# Weighted-norm preconditioners for a multi-layer tide model

@article{Cotter2022WeightednormPF, title={Weighted-norm preconditioners for a multi-layer tide model}, author={Colin J. Cotter and Robert C. Kirby and Hunter Morris}, journal={ArXiv}, year={2022}, volume={abs/2207.02116} }

. We derive a linearized rotating shallow water system modeling tides, which can be discretized by mixed ﬁnite elements. Unlike previous models, this model allows for multiple layers stratiﬁed by density. Like the single-layer case [20] a weighted-norm preconditioner gives a (nearly) parameter-robust method for solving the resulting linear system at each time step, but the all-to-all coupling between the layers in the model poses a signiﬁcant challenge to eﬃciency. Neglecting the inter-layer…

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