Weighted-norm preconditioners for a multi-layer tide model

07/05/2022
by   Colin J. Cotter, et al.
0

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 <cit.> 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.

READ FULL TEXT
research
03/03/2020

Preconditioning mixed finite elements for tide models

We describe a fully discrete mixed finite element method for the lineari...
research
05/01/2021

A family of mixed finite elements for nearly incompressible strain gradient elastic models

We propose a family of mixed finite elements that are robust for the nea...
research
06/14/2019

Supracentrality Analysis of Temporal Networks with Directed Interlayer Coupling

We describe centralities in temporal networks using a supracentrality fr...
research
11/08/2019

Probing the robustness of nested multi-layer networks

We consider a multi-layer network with two layers, L_1, L_2. Their intra...
research
02/07/2022

Universality of parametric Coupling Flows over parametric diffeomorphisms

Invertible neural networks based on Coupling Flows CFlows) have various ...
research
07/25/2020

Flexible and efficient discretizations of multilayer models with variable density

We show that the semi-implicit time discretization approaches previously...
research
04/27/2023

A One-Dimensional Symmetric Force-Based Blending Method for Atomistic-to-Continuum Coupling

Inspired by the blending method developed by [P. Seleson, S. Beneddine, ...

Please sign up or login with your details

Forgot password? Click here to reset