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Conformal invariants in simply connected domains. (English) Zbl 1459.65035

Summary: This paper studies the numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The used method is based on the boundary integral equation with the generalized Neumann kernel. Several numerical examples are presented. The performance and accuracy of the presented method is validated by considering several model problems with known analytic solutions.

MSC:

65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
65E10 Numerical methods in conformal mappings
30C85 Capacity and harmonic measure in the complex plane
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
30C30 Schwarz-Christoffel-type mappings
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References:

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