Laplacian transfer across a rough interface: numerical resolution in the conformal plane |
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| Institution: | 1. Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil;2. Laboratoire de Physique de la Matière Condensée, UMR CNRS 7643, Ecole Polytechnique, 91128 Palaiseau Cedex, France;3. International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil;1. Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science & Technology, Nanjing 210-044, China;2. School of Computer & Software, Nanjing University of Information Science & Technology, Jiangsu, Nanjing 210-044, China;3. Huafeng Meteorological Media Group, Beijing 100080, China;4. Computer Science Department, College of Computer and Information Sciences, King Saud University, Riyadh 11362, Saudi Arabia |
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| Abstract: | We use a conformal mapping technique to study the Laplacian transfer across a rough interface. Natural Dirichlet or Von Neumann boundary condition are simply read by the conformal map. Mixed boundary condition, albeit being more complex can be efficiently treated in the conformal plane. We show in particular that an expansion of the potential on a basis of evanescent waves in the conformal plane allows to write a well-conditioned 1D linear system. These general principle are illustrated by numerical results on rough interfaces. |
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