Details of Grant 

EPSRC Reference:	EP/C511026/1
Title:	Adaptivity and Integration Schemes In The Plane Wave Basis BEM For Helmholtz Problems
Principal Investigator:	Trevelyan, Professor J
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Department:	Engineering and Computing Sciences
Organisation:	Durham, University of
Scheme:	Standard Research (Pre-FEC)
Starts:	01 October 2005	Ends:	30 September 2008	Value (£):	145,586
EPSRC Research Topic Classifications:	Acoustics
EPSRC Industrial Sector Classifications:	Aerospace, Defence and Marine Transport Systems and Vehicles
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Summary on Grant Application Form
At Durham we have developed a new way of simulating how sound waves spread from obstacles or from vibrating objects. This lets us understand more about how the shape of objects causes areas surrounding them to be noisy or quiet. Engineers designing these objects can then use these methods to make them more effective. This might mean making quieter cars and planes, etc., but it might also mean less detectable military aircraft, more effective medical body scanners, reduced interference in communications, and many other benefits to society.One way these simulations are done using computer software involves dividing up the surface area of the object being analysed into many small three or four-sided surfaces called 'boundary elements'. We can write mathematical equations relating the sound pressures over the elements, and solve them all together like you might have done with simultaneous equations - except we may have thousands of equations.Boundary elements suffered from a problem, though. The elements could be no larger than 25% of the wavelength. This meant that for high pitched noises, which have a short wavelength, you could need millions of elements. This was a problem because computers had limited memory and such large models could not be run. The 20 million elements needed to analyse radar waves round a Boeing 747 is far too many for today's computers.At Durham, we have developed a new type of boundary element which can cover an area spanning many wavelengths. This overcomes some of the limitations of the earlier methods. The idea is that we say the sound wave at any point is the sum of lots of simple waves going in different directions. The more directions we choose, generally the better answers we get, but we have to be careful as the simultaneous equations become very difficult to solve if we choose too many.We found that this new method gave errors up to 100 million times smaller than the earlier boundary elements, and also allowed us to go up to 15 times the frequency we could analyse with the earlier elements. But these remarkable new benefits come at a cost; more difficult calculations (called integrations). The first project was mostly concerned with developing the new element type and showing its capabilities and benefits. We now hope to look at ways of accelerating the computation. We are going to do this in two ways:1. We will start out with just a few wave directions and then, as the analysis progresses, automatically calculate what the errors are, and where they are greatest. Then we add more wave directions in the problem areas and update the solution. We keep doing this until the program finds the errors are small enough and we have reached a good solution. By doing this we hope that the total number of calculations will be much fewer than we have had to use before. This type of analysis is normally called 'adaptive'.2. We will look at innovative ways of doing the integrations, by looking more carefully at the patterns over each element and designing ways of integrating that can change from one element to the next. This will also reduce the total number of calculations.If this work is successful it will mean that engineers in industry will be able to benefit from faster and more accurate acoustic simulations.
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