225 research outputs found
Numerical computation of the conformal map onto lemniscatic domains
We present a numerical method for the computation of the conformal map from
unbounded multiply-connected domains onto lemniscatic domains. For -times
connected domains the method requires solving boundary integral
equations with the Neumann kernel. This can be done in
operations, where is the number of nodes in the discretization of each
boundary component of the multiply connected domain. As demonstrated by
numerical examples, the method works for domains with close-to-touching
boundaries, non-convex boundaries, piecewise smooth boundaries, and for domains
of high connectivity.Comment: Minor revision; simplified Example 6.1, and changed Example 6.2 to a
set without symmetr
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
Nelikulmion modulin numeerinen laskenta
The module of a quadrilateral is a positive real number which divides quadrilaterals into conformal equivalence classes. This is an introductory text to the module of a quadrilateral with some historical background and some numerical aspects. This work discusses the following topics:
1. Preliminaries 2. The module of a quadrilateral 3. The Schwarz-Christoffel Mapping 4. Symmetry properties of the module 5. Computational results 6. Other numerical methods
Appendices include: Numerical evaluation of the elliptic integrals of the first kind. Matlab programs and scripts and possible topics for future research.
Numerical results section covers additive quadrilaterals and the module of a quadrilateral under the movement of one of its vertex.Nelikulmion moduli on positiivinen reaaliluku, joka jakaa nelikulmiot konformisiin ekvivalenssi luokkiin. Tämä on johdanto teksti nelikulmion moduliin ja sen numeeriseen laskentaan. Lisäksi työssä on näiden alojen historiaa. Työssä käsitellään mm. seuraavia asioita:
1. Esitiedot 2. Nelikulmion modulin määritelmä 3. Schwarz-Christoffel kuvaus 4. Nelikulmion modulin symmetriaominaisuuksia 5. Laskennallisia tuloksia 6. Muita numeerisia menetelmiä
Liitteet sisältävät: Elliptisten, ensimmäisen luokan, integraalien numeerinen laskeminen. Matlab ohjelmia, joita on käytetty työssä ja ehdotuksia tutkimuskohteiksi.
Laskennallisissa tuloksissa osiossa tutkitaan summautuvia nelikulmioita ja nelikulmion modulia. Lisäksi tutkitaan miten nelikulmion moduli muuttuu kun yksi sen kärkipiste liikkuu
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