Premium
Acoustic simulations with higher order finite and infinite elements
Author(s) -
Estorff Otto von,
Petersen Steffen,
Biermann Jan
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700947
Subject(s) - finite element method , convergence (economics) , krylov subspace , polynomial , mathematics , degree of a polynomial , stability (learning theory) , helmholtz equation , helmholtz free energy , basis (linear algebra) , basis function , subspace topology , iterative method , mathematical optimization , mathematical analysis , computer science , physics , geometry , economics , boundary value problem , economic growth , thermodynamics , quantum mechanics , machine learning
The efficiency of finite element based simulations of Helmholtz problems is primarily affected by two facts. First, the numerical solution suffers from the so‐called pollution effect, which leads to very high element resolutions at higher frequencies. Furthermore, the spectral properties of the resulting system matrices, and hence the convergence of iterative solvers, deteriorate with increasing wave numbers. In this contribution the influence of different types of polynomial basis functions on the efficiency and stability of interior as well as exterior acoustic simulations is analyzed. The current investigations show that a proper choice for the polynomial shape approximation may significantly increase the performance of Krylov subspace methods. In particular, the efficiency of higher order finite and infinite elements based on Bernstein polynomial shape approximation and the corresponding iterative solution strategies is assessed for practically relevant numerical examples including the sound radiation from rolling vehicle tires. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)