Abstract
At the ANZIAM conference in Hobart in February 2018, there were several talks on the solution of Laplace problems in multiply connected domains by means of conformal mapping. It appears to be not widely known that such problems can also be solved by the elementary method of series expansions with coefficients determined by least-squares fitting on the boundary. (These are not convergent series; the coefficients depend on the degree of the approximation.) Here we give a tutorial introduction to this method, which converges at an exponential rate if the boundary data are sufficiently well-behaved. The mathematical foundations go back to Runge in 1885 and Walsh in 1929. One of our examples involves an approximate Cantor set with up to 2048 components.
Publisher
Cambridge University Press (CUP)
Subject
Mathematics (miscellaneous)
Reference58 articles.
1. Potential Theory in the Complex Plane
2. Über die Beugung elektromagnetischer Wellen an parallelen, unendlich langen Kreiszylindern
3. [29] C. C. Green , M. A. Snipes and L. A. Ward , “Using the Schottky–Klein prime function to compute harmonic measure distribution functions of a class of multiply connected planar domains”, ANZIAM Conference 2018, 8 February 2018; http://www.maths.utas.edu.au/anziam2018/ documents/ANZIAM2018Handbook.pdf.
4. Lectures on Complex Approximation
5. A new version of the Fast Multipole Method for the Laplace equation in three dimensions
Cited by
18 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献