EPSRC Reference: 
EP/V002929/1 
Title: 
Functional Underpinnings of SummationByParts Finite Differences 
Principal Investigator: 
Brambley, Dr EJ 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of Warwick 
Scheme: 
New Investigator Award 
Starts: 
01 January 2021 
Ends: 
31 December 2023 
Value (£): 
295,057

EPSRC Research Topic Classifications: 
Continuum Mechanics 
Numerical Analysis 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Computer simulations are regularly used in engineering design, for example to predict the weight a particular design of bridge can support, or how to optimize the shape of a car to minimize drag. Computer simulations are also used throughout science, for example inferring the structure of the centre of the earth from the way seismic waves are transmitted and reflected. Most computer simulations start with a set of governing equations, and then simulate those equations using one of a few different numerical techniques. Two numerical techniques specific to this project are called finite elements and finite differences.
The right technique is needed to solve each problem. Finite elements are often used to simulate solids, such as how bridges support weight. Finite differences are more commonly used to simulate waves, and in particular this project has in mind aeroacoustics simulations used to reduce noise in aircraft engines. A special class of finite differences, called SummationByParts (SBP) finite differences, seem to perform particularly well at this. Interestingly, in my research I have noticed that this class of finite differences has a number of similarities to finite elements that have not been noticed before. The purpose of this project is to investigate this theoretically to see what the similarities and differences are (gaining new knowledge), and then to see how these similarities can be taken advantage of in order to produce better computer simulations (new techniques).
The final part of this project aims to engage with companies who use computer simulations and who could benefit from these new techniques, to try to help them start using the new techniques.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


Sectors submitted by the Researcher 
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Project URL: 

Further Information: 

Organisation Website: 
http://www.warwick.ac.uk 