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On the curvature of...
On the curvature of an inner curve in a Schwarz-Christoffel mapping
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- Andersson, Anders (författare)
- Växjö universitet,Matematiska och systemtekniska institutionen
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(creator_code:org_t)
- Växjö universitet, Växjö, 2007
- Engelska 7 s.
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Serie: Reports from MSI, 1650-2647 ; 07015
- Relaterad länk:
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https://urn.kb.se/re...
Abstract
Ämnesord
Stäng
- In the so called outer polygon method, an approximative conformal mapping for a given simply connected region \Omega is constructed using a Schwarz-Christoffel mapping for an outer polygon, a polygonal region of which \Omega is a subset. The resulting region is then bounded by a C^\infty -curve, which among other things means that its curvature is bounded. In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz-Christoffel mapping from R, the unit disk or upper halfplane, to a polygonal region P of a curve inside R. From the Schwarz-Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- curvature
- Schwarz-Christoffel mapping
- inner curve
- outer polygon
- Mathematical analysis
- Analys
- Applied mathematics
- Tillämpad matematik
- Numerical analysis
- Numerisk analys
- Mathematics
- Matematik
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