A three-dimensional adaptive method based on the iterative grid redistribution

In this paper, we develop a three-dimensional adaptive method based on iterative grid redistribution technique introduced in [J. Comput. Phys. 159 (2000) 246]. The key step for the successful implementation is a fast algorithm for grid generation, which is composed of solving the linear grid equation systems and an efficient method for inverting a map by computing iso-surface intersections. To carry out the three-dimensional calculations, the whole procedure is also parallelized on a PC cluster. The improved and extended three-dimensional adaptive method is applied to solve PDEs with singular solutions that have three-dimensional structures. Numerical experiments have demonstrated the methodʹs effectiveness.