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Lagrange Interpolation (lagrange + interpolation)

Distribution by Scientific Domains

Engineering	40%

Selected Abstracts

High-order stable interpolations for immersed boundary methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2006
Nikolaus Peller
Abstract The analysis and improvement of an immersed boundary method (IBM) for simulating turbulent flows over complex geometries are presented. Direct forcing is employed. It consists in interpolating boundary conditions from the solid body to the Cartesian mesh on which the computation is performed. Lagrange and least squares high-order interpolations are considered. The direct forcing IBM is implemented in an incompressible finite volume Navier,Stokes solver for direct numerical simulations (DNS) and large eddy simulations (LES) on staggered grids. An algorithm to identify the body and construct the interpolation schemes for arbitrarily complex geometries consisting of triangular elements is presented. A matrix stability analysis of both interpolation schemes demonstrates the superiority of least squares interpolation over Lagrange interpolation in terms of stability. Preservation of time and space accuracy of the original solver is proven with the laminar two-dimensional Taylor,Couette flow. Finally, practicability of the method for simulating complex flows is demonstrated with the computation of the fully turbulent three-dimensional flow in an air-conditioning exhaust pipe. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Missing data estimation for 1,6,h gaps in energy use and weather data using different statistical methods

INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 13 2006
David E. Claridge
Abstract Analysing hourly energy use to determine retrofit savings or diagnose system problems frequently requires rehabilitation of short periods of missing data. This paper evaluates four methods for rehabilitating short periods of missing data. Single variable regression, polynomial models, Lagrange interpolation, and linear interpolation models are developed, demonstrated, and used to fill 1,6,h gaps in weather data, heating data and cooling data for commercial buildings. The methodology for comparing the performance of the four different methods for filling data gaps uses 11 1-year data sets to develop different models and fill over 500 000 ,pseudo-gaps' 1,6,h in length for each model. These pseudo-gaps are created within each data set by assuming data is missing, then these gaps are filled and the ,filled' values compared with the measured values. Comparisons are made using four statistical parameters: mean bias error (MBE), root mean square error, sum of the absolute errors, and coefficient of variation of the sum of the absolute errors. Comparison based on frequency within specified error limits is also used. A linear interpolation model or a polynomial model with hour-of-day as the independent variable both fill 1,6 missing hours of cooling data, heating data or weather data, with accuracy clearly superior to the single variable linear regression model and to the Lagrange model. The linear interpolation model is the simplest and most convenient method, and generally showed superior performance to the polynomial model when evaluated using root mean square error, sum of the absolute errors, or frequency of filling within set error limits as criteria. The eighth-order polynomial model using time as the independent variable is a relatively simple, yet powerful approach that provided somewhat superior performance for filling heating data and cooling data if MBE is the criterion as is often the case when evaluating retrofit savings. Likewise, a tenth-order polynomial model provided the best performance when filling dew-point temperature data when MBE is the criterion. It is possible that the results would differ somewhat for other data sets, but the strength of the linear and polynomial models relative to the other models evaluated seems quite robust. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Lagrange interpolation and finite element superconvergence,

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2004
Bo Li
Abstract We consider the finite element approximation of the Laplacian operator with the homogeneous Dirichlet boundary condition, and study the corresponding Lagrange interpolation in the context of finite element superconvergence. For d -dimensional Qk -type elements with d , 1 and k , 1, we prove that the interpolation points must be the Lobatto points if the Lagrange interpolation and the finite element solution are superclose in H1 norm. For d -dimensional Pk -type elements, we consider the standard Lagrange interpolation,the Lagrange interpolation with interpolation points being the principle lattice points of simplicial elements. We prove for d , 2 and k , d + 1 that such interpolation and the finite element solution are not superclose in both H1 and L2 norms and that not all such interpolation points are superconvergence points for the finite element approximation. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 33,59, 2004. [source]