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SpringerBriefs in Mathematics of Planet Earth

Compatible Finite Element Methods for Geophysical Flows

Automation and Implementation Using Firedrake

Authors: Gibson, Th.H., McRae, A.T.T., Cotter, C.J., Mitchell, L., Ham, D.A.

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  • Documents the science behind geophysical fluid dynamics, particularly for atmospheric flows
  • Introduces the Firedrake finite element package, a free and open-source tool for scientific computing
  • Showcases the development and analysis of compatible finite element techniques
  • Contains detailed examples and tutorials for various applications
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eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-030-23957-2
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  • Included format: PDF
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Softcover $59.99
price for USA in USD
  • ISBN 978-3-030-23956-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.


About the authors

Thomas Gibson is a PhD student in the Department of Mathematics at Imperial College London. He is supported and funded by the EPSRC Centre for Doctoral Training in The Mathematics of Planet Earth. His current interests are in the development of scalable numerical algorithms for simulating climate, weather, and ocean dynamics. He is an active developer of the Firedrake project.

Andrew McRae is a Research Associate working on reduced-precision weather forecasting in the Department of Physics at Oxford University. He received his PhD from Imperial College London on the use of finite element methods for weather prediction.

Colin Cotter is a Reader in Numerical Analysis and Scientific Computing at Imperial College London. His research focusses on the design, analysis, and implementation of numerical methods for weather forecasting, ocean modelling, and climate simulation.

Lawrence Mitchell is an Assistant Professor in the Department of Computer Science at Durham University. He received his PhD from the University of Edinburgh in condensed matter physics. His current research is in the development of scientific software for unstructured mesh problems and scalable solver algorithms for discretized PDEs. He is a leading developer of the Firedrake project.

David Ham is a Senior Lecturer in the Department of Mathematics at Imperial College London. His research interests center on the development of high-level abstractions for scientific computing. His interests span computational and computer science and include both new numerical schemes for geophysical fluid dynamics and novel approaches to their implementation. He is the founding developer of the Firedrake project.


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-030-23957-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-030-23956-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Compatible Finite Element Methods for Geophysical Flows
Book Subtitle
Automation and Implementation Using Firedrake
Authors
Series Title
SpringerBriefs in Mathematics of Planet Earth
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive licence to Springer Nature Switzerland AG
eBook ISBN
978-3-030-23957-2
DOI
10.1007/978-3-030-23957-2
Softcover ISBN
978-3-030-23956-5
Series ISSN
2509-7326
Edition Number
1
Number of Pages
VIII, 118
Number of Illustrations
7 b/w illustrations, 18 illustrations in colour
Topics