Towards Finite Element Modeling of the Accoustics of Human Head
In this paper, a new formulation for acoustics coupled with linear elasticity is presented. The primary objective of the work is to develop a three dimensional hp adaptive finite element method code destinated for modeling of acoustics of human head. The code will have numerous applications e.g. in designing hearing protection devices for individuals working in high noise environments. The presented work is in the preliminary stage. The variational formulation has been implemented and tested on a sequence of meshes with concentric multi-layer spheres, with material data representing the tissue (the brain), skull and the air. Thus, an efficient solver for coupled elasticity/acoustics problems has been developed, and tested on high contrast material data representing the human head.
[1] H. Kopka and P. W. Daly, A Guide to LATEX, 3rd ed. Harlow, England:
Addison-Wesley, 1999.
[2] Y.C. Chang and L. Demkowicz, Scattering on a spherical shell problem.
Comparison of 3D elasticity and Kirchhoff shell theory results. Computer
Assisted Mechanics and Engineering Science, 2:207229, 1995.
[3] L. Demkowicz. Computing with hp Finite Elements. I.One- and Two-
Dimensional Elliptic and Maxwell Problems. Chapman & Hall/CRC
Press, Taylor and Francis, 2006.
[4] L. Demkowicz, J. Kurtz, D. Pardo, M. Paszy'nski, W. Rachowicz, and
A. Zdunek, Computing with hp Finite Elements. II Frontiers: Three-
Dimensional Elliptic and Maxwell Problems with Applications. Chapman
& Hall/CRC Press, Taylor and Francis, 2007.
[5] P. Geng, J.T. Oden, and R.A. van de Geijn. A parallel multifrontal algorithm
and its implementation. Computer Methods in Applied Mechanics
and Engineering, 149:289301, 1997.
[6] A. Majda. Compressible Fluid Flow and Systems of Conservation Laws
in Several Space Variables, volume 53 of Applied Mathematical Sciences,
Springer-Verlag, New York, 1984.
[7] Ch. Michler, L. Demkowicz, J. Kurtz, and D. Pardo. Improving the
performance of perfectly matched layers ny means of hp-adaptivity. ICES-
Report, 06-17, The University of Texas at Austin, 2006.
[8] MUMPS: a multifrontal massively parallel sparse direct solver,
http://www.enseeiht.fr/lima/apo/MUMPS/.
[9] M. Paszy'nski, Performance of Multi Level Parallel Direct Solver for hp
Finite Element Method, Lecture Notes in Computer Science, 4967:1303-
1312, 2007.
[10] M. Paszy'nski, D. Pardo, C. Torres-Verdin, L. Demkowicz, and V. Calo,
A Multi-Level Direct Substructuring Multi-Frontal Parallel Direct Solver
for hp-Finite Element Method, ICES-Report, 07-33, The University of
Texas at Austin, 2007
[11] P.-O. Persson and G. Strang. A simple mesh generator in matlab. SIAM
Review, 46(2):329 345, 2004.
[12] W. Schroeder, K. Martin and B. Lorensen. The Visualization Toolkit An
Object-Oriented Approach To 3D Graphics, 3rd Edition. Kitware, Inc.,
(http://www.kitware.com).
[13] T. Walsh and L. Demkowicz. A parallel multifrontal solver for hpadaptive
finite elements. Technical Report 1, TICAM, The University of
Texas at Austin, 1999.
[14] T. Walsh, L. Demkowicz and R. Charles. Boundary element modeling
of the external human auditory system. J. Acoust. Soc. Am., 115(3), 2004.
[15] Y. Zhang, C. Bajaj, and B-S Sohn. 3D finite element meshing from
imaging data. The special issue of Computer Methods in Applied Me-
chanics and Engineering (CMAME) on Unstructured Mesh Generation,
194(48-49):50835106, 2005.
[1] H. Kopka and P. W. Daly, A Guide to LATEX, 3rd ed. Harlow, England:
Addison-Wesley, 1999.
[2] Y.C. Chang and L. Demkowicz, Scattering on a spherical shell problem.
Comparison of 3D elasticity and Kirchhoff shell theory results. Computer
Assisted Mechanics and Engineering Science, 2:207229, 1995.
[3] L. Demkowicz. Computing with hp Finite Elements. I.One- and Two-
Dimensional Elliptic and Maxwell Problems. Chapman & Hall/CRC
Press, Taylor and Francis, 2006.
[4] L. Demkowicz, J. Kurtz, D. Pardo, M. Paszy'nski, W. Rachowicz, and
A. Zdunek, Computing with hp Finite Elements. II Frontiers: Three-
Dimensional Elliptic and Maxwell Problems with Applications. Chapman
& Hall/CRC Press, Taylor and Francis, 2007.
[5] P. Geng, J.T. Oden, and R.A. van de Geijn. A parallel multifrontal algorithm
and its implementation. Computer Methods in Applied Mechanics
and Engineering, 149:289301, 1997.
[6] A. Majda. Compressible Fluid Flow and Systems of Conservation Laws
in Several Space Variables, volume 53 of Applied Mathematical Sciences,
Springer-Verlag, New York, 1984.
[7] Ch. Michler, L. Demkowicz, J. Kurtz, and D. Pardo. Improving the
performance of perfectly matched layers ny means of hp-adaptivity. ICES-
Report, 06-17, The University of Texas at Austin, 2006.
[8] MUMPS: a multifrontal massively parallel sparse direct solver,
http://www.enseeiht.fr/lima/apo/MUMPS/.
[9] M. Paszy'nski, Performance of Multi Level Parallel Direct Solver for hp
Finite Element Method, Lecture Notes in Computer Science, 4967:1303-
1312, 2007.
[10] M. Paszy'nski, D. Pardo, C. Torres-Verdin, L. Demkowicz, and V. Calo,
A Multi-Level Direct Substructuring Multi-Frontal Parallel Direct Solver
for hp-Finite Element Method, ICES-Report, 07-33, The University of
Texas at Austin, 2007
[11] P.-O. Persson and G. Strang. A simple mesh generator in matlab. SIAM
Review, 46(2):329 345, 2004.
[12] W. Schroeder, K. Martin and B. Lorensen. The Visualization Toolkit An
Object-Oriented Approach To 3D Graphics, 3rd Edition. Kitware, Inc.,
(http://www.kitware.com).
[13] T. Walsh and L. Demkowicz. A parallel multifrontal solver for hpadaptive
finite elements. Technical Report 1, TICAM, The University of
Texas at Austin, 1999.
[14] T. Walsh, L. Demkowicz and R. Charles. Boundary element modeling
of the external human auditory system. J. Acoust. Soc. Am., 115(3), 2004.
[15] Y. Zhang, C. Bajaj, and B-S Sohn. 3D finite element meshing from
imaging data. The special issue of Computer Methods in Applied Me-
chanics and Engineering (CMAME) on Unstructured Mesh Generation,
194(48-49):50835106, 2005.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51678", author = "Maciej Paszynski and Leszek Demkowicz and Jason Kurtz", title = "Towards Finite Element Modeling of the Accoustics of Human Head", abstract = "In this paper, a new formulation for acoustics coupled with linear elasticity is presented. The primary objective of the work is to develop a three dimensional hp adaptive finite element method code destinated for modeling of acoustics of human head. The code will have numerous applications e.g. in designing hearing protection devices for individuals working in high noise environments. The presented work is in the preliminary stage. The variational formulation has been implemented and tested on a sequence of meshes with concentric multi-layer spheres, with material data representing the tissue (the brain), skull and the air. Thus, an efficient solver for coupled elasticity/acoustics problems has been developed, and tested on high contrast material data representing the human head.
", keywords = "finite element method, acoustics, coupled problems,biomechanics", volume = "2", number = "12", pages = "889-10", }
