scientific software and services

Natural Frequencies of a Linear Elastica Carrying Any Number of Sprung Masses

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