686 research outputs found
Conjugate Function Method for Numerical Conformal Mappings
We present a method for numerical computation of conformal mappings from
simply or doubly connected domains onto so-called canonical domains, which in
our case are rectangles or annuli. The method is based on conjugate harmonic
functions and properties of quadrilaterals. Several numerical examples are
given.Comment: 23 pages, 15 figures, 5 table
On moduli of rings and quadrilaterals: algorithms and experiments
Moduli of rings and quadrilaterals are frequently applied in geometric
function theory, see e.g. the Handbook by K\"uhnau. 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 -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 -FEM
algorithm applies to the case of non-polygonal boundary and report results with
concrete error bounds
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