Isogeometric partition-of-unity boundary integral method for acoustic wave scattering problems

Peake, M.J.; Trevelyan, J.; Coates, G.; Menshykov, O.

Abstract

Isogeometric analysis is the concept of using the same functions that describe a geometry in computer-aided design to approximate unknown elds in numerical simulations. This has become a topic of considerable interest to the boundary integral methods community. This paper introduces an eXtended Isogeometric Boundary Element Method (XIBEM), in which isogeometric functions approximating wave potential are enriched using the partition-of-unity method. In this new method, the isogeometric basis is formed from a space of non-uniform rational B-spline (NURBS) functions multiplied by families of plane waves. Using numerical examples, it is shown that this reduces the total number of equations that need to be solved for a given frequency and geometry of problem; this improves the accuracy of and extends the supported frequency range of the boundary element method to include short wave diraction problems.

Citation

Peake, M., Trevelyan, J., Coates, G., & Menshykov, O. (2013, July). Isogeometric partition-of-unity boundary integral method for acoustic wave scattering problems. Presented at 9th UK Conference on Boundary Integral Methods (UKBIM9), Aberdeen, UK

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 9th UK Conference on Boundary Integral Methods (UKBIM9)
• Start Date: Jul 8, 2013
• End Date: Jul 9, 2013
• Publication Date: Jul 1, 2013
• Deposit Date: Feb 22, 2013
• Publicly Available Date: Aug 12, 2016
• Publisher: University of Aberdeen
• Book Title: Proceedings of the 9th UK Conference on Boundary Integral Methods, University of Aberdeen, UK, 8-9th July 2013.
• Public URL: https://durham-repository.worktribe.com/output/1156387
• Publisher URL: http://www.abdn.ac.uk/engineering/events/accepted-abstracts-190.php