Minimization of the Truncation Error by Grid Adaptation

Yamaleev, Nail K.

doi:10.1006/jcph.2001.6745

Cited by 21 publications

(25 citation statements)

References 19 publications

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“…While the adaptive mesh approach based upon equidistribution attempts to minimize the error in regions of strong gradients and local extrema, another possibility in reducing numerical error is to attempt to find a mesh distribution which equidistributes or minimizes the local truncation error or its estimate [37,38,39,40,41]. In this current paper, the approach we will use in this class of mesh adaptation methods is similar in concept to that presented by Klopfer and McRae [38].…”

Section: Time-varying Mesh Adaptationmentioning

confidence: 86%

Adaptive finite difference solutions of Liouville equations in computational uncertainty quantification

Razi

Attar

Vedula

2015

Reliability Engineering & System Safety

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Section: Time-varying Mesh Adaptationmentioning

confidence: 86%

Adaptive finite difference solutions of Liouville equations in computational uncertainty quantification

Razi

Attar

Vedula

2015

Reliability Engineering & System Safety

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“…may be used for the search of the optimal sensor location similarly to the methods of computation of grid adaptation [24]. T obs int corresponds to the norm of T 0 in a metric engendered by the matrix H E = A * A:…”

Section: Problem Statementmentioning

confidence: 99%

“…In some works the minimization of either the local error of approximation [24][25][26] or the error of some goal functional [27] is used for the retrieval of an optimum computational grid. It is interesting to extend this approach for the search of the optimum sensor locations.…”

Section: Introductionmentioning

confidence: 99%

Criteria of optimality for sensors' location based on adjoint transformation of observation data interpolation error

Alekseev

Navon

2009

Numerical Methods in Fluids

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SUMMARYCriteria of optimality for sensors' location are addressed using an interpolation error transformed by especial adjoint problems. The considered criteria correspond to the analysis error in certain Hessian-based metrics and to the error of some forecast aspect. Both criteria are obtained using adjoint problems that provide computation without the direct use of the Hessian. For a linear inverse heat conduction problem, these criteria are compared and demonstrated promising results when compared with a criterion based on the norm of the interpolation error of observation data. Approaches to sensor set modification using either redistribution of sensors' or refinement of the sensors grid (insertion of additional sensors) are also compared.

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“…These methods are precisely studied and relevant numerical strength and drawbacks are investigated. Regarding these schemes, some of important numerical features are: 1) source of numerical errors: truncation and roundoff errors, [56]; 2) effect of grid/element irregularities on truncation error and corresponding dissipation and dispersion phenomena [57]; 3) internal reflections from grids/element faces [58][59][60][61][62][63][64][65]; 4) the inherent dissipation property [66,67]. These features lead in general to numerical (artificial) dissipation and dispersion phenomena.…”

Section: Introductionmentioning

confidence: 99%