A simple immersed interface method for 3D Poisson equation with jump conditions

• Main Authors: Chang, Yu-Lun, 張毓倫
• Other Authors: Lai, Ming-Chih
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/78064286775806472997

碩士 === 國立交通大學 === 應用數學系數學建模與科學計算碩士班 === 102 === In this paper, we extend a simple version of the immersed interface method (IIM) for 2D Poisson problems to 3D with jump conditions across the interface. The numerical method is based on applying the Taylor's expansions along the normal direction and incorporating the solution and its normal derivative jumps into the finite difference approximations. Then, we can apply some efficient iterative solvers such as the conjugate gradient method to solve the discretized Laplacian linear system. The numerical results show that the scheme is indeed second-order accurate.