×

On the determination of boundary collocation points for solving some problems for the Laplace operator. (English) Zbl 0569.65083

Methods for the determination of boundary collocation points for solving certain problems for the Laplace operator are investigated. A nonlinear minimization problem whose solution is a set of collocation points is formulated and the numerical solution of a closely related minimization problem is studied by solving certain linear integral equation.
Reviewer: C.L.Koul

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bates, R. H.T., Analytic constraints on electromagnetic field computations, IEEE Trans. Microwave Theory Tech., 23, 605-623 (1975)
[2] Bates, R. H.T.; Ng, F. L., Point matching computation of transverse resonances, Internat. J. Numer. Methods. Engrg., 6, 155-168 (1973) · Zbl 0251.65073
[3] Collatz, L., The Numerical Treatment of Differential Equations (1966), Springer: Springer Berlin · Zbl 0221.65088
[4] Jaswon, M. A.; Symm, G. T., Integral Equation Methods in Potential Theory and Elastostatics (1977), Academic Press: Academic Press London · Zbl 0414.45001
[5] Reichel, L., On the determination of boundary collacation points for solving some problems for the Laplace operator, (Report TRITA-8006 (1980), Dept. of Comp. Sci., Royal Institute of Technology: Dept. of Comp. Sci., Royal Institute of Technology Stockholm)
[6] Riesz, F.; Sz-Nagy, B., Leçons d’Analyse Functionelle (1952), Akadéminai Kiadó: Akadéminai Kiadó Budapest
[7] Tsuji, M., Potential Theory in Modern Function Theory (1959), Maruzen: Maruzen Tokyo · Zbl 0087.28401
[8] Walsh, J. L., Interpolation and Approximation by Rational Functions in the Complex Domain (1965), American Mathematical Society,: American Mathematical Society, Providence, RI · Zbl 0146.29902
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.