Multigrid Method for Elliptic Equations with Discontinuous Coefficients

• Main Authors: Chao-Mei Liu, 劉昭玫
• Other Authors: I-Liang Chern
• Format: Others
• Language: en_US
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/26860329485784364054

碩士 === 國立臺灣大學 === 數學研究所 === 89 === A first-order accurate multgrid method combining with idea of harmonic averaging finite volume method is proposed for solving the elliptic equation: $$-\nabla\cdot (\varepsilon\nabla u )=f$$ in a two dimensional region $\Omega$ with Dirichlet boundary conditions. Here,the coefficient $\varepsilon$ is assumed to be discontinuous across an interface and the source term f is allowed to be a delta function. The underlying grid is regular. The difficulty of discontinuous coefficients is resolved by taking its harmonic averages in finite volume discretization. A multigrid acceleration is adopted to achieve linear convergent rate.