Interpolation on arbitrary regions in the complex plane
type: Item
instance of: scholarly article
title: Interpolation on arbitrary regions in the complex plane
zbMATH Open document ID: 0880.65004
author: O. Diekmann
published in: Applied and Computational Harmonic Analysis
publication date: 1997-09-28T00:00:00Z
review text: A fast and stable numerical algorithm is presented for the interpolation from an arbitrary Jordan curve in the complex plane to the region bounded by that curve. Computation of such stable interpolation points is based on the solution of the modified Symm's integral equation [cf. \textit{V. Rokhlin}, J. Comput. Phys. 60, 187-207 (1985; Zbl 0629.65122)]. The algorithm combines the classical analytical apparatus with the fast multipole method to obtain an order \(O(N^{1.5})\) procedure for the determination of interpolation nodes with \(N\) the number of nodes in the discretization of the given curve and an order \(O(M+K)\) procedure for the actual interpolation from the \(M\) nodes on the boundary of the region to \(K\) nodes inside the region. The performance of the algorithm is illustrated with several numerical examples.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 1045589
zbMATH Keywords: Interpolation
zbMATH Keywords: Jordan Curve
zbMATH Keywords: nodes in the boundary and inside
zbMATH Keywords: algorithm
zbMATH Keywords: Symm's integral equation
zbMATH Keywords: fast multipole method
zbMATH Keywords: numerical examples
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
full work available at URL: acha.1997.0215
OpenAlex ID: W1969589159
cites work: On the connection between thin vortex layers and vortex sheets
cites work: A rectangular quadrature method for logarithmically singular integral equations of the first kind
cites work: A Fast Adaptive Multipole Algorithm for Particle Simulations
cites work: Q3999241
cites work: Fast Algorithms for Polynomial Interpolation, Integration, and Differentiation
cites work: Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
cites work: A fast algorithm for particle simulations
cites work: Q4310151
cites work: Q3359644
cites work: Q3699980
cites work: Some applications of a galerkin‐collocation method for boundary integral equations of the first kind
cites work: High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions
cites work: The Cauchy kernel, the Szegö kernel, and the Riemann mapping function
cites work: Q3994552
cites work: Linear integral equations
cites work: A Fast Algorithm for the Numerical Evaluation of Conformal Mappings
cites work: On Polynomial Approximation in the Complex Plane with Application to Conformal Mapping
cites work: A fast method for solving certain integral equations of the first kind with application to conformal mapping
cites work: Rapid solution of integral equations of classical potential theory
cites work: End-point corrected trapezoidal quadrature rules for singular functions
cites work: Q3857636
cites work: Q3689126
cites work: Q5762274
DOI: 10.1006/ACHA.1997.0215
description: scientific article; zbMATH DE number 1045589