More than a decade ago, Bramble, Pasciak and Xu developed a framework inanalyzing the multigridmethods with nonnested spaces or non-inherited quadratic forms. It wassubsequently known as the BPX multigrid framework, ...
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More than a decade ago, Bramble, Pasciak and Xu developed a framework inanalyzing the multigridmethods with nonnested spaces or non-inherited quadratic forms. It wassubsequently known as the BPX multigrid framework, which was widely used in the analysis ofmultigrid and domain decomposition methods. However, the framework has an apparent limit in theanalysis of nonnestedv-cyclemethods, and it produces a variable v-cycle, or nonuniform convergencerate v-cyclemethods, or other nonoptimal results in analysis thus far. This paper completes along-time effort in extending the BPX multigrid framework so that it truly covers the nonnestedv-cycle. We will apply the extended BPX framework to the analysis of many v-cyclenonnestedmultigridmethods. Some of them were proven previously only for two-level and W-cycle *** numerical results are presented to support the theoretical analysis of this paper.
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