An Extrapolation Cascadic Multigrid Method for Elliptic Problems on Reentrant Domains (Advances in Applied Mathematics and Mechanics, 2021)
This paper proposes an extrapolation cascadic multigrid (EXCMG) methodto solve elliptic problems in domains with reentrant corners. On a class of λ-gradedmeshes, we derive some new extrapolation formulas to construct a high-order approximationto the finite element solution on the next finer mesh using the numerical solutionson two-level of grids (current and previous grids). Then, this high-order approximationis used as the initial guess to reduce computational cost of the conjugategradient method. Recursive application of this idea results in the EXCMG methodproposed in this paper. Finally, numerical results for a crack problem and an $L$-shapedproblem are presented to verify the efficiency and effectiveness of the proposed EXCMGmethod.