Abstract
In many practical cases the usefulness of the Schwarz-Christoffel method to solve two-dimensional field problems (Laplace equation with Dirichlet boundary conditions) is limited by the presence of transcendental functions of complex variables. We demonstrate here a new technique whereby, in lieu of qualitative plots of equipotential surfaces and flux lines, field components and potential can be expressed as real power series of the coordinates (x, y). The convergence of these series is only limited by the proximity of singular points corresponding to the physical convex corners. By choosing suitable points on the boundary around which the series of expansion are developed, fringing field components in the regions of interest between the boundaries can be computed directly. In some cases the series converges rapidly and assumes a remarkably simple form.
Similar content being viewed by others
References
Morse, P. M. and Feshbach, Methods of Theoretical Physics, Part I, McGraw-Hill, New York 1953.
Mee, C. D., The Physics of Magnetic Recording, North Holland, Amsterdam 1964.
Karlquist, O., Trans. Roy. Inst. Tech. (Stockholm, Sweden) No. 86 (1954) 3.
Merservey, R., Phys. Fluids 8 (1965) 1209.
Binns, K. J. and P. J. Lawrenson, Analysis and Computation of Electric and Magnetic Field Problems, Macmillan, New York 1963.
Muskhelishvili, N. I., Singular Integral Equations, p. 107, Noordhoff, Groningen (Holland) 1953.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wang, H.S.C. On the solution of certain field problems by the schwarz-christoffel method. Appl. sci. Res. 21, 165–175 (1969). https://doi.org/10.1007/BF00411604
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00411604