Parallel ADI Smoothers for Multigrid
Alternating Direction Implicit(ADI)methods have been in use since 1954 for the solution of both parabolic and elliptic partial differential equations.The convergence of these methods can be dramatically accelerated when good estimates of the eigenvalues of the operator are available,However,in the case of computation on parallel computers,the solution of tridiagonal systems imposes an unreasonable overhead.We discuss methods to lower the overhead imposed by the solution of the corresponding tridiagonal systems.The proposed method has the same convergence properties as a standard ADI method,but all of the solves run in approximately the same time as the “fast direction.Hence,this acts like a transpose-free method while still maintaining the smoothing properties of ADI.Algorithms are derived and convergence theory is provided.
Partial differential equations Distributed/parallel computing Alternating direction implicit method Iterative algorithms
Craig C.Douglas Gundolf Hasse
University of Wyoming School of Energy Resources and Mathematics Department Laramie,WY 82081-1000,US Karl-Franzens-University Graz Institute for Mathematics and Scientific Computing Heinrichstr.36,Room
国际会议
英国伦敦
英文
100-104
2013-09-02（万方平台首次上网日期，不代表论文的发表时间）