Diwan, G;
Mohamed, MS;
(2019)
Pollution studies for high order isogeometric analysis and finite element for acoustic problems.
Computer Methods in Applied Mechanics and Engineering
, 350
pp. 701-718.
10.1016/j.cma.2019.03.031.
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Abstract
It is well known that Galerkin finite element methods suffer from pollution error when solving wave problems. To reduce the pollution impact on the solution different approaches were proposed to enrich the finite element method with wave-like functions so that the exact wavenumber is incorporated into the finite element approximation space. Solving wave problems with isogeometric analysis was also investigated in the literature where the superior behaviour of isogeometric analysis due to higher continuity in the underlying basis has been studied. Recently, a plane wave enriched isogeometric analysis was introduced for acoustic problems. However, it remains unquantified the impact of these different approaches on the pollution or how they perform compared to each other. In this work, we show that isogeometric analysis outperforms finite element method in dealing with pollution. We observe similar behaviour when both the methods are enriched with plane waves. Using higher order polynomials with fewer enrichment functions seems to improve the pollution compared to lower order polynomials with more functions. However, the latter still leads to smaller errors using similar number of degrees of freedom. In conclusion, we propose that partition of unity isogeometric analysis can be an efficient tool for wave problems as enrichment eliminates the need for domain re-meshing at higher frequencies and also due to its ability to capture the exact geometry even on coarse meshes as well as its improved pollution behaviour.
| Type: | Article |
|---|---|
| Title: | Pollution studies for high order isogeometric analysis and finite element for acoustic problems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.cma.2019.03.031 |
| Publisher version: | https://doi.org/10.1016/j.cma.2019.03.031 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Pollution error, Finite element method, Isogeometric analysis, Partition of unity, Wave problems, Wave scattering, Helmholtz equation |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10071530 |
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