An Analysis of Fat Boundary Method with Respect to Algorithmic Parameters and an Interpolation Method for Dual Fat Boundary Method

Abstract

有限元法在学术界和工程界都取得了巨大的成功，然而有限元法也存在一些问题。例如，为了避免网格畸变，需要花费大量的时间进行有限元计算的前处理。目前已经开发了一些不匹配网格方法来解决这个问题。近年来，宽边界法(Fat Boundary Method)被提出并应用于弹性力学领域，而双宽边界法(Dual Fat Boundary Method)是宽边界法的一种改进。这些方法都需要通过迭代法进行求解。本文研究了宽边界法与迭代相关的算法参数对迭代的影响，并提出了一种基于双宽边界法的插值方法，以降低计算成本。 Finite Element Method (FEM) has achieved a great success both in the field of academic and engi-neering. However, there are some problems for FEM. For example, the mesh generation procedure consumes a lot of time for an engineering problem to avoid mesh distortion. Some fictitious domain methods have been developed to tackle this problem. Recently, the Fat Boundary Method (FBM) has been proposed and applied to elasticity and as an improvement of FBM, the Dual Fat Boundary Method (DFBM) is proposed. These methods need an iteration procedure. In this article, the algorithmic parameters related to the iteration of FBM are studied and an interpolation method based on DFBM is proposed to reduce computational costs.