On the solution of certain field problems by the schwarz-christoffel method

✍ Scribed by Wang, H. S. C.

• Publisher: Springer
• Year: 1969
• Tongue: English
• Weight: 379 KB
• Volume: 21
• Category: Article
• ISSN: 0003-6994
• DOI: 10.1007/bf00411604

✦ Synopsis

Ill 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, ill lieu of qualitative plots of equipotential surfaces and flux lines, field components and potential can be expressed as veal 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. Ill some cases the series converges rapidly and assumes a remarkably simple form.