求解二次Lagrangian有限元方程的瀑布型多重网格法

摘要

针对二次Lagrangian有限元方程,通过将新外推公式和二次插值技巧相结合,为细层提供好的初始值,设计了新的瀑布型多重网格法.数值实验表明,与基于部分几何信息的代数多重网格法相比,新算法有更好的精度和效率.%A new cascadic multigrid method is introduced for a quadratic Lagrangian finite element equation, based on the better initial values on refined grid provided by combining the new extrapolation formula and quadratic interpolation.The numerical experiment results show that the method is of higher accuracy and efficiency than the algebraic multigrid based on geometry information.