Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems
Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems
Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design
Journal of Computational Physics
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This paper describes a new approach of the Multilevel optimization method (MLO) studied in Refs. 4 and 11. The previous approach of the multilevel method was a multiplicative or serial method since each level is addressed sequentially; it presents, as MG methods, a mesh-independent convergence rate. It is more costly than MG methods, but easier to implement. In order to smooth all the frequency components of the error, the V-cycle strategy is used and it results in several cost functional evaluations per cycle. The proposed new strategy is based on an additive approach. A new preconditioner is deduced from this multilevel method, which provides a better efficiency than the previous method since all frequencies are addressed in only one optimization iteration. An abstract analysis seems to indicate a mesh independent convergence rate. All application to unstructured meshes is derived by combining with a volume agglomeration approach and illustrates the behavior predicted by the theory.