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Finite Element Method for two dimensional Westervelt Equation

Bachelor thesis (2021)

Authors

L.J.F. Hendriks Electrical Engineering, Mathematics and Computer Science

Contributors

M. D. Verweij ImPhys/Medical Imaging (mentor)
D.J.P. Lahaye Mathematical Physics (mentor)
A.W. Heemink Mathematical Physics (graduation committee member)
Dirk Jacob Eric Verschuur ImPhys/Computational Imaging (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2021 Leo Hendriks
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Published Date

05-10-2021

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

This essay shows a two dimensional implementation of the finite element method for the Westervelt equation. To do this the finite element method is first applied to the linear wave equation, then to non-linear diffusion and finally to the Westervelt equation. Both an element by element and a faster vectorized implementation are given for the finite element method. To verify the numerical solution two analytical solutions are used. The first is a one dimensional wave and the second a circularly symmetric wave.

We found that the two-dimensional implementation was successful in computing the Westervelt equation. The error of the solution scales with the mesh size with a power of around 1.7. It was also found that the time step used to compute the solution needs to be small enough for the implementation to converge.

Files

210921_BEP_Westervelt.pdf
(pdf | 2.28 Mb)
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