# hpfem/esco2012-boa

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 \title{Modeling of Loud-Speaker with $hp$-Adaptive Methods} \tocauthor{L. Koudela} \author{} \institute{} \maketitle \begin{center} {\large Lukas Koudela}\\ University of West Bohemia\\ {\tt koudela@kte.zcu.cz} \\ \vspace{4mm}{\large Pavel Karban}\\ University of West Bohemia\\ {\tt karban@kte.zcu.cz} \\ \vspace{4mm}{\large Antonin Predota}\\ University of West Bohemia\\ {\tt apredota@kte.zcu.cz} \\ \vspace{4mm}{\large Oldrich Turecek}\\ University of West Bohemia\\ {\tt turecek@ket.zcu.cz} \\ \vspace{4mm}{\large Ladislav Zuzjak}\\ University of West Bohemia\\ {\tt zuzjak@ket.zcu.cz} \end{center} \section*{Abstract} This paper deals with the numerical solution of the acoustic field. Two objectives are followed. The first one is to create a computational model of the loud-speaker with respecting the possibility of diaphragm stiffness. \cite{1kk} The second goal is to obtain directional characteristics of the model with the help of the finite element method. \cite{3kk} The mathematical model is described by the Helmhotz differential equation describing the distribution of the acoustic field. The numerical solution is performed by a fully adaptive higher-order finite element method developed by the hpfem.org group. \cite{2kk} The results of modeling are compared with the results obtained using a commercial software and verified by measurement. The measurement is realized in the anechoic chamber and based on standard. \cite{4kk} The low-frequency speaker is used in suitable frequency range to avoid the diaphragm uncontrolled breakup. \bibliographystyle{plain} \begin{thebibliography}{10} \bibitem{1kk} {\sc J. Borwick}. {Loudspeaker and Headphone Handbook}. Focal Press 2001. \bibitem{2kk} {\sc P.Solin et al.}. {Hermes - Higher-Order Modular Finite Element System}. http://hpfem.org/. \bibitem{3kk} {\sc P. Solin and J. Cerveny and I. Dolezel}. {Arbitrary-Level Hanging Nodes and Automatic Adaptivity in the hp-FEM}. Math. Comput. Simul., Vol. 77, p. 117-132, 2008. \bibitem{4kk} {\sc CSN JC 60268-5}. {Electroacoustic devices}. Part 5: Loudspeakers. \end{thebibliography}