Premium
Efficient implementation of high‐order finite elements for Helmholtz problems
Author(s) -
Bériot Hadrien,
Prinn Albert,
Gabard Gwénaël
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5172
Subject(s) - finite element method , a priori and a posteriori , robustness (evolution) , helmholtz free energy , computer science , interpolation (computer graphics) , mathematical optimization , algorithm , helmholtz equation , mathematics , engineering , structural engineering , artificial intelligence , mathematical analysis , chemistry , physics , epistemology , quantum mechanics , gene , boundary value problem , motion (physics) , philosophy , biochemistry
Summary 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 (FEM) 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 minimizing the cost. This is achieved using a simple local a priori error indicator. For simulations involving several frequencies, the use of hierarchical 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. © 2016 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.