Monotone Piecewise Bicubic Interpolation

Carlson, R.E.; Fritsch, F.N.

doi:10.1137/0722023

Cited by 164 publications

(84 citation statements)

References 3 publications

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“…Another major point of concern that is reflected in Figure 1 to negative weights which, clearly, are not physical and suggests that the source of the problem stems from the non-monotonic interpolation employed in this case. To remedy this problem, we have repeated the simulation with the monotonic interpolation of Williamson and Rasch (1989), and Carlson and Fritsch (1985). Results for this case are presented in Figure 1(b) and now show weights that remain non-negative for the duration of the computation.…”

Section: Resultsmentioning

confidence: 99%

A hybrid grid/particle filter for Lagrangian data assimilation. II: Application to a model vortex flow

Salman

2008

Quart J Royal Meteoro Soc

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ABSTRACT:We apply our hybrid filter to a regularised vortex model of a co-rotating vortex pair. To illustrate the main advantages of our formulation over existing filters, we compare our method to the perturbed observation Ensemble Kalman filter and a particle filter with Gaussian resampling. Our numerical simulations show that both the hybrid and particle filters can track the true vortex positions even when tracer position data is assimilated infrequently into our model. In contrast, the Ensemble Kalman filter diverges in this parameter range as was recently observed in the more realistic shallow-water model simulations of Salman et al. We have found that our hybrid method can track the true system with as few as 20 members for the vortex model flow. The particle filter on the other hand requires an ensemble comprising in excess of 160 members. The hybrid filter, therefore, provides one solution to the filter divergence problem that has been identified in recent work on Lagrangian data assimilation.

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Section: Resultsmentioning

confidence: 99%

A hybrid grid/particle filter for Lagrangian data assimilation. II: Application to a model vortex flow

Salman

2008

Quart J Royal Meteoro Soc

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“…This is achieved by fitting the empirical cumulative distribution functions from the reference case with a Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) [19]. Since this interpolation method is monotone it provides a valid cumulative distribution.…”

Section: Input Datamentioning

confidence: 99%

Assignment of Electrical Properties to Power Grid Topologies

Schweitzer

Scaglione²,

Hedman³

2018

Proceedings of the 51st Hawaii International Conference on System Sciences

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Abstract-Power systems are often described in terms of graphs, with various properties like load and impedance associated with the nodes and edges. These properties are coupled to the graph's topology, reflecting the great deal of engineering design in the power system. With the goal of automating the creation of usable synthetic cases, the problem of assigning these properties is considered. It is formulated as a Mixed Integer Program (MIP), which aims to minimize the angle differences between adjacent nodes in the system. Since the problem quickly balloons in size, a decomposition into smaller zones is explored, that enables scaling the problem to larger system sizes. Experiments demonstrate the efficacy and viability of the approach.

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“…In the methods presented here, the interpolation among the reduced-order system matrices is performed elementwise, so standard techniques for interpolation of scalar values can be applied. Cubic spline interpolants [36,37] are used in this work. Our specific approaches are described in the following subsections for a general reduced-order matrix M .…”

Section: Interpolation Of Reduced-order Modelsmentioning

confidence: 99%

“…Spline interpolation among matrices as a function of the parameters z is performed with cubic splines [36,37]. The set of n z reduced-order system matrices M i , i = 1, .…”

Section: Spline Interpolationmentioning

confidence: 99%

Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis

Degroote

Vierendeels

Willcox

2009

Numerical Methods in Fluids

111

117

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SUMMARYModel reduction has significant potential in design, optimization and probabilistic analysis applications, but including the parameter dependence in the reduced-order model (ROM) remains challenging. In this work, interpolation among reduced-order matrices is proposed as a means to obtain parametrized ROMs. These ROMs are fast to evaluate and solve, and can be constructed without reference to the original full-order model. Spline interpolation of the reduced-order system matrices in the original space and in the space tangent to the Riemannian manifold is compared with Kriging interpolation of the predicted outputs. A heuristic criterion to select the most appropriate interpolation space is proposed. The interpolation approach is applied to a steady-state thermal design problem and probabilistic analysis via Monte Carlo simulation of an unsteady contaminant transport problem.

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Monotone Piecewise Bicubic Interpolation

Cited by 164 publications

References 3 publications

A hybrid grid/particle filter for Lagrangian data assimilation. II: Application to a model vortex flow

A hybrid grid/particle filter for Lagrangian data assimilation. II: Application to a model vortex flow

Assignment of Electrical Properties to Power Grid Topologies

Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis

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