Abstract
When the Partition of Unity Method is applied to a discretised integral equation form of the Helmholtz operator, the computational cost is dominated by the evaluation of highly oscillatory integrals over discretisations. This paper presents a new numerical approach that is based on a coordinate transformation to a secondary discretisation that is aligned with an approximation to the curvilinear coordinate in which oscillation is taking place. This transforms a 2D surface integral into an equivalent set of 1D integrals that may be evaluated cheaply yet accurately. A method is proposed for dealing efficiently with difficulties that occurred at the edges of elements in previous work.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
