The Multilevel Preconditioner Sample Clauses

The Multilevel Preconditioner. While inexact factorization methods are a promising technique for approximating the inverse of the regularized Xxxxxxx system Aε−1, in this thesis we focus on a geometric multigrid method. Multigrid methods have experienced an increasing popularity for a large range of problems, including the solution of indefinite problems (see, e.g. [87,102] in the context of constrained optimization problems and fluid-structure interaction, k=1 respectively). Let {Ak}L be the linear system matrices representing the discretiza- k=1 tion of (4.21) on a sequence of L meshes, Ak−1 being on a coarser mesh than Ak. Let further {Pk}L−1 be the natural interpolation matrices relating variationally the system matrix Ak to its coarser counterpart Ak−1, and let y be the generic input vec- tor, x the corresponding output vector and σ, ν, A and tol be given constants, where A represents the current level and tol the given tolerance. We propose the following recursive preconditioner:
Sample 1
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