Abstract
In this paper, a high-order hybrid mixed finite element method for solving the two-dimensional Helmholtz equation with high wave numbers is presented. The novelty of this method is in using a discrete eigenfunction basis for solving the hybrid problem. Such a basis allows an inexpensive elimination of the inner degrees of freedom, which considerably reduces the size of the resulting linear system. On a rectangular grid with hanging nodes, the eigenfunction basis is constructed by solving a one-dimensional eigenvalue problem for each pair of edge length and polynomial order in the mesh. The eigenvalue problem can be solved efficiently for polynomial orders up to one thousand. Together with the reduced size of the linear system, this makes it possible to work with very high order basis functions, and consequently high frequency waves can be resolved on a coarse mesh. The hp-refinement is used to obtain an accurate solution for a minimal number of degrees of freedom. The effectiveness of our approach is demonstrated with numerical examples using polynomials of the degree up to one thousand.
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.
