Finite Element Method Computations of the Acoustics of the Human Head Based on the Projection Based Interpolation Data

Marcin Sieniek, Piotr Gurgul, Maciej Paszyński^*

Department of Computer Science, AGH University of Science and Technology, Kraków, Poland.

DOI: 10.4236/jamp.2014.212119                

Abstract

In this paper we present the Projection Based Interpolation (PBI) technique for construction of continuous approximation of MRI scan data of the human head. We utilize the result of the PBI algorithm to perform three dimensional (3D) Finite Element Method (FEM) simulations of the acoustics of the human head. The computational problem is a multi-physics problem modeled as acoustics coupled with linear elasticity. The computational grid contains tetrahedral finite elements with the number of equations and polynomial orders of approximation varying locally on finite element edges, faces, and interiors. We utilize our own out-of-core parallel direct solver for the solution of this multi-physics problem. The solver minimizes the memory usage by dumping out all local systems from all nodes of the entire elimination tree during the elimination phase.

Keywords

Finite Element Method, Projection Based Interpolation, Acoustics of the Human Head

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Sieniek, M. and Paszyński, M. (2014) Subtree Reuse in Multi-Frontal Solvers for Regular Grids in Step-and-Flash Imprint Nanolithography Modeling. Advanced Engineering Materials, 16, 231-240. http://dx.doi.org/10.1002/adem.201300267
[2]	Demkowicz, L., Gatto, P., Kurtz, J., Paszynski, M., Rachowicz, W., Bleszynski, E., Bleszynski, M., Hamilton, M. and Champlin, C. (2010) Modeling of Bone Conduction of Sound in the Human Head Using hp Finite Elements I. Code Design and Verification. Computer Methods in Applied Mechanics and Engineering, 200, 1757-1773. http://dx.doi.org/10.1016/j.cma.2011.02.001
[3]	Paszyński, M. (2013) Minimizing the Memory Usage with Parallel Out-of-Core Multi-Frontal Direct Solver. Computer Assisted Mechanics and Engineering Sciences, 20, 15-41.
[4]	Demkowicz, L., Kurtz, J., Pardo, D., Paszyński, M., Rachowicz, W. and Zdunek, A. (2007) Computing with hp-Ada- ptive Finite Elements, vol. II. Three Dimensional Elliptic and Maxwell Problems with Applications. Chapmann & Hall, CRC Press.
[5]	Paszyński, M., Pardo, D., Torres-Verdin, C., Demkowicz, L. and Calo, V. (2010) A Parallel Direct Solver for the Self-Adaptive hp Finite Element Method. Journal of Parallel and Distributed Computing, 70, 270-281. http://dx.doi.org/10.1016/j.jpdc.2009.09.007
[6]	Paszyński, M. and Schaefer, R. (2010) Graph Grammar Driven Parallel Partial Differential Equation Solver. Concurrency & Computations, Practise & Experience, 22, 1063-1097.
[7]	Paszyński, M., Pardo, D. and Paszyńska, A. (2010) Parallel Multi-Frontal Solver for p Adaptive Finite Element Modeling of Multi-Physics Computational Problems. Journal of Computational Science, 1, 48-54. http://dx.doi.org/10.1016/j.jocs.2010.03.002