BOUNDARY INTEGRAL EQUATION METHODS FOR HIGH FREQUENCY SCATTERING PROBLEMS
Lead Research Organisation:
University of Reading
Department Name: Mathematics and Statistics
Abstract
Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.
Publications
Barnett A
(2010)
An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons
in SIAM Journal on Scientific Computing
Betcke T
(2010)
Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation
in Numerical Methods for Partial Differential Equations
Chandler-Wilde S
(2015)
A High Frequency Boundary Element Method for Scattering by Convex Polygons with Impedance Boundary Conditions
in Communications in Computational Physics
Chandler-Wilde S
(2012)
Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering
in Acta Numerica
Chandler-Wilde S
(2018)
Well-Posed PDE and Integral Equation Formulations for Scattering by Fractal Screens
in SIAM Journal on Mathematical Analysis
Chandler-Wilde S
(2015)
Wavenumber-Explicit Continuity and Coercivity Estimates in Acoustic Scattering by Planar Screens
in Integral Equations and Operator Theory
Chandler-Wilde S
(2014)
A high frequency boundary element method for scattering by a class of nonconvex obstacles
in Numerische Mathematik
Chandler-Wilde, S N
(2015)
Unified Transform for Boundary Value Problems: Applications and Advances
Groth S
(2013)
Hybrid numerical-asymptotic approximation for high-frequency scattering by penetrable convex polygons
in IMA Journal of Applied Mathematics
Hewett D
(2013)
A High Frequency $hp$ Boundary Element Method for Scattering by Convex Polygons
in SIAM Journal on Numerical Analysis
| Description | The project was concerned with the invention, analysis and implementation of new numerical methods for computer simulation of high frequency wave scattering problems. These problems have diverse applications, for example in modelling radar, sonar, acoustic noise barriers, medical ultrasound, and scattering of radiation by atmospheric particles. The chief technological difficulty which was tackled in the project was that of computing accurately wave solutions that are highly oscillatory. This project was tackled by researchers in the mathematical sciences departments at the Universities of Reading and Bath, working with project partners at the Met Office, the Institute of Cancer Research, Schlumberger Cambridge Research, and BAE Systems. Conventional numerical schemes (finite element methods, finite difference methods, conventional boundary integral equation methods) are very expensive when the frequency is high. For example, computing scattering by an obstacle that is several hundred wavelengths long using a conventional boundary integral equation method (and this is the most efficient of the methods) requires many hours on a top-of-the-range parallel computer. Further, each halving of the wavelength (corresponding to doubling the frequency) increases the cost by at least a multiple of 4. The point of the project was to investigate, by a combination of computational experiment and detailed mathematical analysis and design, whether it is possible to devise numerical schemes for scattering problems (based on boundary integral equation methods) that have hugely lower cost, in particular that require no or negligible increase in computation time as the frequency increases. To a very significant extent the project was very successful. In particular, for large classes of scattering obstacles that are two-dimensional, in the sense that they have a cross-section that is invariant in some given direction, we have devised numerical schemes that achieve this goal. Precisely, we have shown that this is possible for cross-sections that are: convex smooth obstacles, convex polygons, convex polygons with curved sides, and certain classes of non-convex polygons. These results have been exhibited in the various papers arising from the project in careful numerical experiments. Of interest to the more technically minded, we have also been able to prove mathematically that the algorithms will perform as we predict, this via careful mathematical argument, using results from the areas of mathematics that are numerical analysis, applied analysis, and asymptotic analysis. The project, while to a large extent a proof of concept, has been successful to the extent that there is substantial follow-up funding. Notably, two of the project partners (Schlumberger Gould Research and the Met Office) are funding between them three PhD Students through the Research Councils CASE arrangements, two at Reading, one at Bath, working to move results from the project specifically into application and/or to develop similar methods in a finite element context. The project has also been successful in developing the careers of outstanding young researchers. Notably, working with our support, the first two postdocs on the project have won their own EPSRC funding for related follow-up work, through a personal Postdoctoral Fellowship and a Career Acceleration Fellowship. |
| Exploitation Route | In follow-up work, in a new funded project with the Met Office, we are exploring whether the methods we have developed can, after further adaptation, be made to work to compute how important classes of atmospheric particles scatter incoming light and other electromagnetic radiation. An ability to do these calculations accurately is a crucial component feeding into computational models of climate change, as scattering by aerosols and ice particles in the atmosphere is a crucial part of the earth's energy balance. In other follow-up work we are exploring, with BAE Systems, whether our methods can be used to increase the accuiracy of and speed up computations they make of electromagnetic scattering problems on ships and aircraft, for example to predict the extent of interference between antennae on different parts of a ship/aircraft. |
| Sectors | Environment,Healthcare |
| URL | http://people.bath.ac.uk/eas25/HF/ |
| Description | EPSRC |
| Amount | £80,000 (GBP) |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 10/2011 |
| End | 03/2015 |
| Description | EPSRC |
| Amount | £795,615 (GBP) |
| Funding ID | EP/H004009/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 10/2009 |
| End | 02/2011 |
| Description | EPSRC |
| Amount | £37,227 (GBP) |
| Funding ID | EP/K000012/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 10/2012 |
| End | 09/2014 |
| Description | EPSRC |
| Amount | £409,428 (GBP) |
| Funding ID | EP/I030042/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 10/2011 |
| End | 09/2013 |
| Description | Government of the Swiss Confederation |
| Amount | £28,634 (GBP) |
| Funding ID | 137294 |
| Organisation | Government of the Swiss Confederation |
| Sector | Public |
| Country | Switzerland |
| Start | 03/2012 |
| End | 02/2014 |
| Description | Government of the Swiss Confederation |
| Amount | £28,634 (GBP) |
| Funding ID | 137294 |
| Organisation | Government of the Swiss Confederation |
| Sector | Public |
| Country | Switzerland |
| Start | 03/2012 |
| End | 02/2014 |
| Description | Met Office |
| Amount | £20,000 (GBP) |
| Organisation | Meteorological Office UK |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 10/2011 |
| End | 03/2015 |
| Description | Met Office |
| Amount | £20,000 (GBP) |
| Organisation | Meteorological Office UK |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 10/2011 |
| End | 03/2015 |
| Description | NERC Grouped |
| Amount | £65,937 (GBP) |
| Funding ID | NE/G012628/1 |
| Organisation | Natural Environment Research Council |
| Sector | Public |
| Country | United Kingdom |
| Start | 01/2010 |
| End | 12/2013 |
| Description | Schlumberger |
| Amount | £20,000 (GBP) |
| Organisation | Schlumberger Limited |
| Department | Schlumberger (France) |
| Sector | Private |
| Country | France |
| Start | 01/2010 |
| End | 12/2013 |
| Description | Schlumberger |
| Amount | £20,000 (GBP) |
| Organisation | Schlumberger Limited |
| Department | Schlumberger Cambridge Research |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 01/2010 |
| End | 12/2013 |