EXTRACTING SINGULARITIES OF CAUCHY INTEGRALS - A KEY POINT OF A FAST SOLVER FOR PLANE POTENTIAL PROBLEMS WITH MIXED BOUNDARY-CONDITIONS

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:44

Article

HAAS, R ; BRAUCHLI, H

关键词: EXTRACTION OF SINGULARITIES;    POTENTIAL PROBLEMS;    MIXED BOUNDARY CONDITIONS;    RIEMANN-HILBERT PROBLEM;    NUMERICAL CONFORMAL MAPPING;   

DOI  :  10.1016/0377-0427(92)90009-M

来源: Elsevier

【 摘 要 】

The authors (1991) proposed an algorithm for solving plane potential problems with mixed boundary conditions. The method is based on a corresponding Riemann-Hilbert problem on the unit disc, onto which the problem has been transformed conformally. Numerically the evaluation of the solution reduces to the computation of Cauchy integrals on the unit, circle, operating on singular functions. Explicit extraction and analytical integration of these singularities up to a certain order is possible by the Schwarz formula. The remaining integral can then be treated accurately applying fast Fourier techniques. Where Haas and Brauchli (1991) focus on a more general description including computed examples, this paper gives the mathematical details concerning the construction of the singular extraction functions. Explicit expressions for their coefficients are derived.

【 授权许可】

Free