EXTRAPOLATION CASCADIC MULTIGRID METHOD(EXCMG) --- A NEW ALGORITHM FOR SOLVING LARGE SCALE ELLIPTIC PROBLEMS
外推瀑布多网格法(EXCMG)——-大规模求解椭圆问题的新算法

Based on an asymptotic expansion of finite element solution, some new extrapolation formulas are derived, which are the exacter approximations to the finite element solution on refined grid (rather than the solution of partial differential equation). A new extrapolation cascadic multigrid method(EXCMG) is proposed based on the better initial values on refined grid provided by the new extrapolation formulas and their quadratic interpolation. The numerical experiments show that the new algorithm is of the high accuracy and efficiency. Finally a large scale elliptic problem of second order is solved in PC.