Finite-element analysis of heat conduction problems with irregular region boundary using multilevel techniques

摘要

An effective finite-element algorithm with fast computation and Ion, memory storage is developed to solve heat transfer problems with an irregular domain and a fixed temperature boundary condition. This algorithm combines the use of the Gauss-Seidel method and a multigrid algorithm and introduces an adjustable factor to correct the irregular boundary to obtain a more accurate result. To illustrate the algorithm, the computational procedures are conducted for heat transfer problems in a quarter circle region. The results show that the numerical solutions are in very good agreement with the exact solutions. The phase-change problem is also investigated in this study. Compared with Tao's results, a good result is presented. This algorithm also can be easily extended to three-dimensional heat transfer problems with fixed temperature boundary conditions. [References: 21]