ON MODULI OF RINGS AND QUADRILATERALS: ALGORITHMS AND EXPERIMENTS



: Hakula H, Rasila A, Vuorinen M

Publisher: SIAM PUBLICATIONS

: 2011

: SIAM Journal on Scientific Computing

: SIAM JOURNAL ON SCIENTIFIC COMPUTING

: SIAM J SCI COMPUT

: 1

: 33

: 1

: 279

: 302

: 24

: 1064-8275

DOI: https://doi.org/10.1137/090763603


Moduli of rings and quadrilaterals are frequently applied in geometric function theory; see, e. g., the handbook by Kuhnau [Handbook of Complex Analysis: Geometric Function Theory, Vols. 1 and 2, North Holland, Amsterdam, 2005]. Yet their exact values are known only in a few special cases. Previously, the class of planar domains with polygonal boundary has been studied by many authors from the point of view of numerical computation. We present here a new hp-FEM algorithm for the computation of moduli of rings and quadrilaterals and compare its accuracy and performance with previously known methods such as the Schwarz-Christoffel Toolbox of Driscoll and Trefethen. We also demonstrate that the hp-FEM algorithm applies to the case of nonpolygonal boundary and report results with concrete error bounds.



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