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Schwarz–Christoffel...
Schwarz–Christoffel Mappings for Nonpolygonal Regions
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- Andersson, Anders (author)
- Jönköping University,Växjö universitet,Matematiska och systemtekniska institutionen,International Center for Mathematical Modeling,JTH, Matematik
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(creator_code:org_t)
- Philadelphia : SIAM, Philadelphia, USA, 2008
- 2008
- English.
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In: SIAM Journal on Scientific Computing. - Philadelphia : SIAM, Philadelphia, USA. - 1064-8275 .- 1095-7197. ; 31:1, s. 94-111
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http://dx.doi.org/10...
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https://urn.kb.se/re...
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Abstract
Subject headings
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- An approximate conformal mapping for an arbitrary region $\varOmega$ bounded by a smooth curve $\varGamma$ is constructed using the Schwarz–Christoffel mapping for a polygonal region in which $\varOmega$ is embedded. An algorithm for finding this so-called outer polygon is presented. The resulting function is a conformal mapping from the upper half-plane or the unit disk to a region $R$, approximately equal to $\varOmega$. $R$ is bounded by a $C^\infty$ curve, and since the mapping function originates from the Schwarz–Christoffel mapping and tangent polygons are used to determine it, important properties of $\Gamma$ such as direction, linear asymptotes, and inflexion points are preserved in the boundary of $R$. The method makes extensive use of existing Schwarz–Christoffel software in both the determination of outer polygons and the calculation of function values. By the use suggested here, the capabilities of such well-written software are extended.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- numerical conformal mapping
- Schwarz-Christoffel mapping
- tangent polygon
- inner region
- outer polygon
- Applied mathematics
- Tillämpad matematik
- Numerical analysis
- Numerisk analys
- Matematik
- Mathematics
Publication and Content Type
- ref (subject category)
- art (subject category)
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