一类椭圆型变分不等式的修正代数多重网格解法及并行计算

提出了一种修正的代数多重网格解法,来求解具有对称二阶椭圆算子的变分不等式的有限元离散问题.该方法基于离散椭圆型变分不等方程的线性互补性,运用积极集策略,对Gauss-Sidel光滑迭代后的近似解进行一个后处理,以满足不等式约束,从而解决了标准代数多重网格法在求解自适应网格上的变分不等式时不收敛的问题.数值实验表明了该算法在一致网格和h-自适应网格上的计算有效性和健壮性.为了减少计算时间,根据该修正算法内在的并行度,提出了一个并行计算格式,数值结果给出了该并行的加速比和效率.

A modified algebraic multigrid algorithm for a class of elliptic variational inequalities and parallization

A modified algebraic multigrid（AMG） algorithm is presented to solve the discrete problems of variational inequalities with symmetric two-order elliptic operator.For the discretized variational inequalities on an h-adaptive mesh,the standard AMG solution did not converge to the exact solution.So an active-set strategy based on the linear complementarity feature of discrete elliptic variational inequalities is introduced.The new algorithm combines the Gauss-Sidel smoother with a post processing to satisfy the inequality constraint for every entry of the solution.The numerical experiments present the efficiency and robustness of the proposed algorithm both on the uniform mesh and on h-adaptive mesh.To shorten computation time,a parallel scheme for the modified AMG algorithm is provided.Numerical experiments illustrate the speedup and efficiency of the parallel scheme.