Publicação
Curvilinear crosscuts of subdivision for a domain decomposition method in numerical conformal mapping
| Resumo: | Let $Q:=\{\Omega;z_1,z_2,z_3,z_4\}$ be a quadrilateral consisting of a Jordan domain $\Omega$ and four distinct points $z_1$, $z_2$, $z_3$ and $z_4$ in counterclockwise order on $\partial \Omega$. We consider a domain decomposition method for computing approximations to the conformal module $m(Q)$ of $Q$ in cases where $Q$ is "long'' or, equivalently, $m(Q)$ is "large''. This method is based on decomposing the original quadrilateral $Q$ into two or more component quadrilaterals $Q_1$, $Q_2,\ldots$ and then approximating $m(Q)$ by the sum of the the modules of the component quadrilaterals. The purpose of this paper is to consider ways for determining appropriate crosscuts of subdivision and, in particular, to show that there are cases where the use of curved crosscuts is much more appropriate than the straight line crosscuts that have been used so far. |
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| Autores principais: | Falcão, M. I. |
| Outros Autores: | Papamichael, N.; Stylianopoulos, N.S. |
| Assunto: | Numerical conformal mapping Quadrilaterals Conformal modules Domain decomposition quadrilateral conformal module |
| Ano: | 1999 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | Let $Q:=\{\Omega;z_1,z_2,z_3,z_4\}$ be a quadrilateral consisting of a Jordan domain $\Omega$ and four distinct points $z_1$, $z_2$, $z_3$ and $z_4$ in counterclockwise order on $\partial \Omega$. We consider a domain decomposition method for computing approximations to the conformal module $m(Q)$ of $Q$ in cases where $Q$ is "long'' or, equivalently, $m(Q)$ is "large''. This method is based on decomposing the original quadrilateral $Q$ into two or more component quadrilaterals $Q_1$, $Q_2,\ldots$ and then approximating $m(Q)$ by the sum of the the modules of the component quadrilaterals. The purpose of this paper is to consider ways for determining appropriate crosscuts of subdivision and, in particular, to show that there are cases where the use of curved crosscuts is much more appropriate than the straight line crosscuts that have been used so far. |
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