BEM++ - A high performance boundary element library

Many modern applications, such as in acoustic noise computations, medical imaging or radar require the solution of complex mathematical models over domains with homogeneous material properties. Consider for example radar scattering from an airplane. The way in which electromagnetic waves are scattered off a plane is only determined by the shape and material of the surface of the plane and not by the surrounding homogeneous medium (the air). Hence, we can reduce the three dimensional model of simulating the electromagnetic waves in the surrounding of a plane to a computation over the two dimensional surface (the boundary) of the plane.Computing solutions of such boundary problems is the task of a boundary element method (BEM). If a computational model can be reformulated as a boundary problem BEM can lead to a significant reduction of the computational complexity since instead of the whole domain only its boundary needs to be discretised. But the nature of the underlying so called boundary integral equations makes these methods more complicated to implement than domain discretisation methods, and implementations have to be carefully designed to be more efficient than domain based methods.While there are many powerful open source software libraries available for domain based methods, such as finite elements, very little software is available for boundary elements, most of which is commercial and tailored for specialised application areas. With this project we are aiming to change this situation by creating a powerful freely available and versatile boundary element library that can be used by researchers for complex simulations, but also by companies as basis for their own applications.A particular emphasis in the design of the library is being put on the support of modern computing infrastructures. In recent years there has been an explosion in computing power, driven by the advent of multicore processors and the use of powerful gaming graphics cards (GPUs) for scientific simulations. The newest generations of GPU processing boards have a peak performance of over one Teraflops for so called single precision floating point operations and still more than 500 Gigaflops in double precision. As a comparison, two of such cards in a single desktop computer allow a performance, which would have been among the top supercomputers of the world only 10 years ago. But software libraries will have to be specifically designed to take advantage of this enormous computing power. In this project we will optimize right from the start the library to give optimal performance on modern multicore and hybrid CPU/GPU computing environments.During the project we specifically focus on two challenging applications from medical imaging. The first one is Diffuse Optical Tomography (DOT). In DOT tumors such as in the breast or brain are detected by their different light absorption and scattering properties from the surrounding tissue. Certain aspects of DOT can be modeled as boundary problems and the library is going to become a core component for DOT computations at the Centre for Medical Imaging Computing at UCL. In TMS parts of the brain are influenced by an external magnetic field. This can be used to study brain functionality but also has the potential to be helpful in treating conditions such as depression. Understanding TMS and its effect on the brain is an important research area and the new library will be an essential component of the numerical simulations of TMS at the Centre for Integrative Neurosciences and Neurodynamics at Reading.The library is not only interesting for medical imaging applications, but can be used in diverse areas, such as acoustic noise design, or electromagnetic applications. We will organise an outreach event at the end of the project to present the library to a wide range of UK engineering companies and to support them in adopting the new software packages into their own applications.

High-quality open source software has become a cornerstone of modern scientific computing. Not only scientists but also many companies rely on high-quality freely available numerical software in the development of their own applications. Well known examples are for example LAPACK, a core component of almost any code that uses dense linear algebra or deal.II, a versatile library for finite element computations. The library BEM++ for boundary element computations will become part of this high-quality open source software infrastructure by providing a modern and flexible framework for the parallel solution of boundary integral equations in areas as diverse as acoustics, diffuse optics and computational electromagnetics. This will not only benefit research in general but have a positive impact on the UK economy. Knowledge transfer from universities to companies is often difficult, especially in Numerical Analysis, where the efficient implementation of advanced numerical algorithms is a challenge in itself, leading to the effect that companies often lag several years behind in the use of modern algorithms. This library will make the world leading knowledge about the solution of boundary integral equations at Durham, Reading and UCL directly available to companies, allowing them to integrate the library into their own numerical simulations. Such an approach has proved to be hugely successful with the LAPACK project that makes new developments in linear algebra directly available to anyone in the world. Not only will companies benefit from the library itself; this project has a huge potential to lead to University Consultancies to UK companies, in which the library will be employed as part of the overall consultancy process. In particular, the wide contacts available via the project partner NAG will be very useful here. Indeed, if the library is successful there is high potential of commercialisation of the whole package of consultancy together with the software in form of a technical consultancy company. In order to start off a wide range of industrial applications of the library an outreach event will be organised at the end of the project to demonstrate the library to UK companies. This will be support by the Industrial Mathematics Knowledge Transfer Network. Also skill development as part of this process is hugely important for the UK economy. In the US and the Euro zone there exists a wide range of scientific computing software projects at Universities, which not only provide local expertise to companies but directly train graduates in areas of high relevance for modern high-tech engineering industries. The UK is still lacking behind in this development and we believe that this project is a valuable part of an overall initiative to strengthen scientific computing in the UK. Not only will the library itself have a positive impact on the UK economy but the focus applications developed as part of the project are areas of important impact. Diffuse Optical Tomography (DOT) at UCL is an important new technology for the detection of tumors in areas, such as the brain or the breasts. UCL is one of the world leading institutions in the development of DOT and the library will be an important component in this development, allowing to simulate DOT on complex models, which have been out of reach with currently available software tools. Also the application in Transcranial Magnetic Stimulation (TMS) at the Centre for Integrative Neuroscience and Neurodynamics at Reading is of high importance for the development of new techniques for 21st century health care. TMS has the potential by using magnetic fields for the stimulation of areas of the brain to be a valuable tool for the treatment of severe depression and other neurological disorders. The library will become an important computational tool for the simulation of TMS, thus benefitting directly the development of this promising area.