- Volume 21 Issue 4
DOI QR Code
APPLIED SYMMETRICAL PRINCIPLE TO SOLVE SCHWARZ-CHRISTOFFEL PARAMETER PROBLEM
- YUAN, MEI (SCHOOL OF RESOURCES AND ENVIRONMENTAL ENGINEERING, WUHAN UNIVERSITY OF TECHNOLOGY) ;
- PENG, HUIQING (SCHOOL OF RESOURCES AND ENVIRONMENTAL ENGINEERING, WUHAN UNIVERSITY OF TECHNOLOGY) ;
- LEI, YUN (SCHOOL OF RESOURCES AND ENVIRONMENTAL ENGINEERING, WUHAN UNIVERSITY OF TECHNOLOGY)
- Published : 2018.10.31
This paper adopted symmetry theory to solve the Schwarz-Christoffel parameter problem for axisymmetric polygons. Numerical conformal mappings were performed to shift the upper half-plane onto polygonal domains. Once the constraint conditions of the problem were treated in a special way such as added or deleted a little area, it turns to be a solution of a singular integral.In this paper, an auxiliary point was suggested to attach to the polygon that obeyed the principle of symmetry, which can accelerate the solving process of the singular integral. After that, several numerical examples, along with an application related to electrostatics, are provided to verify its feasibility and simplification. When the distance from the auxiliary point to polygon is controlled under 1E-08, the accuracy can be controlled within 1E-09, accuracy and consequences of the calculation basically meet the ordinary requirement.
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