The proposed algorithm combines the optimal convergence rate of the Bramble-Pasciak-Xu (BPX) preconditioner and a natural treatment of local refinement by the hierarchical basis multigrid (HBM) method. The BPX-HBM combination blends the best features of both methods and is applied to 3D magnetostatic scalar potential problems with first order tetrahedral elements. Adaptive local mesh refinement is incorporated in the overall computational process.
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Tsukerman et al. (1999) studied this question.
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