327 Interdisciplinary Advances in Boundary Element Methods

Chris Wojtan, IST Austria
David Hahn, IST Austria
Boundary element methods are of interest for a wide variety of numerical simulations because the required degrees of freedom scale with the surface area of the computational domain, rather than the volume as with many other simulation methods. As such, boundary elements promise good computational complexity as well as direct applicability to surface-based geometric models used in CAD engineering as well as 3D animation (and many other fields of research).
Nevertheless, the BEM imposes more stringent restrictions on the type of physical phenomena and material behavior that can be simulated than some of its volumetric counterparts. Similarly, a straightforward implementation of BEM will not scale well due to the dense matrices involved, requiring fast approximation methods to obtain good performance in practice.
In recent years researchers have developed numerous novel applications based on the boundary element framework including time-dependent structural mechanics, isogeometric approaches working directly on CAD data, applications for geometry processing and shape optimization, fracture mechanics, as well as acoustics and free-surface fluid flow. Similarly, the underlying mathematical and numerical methods are steadily advancing, with ongoing research, for example, on dual reciprocity methods as well as fast multipole approximations.
In this session we hope to bring together researchers from various fields who have helped to make boundary element methods faster and applicable to an ever increasing range of simulation tasks in the fields of mechanical engineering, computational physics, computer graphics and more. We also wish to facilitate communication between the various disciplines and inspire new research towards novel surface-based numerical simulation methods.