WANG Yufeng, JI Anzhao, CUI Jianbin. Numerical Solution of Schwarz-Christoffel Transformation From Rectangles to Arbitrary Polygonal Domains[J]. Applied Mathematics and Mechanics, 2019, 40(1): 75-88. doi: 10.21656/1000-0887.390050
Citation: WANG Yufeng, JI Anzhao, CUI Jianbin. Numerical Solution of Schwarz-Christoffel Transformation From Rectangles to Arbitrary Polygonal Domains[J]. Applied Mathematics and Mechanics, 2019, 40(1): 75-88. doi: 10.21656/1000-0887.390050

Numerical Solution of Schwarz-Christoffel Transformation From Rectangles to Arbitrary Polygonal Domains

doi: 10.21656/1000-0887.390050
  • Received Date: 2018-01-29
  • Rev Recd Date: 2018-04-23
  • Publish Date: 2019-01-01
  • With the Schwarz-Christoffel transformation method, a mathematical model of conformal mapping from polygonal domains to strip domains was established. For constraint conditions and singular integral problems in the model, the reciprocal transformation between complex parameters and real parameters was conducted based on the Riemann principle, which eliminates constraint conditions of the nonlinear system. By means of reasonable integration paths, the singular integral in the model was transformed into the Gauss-Jacobi integral, and the nonlinear system model was solved with the Levenberg-Marquardt algorithm. According to the first class elliptic function characteristics, the mathematical model of conformal mapping from rectangular domains to strip domains was built, and the relationship between the rectangular boundary and the strip boundary was obtained through calculation of the complex parameter elliptic function. At last, an 8-point polygonal domain and a 27-point irregular strip domain were calculated to map the irregular closed domain boundary to the rectangular domain boundary. The orthogonal grid in the rectangular domain still meets orthogonality in the polygonal domain after mapping. This study provides a foundation for numerical calculation of mapping from irregular domains to regular ones.
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