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Robust Multigrid Methods (Paperback, 1989 Ed.)
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Robust Multigrid Methods (Paperback, 1989 Ed.)
Series: Notes on numerical fluid mechanics, Vol 23
Expected to ship within 10 - 15 working days
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In full multigrid methods for elliptic difference equations one
works on a sequence of meshes where a number of pre- and/or
postsmoothing steps are performed on each level. As is well known
these methods can converge very fast on problems with a smooth
solution and a regular mesh, but the rate of convergence can be
severely degraded for problems with unisotropy or discontinuous
coefficients unless some form of robust smoother is used. Also
problems can arise with the increasingly coarser meshes because for
some types of discretization methods, coercivity may be lost on
coarse meshes and on massively parallel computers the computation
cost of transporting information between computer processors
devoted to work on various levels of the mesh can dominate the
whole computing time. For discussions about some of these problems,
see (11). Here we propose a method that uses only two levels of
meshes, the fine and the coarse level, respec tively, and where the
corrector on the coarse level is equal to a new type of
preconditioner which uses an algebraic substructuring of the
stiffness matrix. It is based on the block matrix tridiagonal
structure one gets when the domain is subdivided into strips. This
block-tridiagonal form is used to compute an approximate
factorization whereby the Schur complements which arise in the
recursive factorization are approximated in an indirect way, i. e."
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