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Compatible Finite Element Methods for Geophysical Flows

Automation and Implementation Using Firedrake

  • Thomas H. Gibson
  • Andrew T.T. McRae
  • Colin J. Cotter
  • Lawrence Mitchell
  • David A. Ham
Book

Part of the Mathematics of Planet Earth book series (MPE)

Also part of the SpringerBriefs in Mathematics of Planet Earth book sub series (SBMPE-WCO)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Thomas H. Gibson, Andrew T. T. McRae, Colin J. Cotter, Lawrence Mitchell, David A. Ham
    Pages 1-16
  3. Thomas H. Gibson, Andrew T. T. McRae, Colin J. Cotter, Lawrence Mitchell, David A. Ham
    Pages 17-38
  4. Thomas H. Gibson, Andrew T. T. McRae, Colin J. Cotter, Lawrence Mitchell, David A. Ham
    Pages 39-54
  5. Thomas H. Gibson, Andrew T. T. McRae, Colin J. Cotter, Lawrence Mitchell, David A. Ham
    Pages 55-74
  6. Thomas H. Gibson, Andrew T. T. McRae, Colin J. Cotter, Lawrence Mitchell, David A. Ham
    Pages 75-108
  7. Back Matter
    Pages 109-118

About this book

Introduction

This book introduces recently developed mixed finite element methods for large-scale geophysical flows that preserve essential numerical properties for accurate simulations. The methods are presented using standard models of atmospheric flows and are implemented using the Firedrake finite element library. Examples guide the reader through problem formulation, discretisation, and automated implementation.

The so-called “compatible” finite element methods possess key numerical properties which are crucial for real-world operational weather and climate prediction. The authors summarise the theory and practical implications of these methods for model problems, introducing the reader to the Firedrake package and providing open-source implementations for all the examples covered.

Students and researchers with engineering, physics, mathematics, or computer science backgrounds will benefit from this book. Those readers who are less familiar with the topic are provided with an overview of geophysical fluid dynamics.


Keywords

computational science finite element method geophysical fluid dynamics composable solvers numerical analysis weather prediction atmospheric science Firedrake atmosphere and ocean flows mathematical software automated code generation composable software abstractions 97N80, 74S05, 58D30

Authors and affiliations

  • Thomas H. Gibson
    • 1
  • Andrew T.T. McRae
    • 2
  • Colin J. Cotter
    • 3
  • Lawrence Mitchell
    • 4
  • David A. Ham
    • 5
  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Department of PhysicsOxford UniversityOxfordUK
  3. 3.Department of MathematicsImperial College London LondonUK
  4. 4.Department of Computer ScienceDurham UniversityDurhamUK
  5. 5.Department of MathematicsImperial College LondonLondonUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-23957-2
  • Copyright Information The Author(s), under exclusive licence to Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-23956-5
  • Online ISBN 978-3-030-23957-2
  • Series Print ISSN 2524-4264
  • Series Online ISSN 2524-4272
  • Buy this book on publisher's site