A computational framework for the regularization of adjoint analysis in multiscale PDE systems
Journal of Computational Physics
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We propose a novel multiscale algorithm for the problem of model assimilation of data. The algorithm allows one to efficiently perform optimal statistical interpolation of observed data from a given forecast wf and vector of observations wo. The core of the new approach is a combination of two multiscale tools: a multiresolution iterative process and a multigrid fast-summation technique. Our approach allows efficient computations related to global filtering and interpolation of the observations, particularly between data-rich and data-sparse areas. In this paper, we describe an iterative process based on a multiresolution simultaneous displacement technique and a localized variational calculation of iteration parameters. We explain how this process can be efficiently combined with the multigrid fast-summation procedure.