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Efficient implementation of high-order finite elements for Helmholtz problems

Efficient implementation of high-order finite elements for Helmholtz problems
Efficient implementation of high-order finite elements for Helmholtz problems
Computational modeling remains key to the acoustic design of various applications, but it is constrained by the cost of solving large Helmholtz problems at high frequencies. This paper presents an efficient implementation of the high-order Finite Element Method for tackling large-scale engineering problems arising in acoustics. A key feature of the proposed method is the ability to select automatically the order of interpolation in each element so as to obtain a target accuracy while minimising the cost. This is achieved using a simple local a priori error indicator. For simulations involving several frequencies, the use of hierarchic shape functions leads to an efficient strategy to accelerate the assembly of the finite element model. The intrinsic performance of the high-order FEM for 3D Helmholtz problem is assessed and an error indicator is devised to select the polynomial order in each element. A realistic 3D application is presented in detail to demonstrate the reduction in computational costs and the robustness of the a priori error indicator. For this test case the proposed method accelerates the simulation by an order of magnitude and requires less than a quarter of the memory needed by the standard FEM.
acoustics, high-order FEM, pFEM, helmholtz problems, frequency sweep
0029-5981
213-240
Beriot, Hadrien
af5a12ac-8347-48b9-9e15-9319a59163a9
Prinn, Albert
d475a18c-6f30-4053-8298-8ee8c1702ecb
Gabard, Gwenael
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Beriot, Hadrien
af5a12ac-8347-48b9-9e15-9319a59163a9
Prinn, Albert
d475a18c-6f30-4053-8298-8ee8c1702ecb
Gabard, Gwenael
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7

Beriot, Hadrien, Prinn, Albert and Gabard, Gwenael (2016) Efficient implementation of high-order finite elements for Helmholtz problems. International Journal for Numerical Methods in Engineering, 106 (3), 213-240. (doi:10.1002/nme.5172).

Record type: Article

Abstract

Computational modeling remains key to the acoustic design of various applications, but it is constrained by the cost of solving large Helmholtz problems at high frequencies. This paper presents an efficient implementation of the high-order Finite Element Method for tackling large-scale engineering problems arising in acoustics. A key feature of the proposed method is the ability to select automatically the order of interpolation in each element so as to obtain a target accuracy while minimising the cost. This is achieved using a simple local a priori error indicator. For simulations involving several frequencies, the use of hierarchic shape functions leads to an efficient strategy to accelerate the assembly of the finite element model. The intrinsic performance of the high-order FEM for 3D Helmholtz problem is assessed and an error indicator is devised to select the polynomial order in each element. A realistic 3D application is presented in detail to demonstrate the reduction in computational costs and the robustness of the a priori error indicator. For this test case the proposed method accelerates the simulation by an order of magnitude and requires less than a quarter of the memory needed by the standard FEM.

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More information

Accepted/In Press date: 6 November 2015
e-pub ahead of print date: 10 November 2015
Published date: 3 April 2016
Keywords: acoustics, high-order FEM, pFEM, helmholtz problems, frequency sweep
Organisations: Acoustics Group

Identifiers

Local EPrints ID: 384370
URI: https://eprints.soton.ac.uk/id/eprint/384370
ISSN: 0029-5981
PURE UUID: 28aaa755-fbde-41f5-a45a-e99bce6462e7

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Date deposited: 07 Dec 2015 15:31
Last modified: 17 Jul 2017 20:05

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