2d polynomial interpolation: A symbolic approach with mathematica

Yazıcı, Adnan
Ergenc, T
This paper extends a previous work done by the same authors on teaching 1d polynomial interpolation using Mathematica [1] to higher dimensions. In this work, it is intended to simplify the the theoretical discussions in presenting multidimensional interpolation in a classroom environment by employing Mathematica's symbolic properties. In addition to symbolic derivations, some numerical tests are provided to show the interesting properties of the higher dimensional interpolation problem. Runge's phenomenon was displayed for 2d polynomial interpolation.


Symbolic polynomial interpolation using Mathematica
Yazıcı, Adnan; Ergenc, T (2004-01-01)
This paper discusses teaching polynomial interpolation with the help of Mathematica. The symbolic power of Mathematica is utilized to prove a theorem for the error term in Lagrange interpolating formula. Derivation of the Lagrange formula is provided symbolically and numerically. Runge phenomenon is also illustrated. A simple and efficient symbolic derivation of cubic splines is also provided.
A 2-0 navier-stokes solution method with overset moving grids
Tuncer, İsmail Hakkı (1996-01-01)
A simple, robust numerical algorithm to localize moving boundary points and to interpolate uniteady solution variables across 2-D, arbitrarily overset computational grids is presented. Overset grids are allowed to move in time relative to each other. The intergrid boundary points are localized in terms of three grid points on the donor grid by a directional search algorithm. The parameters of the search algorithm give the interpolation weights at the localized boundary point. The method is independent of nu...
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Ergül, Özgür Salih (2006-07-14)
In this paper the Lagrange interpolation employed in the multilevel fast multipole algorithm (MLFMA) is considered as part of the efforts to obtain faster and more efficient solutions for large problems of computational electromagnetics. For the translation operator, this paper presents the choice of the parameters for optimal interpolation. Also, for the aggregation and disaggregation processes, the interpolation matrices are discussed and an efficient way of improving the accuracy by employing the poles a...
Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equations
Karasözen, Bülent; Kucukseyhan, Tugba (2015-09-18)
We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space by the discontinuous Galerkin (dG) method and in time by the backward Euler method. Applying POD-DEIM (discrete empirical interpolation method) to the full order model (FOM) for different values of the parameter in the bistable nonlinearity, we show that using few POD and DEIM modes...
Two-Step Lagrange Interpolation Method for the Multilevel Fast Multipole Algorithm
Ergül, Özgür Salih; Gurel, L. (Institute of Electrical and Electronics Engineers (IEEE), 2009)
We present a two-step Lagrange interpolation method for the efficient solution of large-scale electromagnetics problems with the multilevel fast multipole algorithm (MLFMA). Local interpolations are required during aggregation and disaggregation stages of MLFMA in order to match the different sampling rates for the radiated and incoming fields in consecutive levels. The conventional one-step method is decomposed into two one-dimensional interpolations, applied successively. As it provides a significant acce...
Citation Formats
A. Yazıcı and T. Ergenc, “2d polynomial interpolation: A symbolic approach with mathematica,” COMPUTATIONAL SCIENCE AND ITS APPLICATIONS - ICCSA 2005, PT 3, pp. 463–471, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62857.