Four- and eight-node hybrid-Trefftz quadrilateral finite element models for helmholtz problem |
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| Authors: | KY Sze GH Liu H Fan |
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| Affiliation: | 1. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong, PR China;2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore;1. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, 14476 Potsdam, Germany;2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA;3. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München, Germany;1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China;2. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 10081, PR China |
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| Abstract: | In this paper, four- and eight-node quadrilateral finite element models which can readily be incorporated into the standard finite element program framework are devised for plane Helmholtz problems. In these models, frame (boundary) and domain approximations are defined. The former is obtained by nodal interpolation and the latter is truncated from Trefftz solution sets. The equality of the two approximations are enforced along the element boundary. Both the Bessel and plane wave solutions are employed to construct the domain approximation. For full rankness, a minimal of four and eight domain modes are required for the four- and eight-node elements, respectively. By using local coordinates and directions, rank sufficient and invariant elements with minimal and close to minimal numbers of domain approximation modes are devised. In most tests, the proposed hybrid-Trefftz elements with the same number of nodes yield close solutions. In absolute majority of the tests, the proposed elements are considerably more accurate than their single-field counterparts. |
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