de Branges–Rovnyak Spaces and Norm-Constrained Interpolation

2014 ◽  
pp. 1-36
Author(s):  
Joseph A. Ball ◽  
Vladimir Bolotnikov
Keyword(s):  
Constrained Interpolation

scholarly journals Application of Dynamically Constrained Interpolation Methodology in Simulating National-Scale Spatial Distribution of PM2.5 Concentrations in China

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 272
Author(s):  
Ning Li ◽  
Junli Xu ◽  
Xianqing Lv
Keyword(s):  
Transport Model ◽  
Ground Level ◽  
Kriging Interpolation ◽  
Model Parameters ◽  
National Scale ◽  
Constrained Interpolation ◽  
Simulation Accuracy ◽  
Interpolation Accuracy ◽  
Geographical Regions ◽  
The Right

Numerous studies have revealed that the sparse spatiotemporal distributions of ground-level PM2.5 measurements affect the accuracy of PM2.5 simulation, especially in large geographical regions. However, the high precision and stability of ground-level PM2.5 measurements make their role irreplaceable in PM2.5 simulations. This article applies a dynamically constrained interpolation methodology (DCIM) to evaluate sparse PM2.5 measurements captured at scattered monitoring sites for national-scale PM2.5 simulations and spatial distributions. The DCIM takes a PM2.5 transport model as a dynamic constraint and provides the characteristics of the spatiotemporal variations of key model parameters using the adjoint method to improve the accuracy of PM2.5 simulations. From the perspective of interpolation accuracy and effect, kriging interpolation and orthogonal polynomial fitting using Chebyshev basis functions (COPF), which have been proved to have high PM2.5 simulation accuracy, were adopted to make a comparative assessment of DCIM performance and accuracy. Results of the cross validation confirm the feasibility of the DCIM. A comparison between the final interpolated values and observations show that the DCIM is better for national-scale simulations than kriging or COPF. Furthermore, the DCIM presents smoother spatially interpolated distributions of the PM2.5 simulations with smaller simulation errors than the other two methods. Admittedly, the sparse PM2.5 measurements in a highly polluted region have a certain degree of influence on the interpolated distribution accuracy and rationality. To some extent, adding the right amount of observations can improve the effectiveness of the DCIM around existing monitoring sites. Compared with the kriging interpolation and COPF, the results show that the DCIM used in this study would be more helpful for providing reasonable information for monitoring PM2.5 pollution in China.

scholarly journals Test functions in constrained interpolation

2012 ◽  
Vol 364 (11) ◽  
pp. 5589-5604 ◽  
Author(s):  
Michael A. Dritschel ◽  
James Pickering
Keyword(s):  
Test Functions ◽  
Constrained Interpolation

Wave Loads on Floaters of Aquaculture Plants

2008 ◽  
Author(s):  
David Kristiansen ◽  
Odd M. Faltinsen
Keyword(s):  
Stokes Equations ◽  
Model Tests ◽  
Staggered Grid ◽  
Physical Parameters ◽  
Surface Zone ◽  
Two Dimensional ◽  
Wave Loads ◽  
Wave Load ◽  
Constrained Interpolation ◽  
Advection Term

This paper addresses wave loads on horizontal cylinders in the free surface zone by means of model tests and numerical simulations. This has relevance for the design of floating fish farms at exposed locations. Two model geometries were tested, where two-dimensional flow conditions were sought. The cylinders were fixed and exposed to regular wave trains. Wave overtopping the models were observed. A two-dimensional Numerical Wave Tank (NWT) for wave load computations is described. The NWT is based on the finite difference method and solves the incompressible Navier-Stokes equations on a non-uniform Cartesian staggered grid. The advection term is treated separately by the CIP (Constrained Interpolation Profile) method. A fractional and validation of the NWT is emphasized. Numerical results from simulations with the same physical parameters as in the model tests are performed for comparison. Deviations are discussed.

A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses

2021 ◽  
Author(s):  
Zhexu Wang ◽  
Rei Kawashima ◽  
Kimiya Komurasaki
Keyword(s):  
Fourth Order ◽  
Fluid Model ◽  
Velocity Distribution Function ◽  
Hall Thruster ◽  
Test Case ◽  
Ionization Source ◽  
Plasma Properties ◽  
Constrained Interpolation ◽  
Derivative Term ◽  
Pic Method

Abstract A 1D1V hybrid Vlasov-fluid model was developed for this study to elucidate ionization oscillations of Hall thrusters (HTs). The Vlasov equation for ions velocity distribution function (IVDF) with ionization source term is solved using a constrained interpolation profile conservative semi-Lagrangian (CIP-CSL) method. The fourth-order weighted essentially non-oscillatory (4th WENO) limiter is applied to the first derivative term to minimize numerical oscillation in the discharge oscillation analyses. The fourth-order spatial accuracy is verified through a 1D scalar test case. Nonoscillatory and high-resolution features of the Vlasov model are confirmed by simulating the test cases of the Vlasov–Poisson (VP) system and by comparing the results with a particle-in-cell (PIC) method. A 1D1V Hall thruster simulation is performed through the hybrid Vlasov-fluid model. The ionization oscillation is analysed. The macroscopic plasma properties are compared with those obtained from a hybrid PIC method. The comparison indicates that the hybrid Vlasov-fluid model yields noiseless results and that the steady-state waveform is calculable in a short time period.

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