A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
ON MODULI OF RINGS AND QUADRILATERALS: ALGORITHMS AND EXPERIMENTS
Tekijät: Hakula H, Rasila A, Vuorinen M
Kustantaja: SIAM PUBLICATIONS
Julkaisuvuosi: 2011
Journal: SIAM Journal on Scientific Computing
Tietokannassa oleva lehden nimi: SIAM JOURNAL ON SCIENTIFIC COMPUTING
Lehden akronyymi: SIAM J SCI COMPUT
Numero sarjassa: 1
Vuosikerta: 33
Numero: 1
Aloitussivu: 279
Lopetussivu: 302
Sivujen määrä: 24
ISSN: 1064-8275
DOI: https://doi.org/10.1137/090763603
Tiivistelmä
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.
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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