A Multiscale Numerical Method for Poisson Problems in Some Ramified Domains with a Fractal Boundary

DOI10.1137/05064583XzbMath1149.35023MaRDI QIDQ5757469

Yves Achdou, Christophe Sabot, Nicoletta Tchou

Publication date: 7 September 2007

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

zbMATH Keywords

partial differential equationsfractal boundaryself-similar domain

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fractals (28A80)

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Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary ⋮ Computing eigenvalues of the Laplacian on rough domains ⋮ Well-Posed PDE and Integral Equation Formulations for Scattering by Fractal Screens ⋮ Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domains ⋮ Boundary value problems with nonhomogeneous Neumann conditions on a fractal boundary ⋮ Diffusion and propagation problems in some ramified domains with a fractal boundary ⋮ EFFECTS OF A CAVITY’S FRACTAL BOUNDARY ON THE FREE FRONT INTERFACE OF THE POLYMER FILLING STAGE

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