scholarly journals The order of the best transfinite interpolation of functions with bounded laplacian with the help of harmonic splines on box partitions

2018 ◽  
Vol 26 (1) ◽  
pp. 82
Author(s):  
D. Skorokhodov
Keyword(s):  
Transfinite Interpolation ◽  
Interpolation Of Functions

We show that the error of the best transfinite interpolation of functions with bounded laplacian with the help of harmonic splines on box partitions comprising $$$N$$$ elements has the order $$$N^{-2}$$$ as $$$N \rightarrow \infty$$$.

scholarly journals Optimization of transfinite interpolation of functions with bounded Laplacian by harmonic splines on box partitions

2016 ◽  
Vol 209 ◽  
pp. 44-57 ◽  
Author(s):  
Dmytro Kuzmenko ◽  
Dmytro Skorokhodov
Keyword(s):  
Transfinite Interpolation ◽  
Interpolation Of Functions

Interpolation of functions in the Brillouin zone and special-point method

1983 ◽  
Vol 26 (5) ◽  
pp. 488-491
Author(s):  
M. L. Zolotarev ◽  
A. S. Poplavnoi
Keyword(s):  
Brillouin Zone ◽  
Point Method ◽  
Special Point ◽  
Interpolation Of Functions

Convex polyhedra in hyperbolic space and interpolation of functions

2011 ◽  
Vol 84 (3) ◽  
pp. 850-853
Author(s):  
O. P. Gladunova ◽  
E. D. Rodionov ◽  
V. V. Slavskii
Keyword(s):  
Hyperbolic Space ◽  
Convex Polyhedra ◽  
Interpolation Of Functions

Grid adaptation for unsteady flow computations

1997 ◽  
Vol 211 (4) ◽  
pp. 237-250 ◽  
Author(s):  
C B Allen
Keyword(s):  
Unsteady Flow ◽  
Unsteady Flows ◽  
Processing Unit ◽  
Flow Solver ◽  
Transfinite Interpolation ◽  
Central Processing ◽  
Grid Adaptation ◽  
Euler Flows ◽  
Adaptation Procedure ◽  
Grid Points

A grid adaptation procedure suitable for use during unsteady flow computations is described. Transfinite interpolation is used to generate structured grids for the computation of steady and unsteady Euler flows past aerofoils. This technique is well suited to unsteady flows, since instantaneous grid positions and speeds required by the flow solver are available directly from the algebraic mapping. A different approach to grid adaptation is described, wherein adaptation is performed by redistributing the interpolation parameters, instead of the physical grid positions. This results in the adapted grid positions, and hence speeds, still being available algebraically. Grid adaptation during an unsteady computation is performed continuously by imposing an ‘adaptation velocity’ on grid points, thereby applying the adaptation over several time steps and avoiding the interpolation of the solution from one grid to another, which is associated with instantaneous adaptation. For both steady and unsteady flows the adapted grid technique is shown to produce sharper shock resolution for a very small increase in CPU (central processing unit) requirements.

scholarly journals Orthogonal structure on a quadratic curve

2020 ◽  
Author(s):  
Sheehan Olver ◽  
Yuan Xu
Keyword(s):  
Weight Function ◽  
Orthogonal Polynomials ◽  
Extension Problem ◽  
Orthogonal Expansions ◽  
Schrödinger’S Equation ◽  
Fourier Extension ◽  
Quadratic Curve ◽  
Interpolation Of Functions ◽  
Fourier Orthogonal Expansions ◽  
Schrödinger's Equation

Abstract Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas and two lines. For an integral with respect to an appropriate weight function defined on any quadratic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. Convergence of the Fourier orthogonal expansions is also studied in each case. We discuss applications to the Fourier extension problem, interpolation of functions with singularities or near singularities and the solution of Schrödinger’s equation with nondifferentiable or nearly nondifferentiable potentials.

Lagrange interpolation of functions of generalized bounded variation

1989 ◽  
Vol 53 (1-2) ◽  
pp. 75-84 ◽  
Author(s):  
Xiehua Sun
Keyword(s):  
Bounded Variation ◽  
Lagrange Interpolation ◽  
Interpolation Of Functions

Interpolation of Functions

2000 ◽  
pp. 33-40
Author(s):  
Vladimir Rovenski
Keyword(s):  
Interpolation Of Functions
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