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arXiv · 2207.02116

Weighted-norm preconditioners for a multi-layer tide model

Colin J. Cotter·Robert C. Kirby·Hunter Morris
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Abstract

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~\cite{kirby2021preconditioning} 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 coupling gives a preconditioner that degrades rapidly as the number of layers increases. By a careful analysis of the matrix that couples the layers, we derive a robust method that requires solving a reformulated system that only involves coupling between adjacent layers. Numerical results obtained using Firedrake confirm the theory.

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Colin J. Cotter, Robert C. Kirby, Hunter Morris. 2022-07-05. Weighted-norm preconditioners for a multi-layer tide model. https://arxiv.org/abs/2207.02116

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