Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals
Mohamed M. S. Nasser, Oona Rainio, Antti Rasila, Матти Вуоринен, Terry C. Wallace, Hang Yu, Xiaohui Zhang
Abstract
Abstract We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs, also called polycircular domains, and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when possible, comparison to exact values or other methods are given. We also analyze the rate of convergence as a function of the number of degrees of freedom. The main ingredients of the computation are boundary integral equations combined with the fast multipole method.
Topics & Concepts
QuadrilateralConformal mapMathematicsComputationMultipole expansionBoundary (topology)Degrees of freedom (physics and chemistry)Moduli spaceRate of convergenceDomain (mathematical analysis)Convergence (economics)Polygon meshModuliFunction (biology)Mathematical analysisApplied mathematicsPure mathematicsGeometryFinite element methodAlgorithmComputer scienceBiologyEconomic growthComputer networkThermodynamicsPhysicsChannel (broadcasting)Evolutionary biologyEconomicsQuantum mechanicsElectromagnetic Scattering and AnalysisNumerical methods in engineeringAlgebraic and Geometric Analysis