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Computational Wave Propagation

The modeling of acoustics and elastic wave fields by numerically approximating the characterizing partial differential equations is a difficult problem. Due to the oscillatory behavior of the fields, standard numerical tools (e.g. finite difference (FD), finite element (FE), and boundary element (BE) methods) need several discretization points per wavelength to lead to sufficient accuracy. Hence, the computational complexity of the methods rapidly becomes intolerable when the field extends over several wavelengths.

Discontinuous Galerkin method

A promising approach for accurately approximating wave fields is the discontinuous Galerkin (DG) method. The approach is originally published by Reed and Hill in 1973 for approximating neutron transport equation. The DG method has several features that make it an attractive candidate for large-scale wave simulations. The variational formulation reduces each element of the computational mesh to a subproblem. With the DG method, the communication between adjacent elements is handled using the numerical flux. On the other hand, the variational form allows for easier parallelization of the solver code and the material parameters, the order of the polynomial basis functions, and the length of the time step can be chosen individually for each subproblem.

2.jpeg 3.jpeg

Acoustic wave scattering from an elastic cylindrical shaped object. Snapshot of the diagonal traction component at time instant 2.6 ms (left) and the pressure spectrogram (backscattering) (right).


Past and present collaborators

  • P. Monk, University of Delaware, Department of Mathematical Sciences

  • J. S. Hesthaven, A. Buffa, Ecole Polytechnique Fédérale de Lausanne

  • O. Dazel, J-P. Groby, A. Duclos, G. Gabard, Université du Maine, Laboratoire d'Acoustique de l'Université du Maine

  • J. Astley, University of Southampton, Institute of Sound and Vibration Research

  • P. Göransson, KTH Royal Institute of Technology, Department of Aeronautical and Vehicle Engineering

  • J. Cuenca, LMS International / Siemens Industry Software

  • N. F. Dudley Ward, University of Canterbury, Civil and Natural Resources Engineering

  • T. Huttunen, IDA

  • S-P. Simonaho, School of Pharmacy, University of Eastern Finland
  • Nokia Bell Labs

Recent publications


J. P. Kaipio, T. Huttunen, T. Luostari, T. Lähivaara, P. B. Monk
A Bayesian approach to improving the Born approximation for inverse scattering with high-contrast materials
Inverse Problems 35 (8): 084001, 2019.


M. Niskanen, O. Dazel, J.-P. Groby, A. Duclos, T. Lähivaara
Characterising poroelastic materials in the ultrasonic range - A Bayesian approach
Journal of Sound and Vibration 456: 30-48, 2019.


M. Niskanen, A. Duclos, O. Dazel, J.-P. Groby, J. Kaipio, T. Lähivaara
Estimating the material parameters of an inhomogeneous poroelastic plate from ultrasonic measurements in water
The Journal of the Acoustical Society of America 146 (4): 2596-2607, 2019.


P. Göransson, J. Cuenca, T. Lähivaara
Parameter estimation in modelling frequency response of coupled systems using a stepwise approach
Mechanical Systems and Signal Processing 126: 161-175, 2019.


T. Lähivaara, L. Kärkkäinen, J. M. J. Huttunen, J. S. Hesthaven
Deep convolutional neural networks for estimating porous material parameters with ultrasound tomography
The Journal of the Acoustical Society of America, 143 (2): 1148-1158, 2018.


V. Pulkki, T. Lähivaara, I. Huhtakallio
Effects of flow gradients on directional radiation of human voice
The Journal of the Acoustical Society of America, 143 (2): 1173-1181, 2018.


M. Niskanen, J.-P. Groby, A. Duclos, O. Dazel, J. C. Le Roux, N. Poulain, T. Huttunen, T. Lähivaara
Deterministic and statistical characterization of rigid frame porous materials from impedance tube measurements
Journal of the Acoustical Society of America, 142 (4): 2407, 2017


N. F. Dudley Ward, T. Lähivaara, S. Eveson
A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case
Journal of Computational Physics, 350: 690-727, 2017


T. Luostari, T. Huttunen and P. Monk
Improvements for the Ultra Weak Variational Formulation
International Journal for Numerical Methods in Engineering, 94(6): 598-624, 2013.


T. Luostari, T. Huttunen and P. Monk.
Error estimates for the ultra weak variational formulation in linear elasticity
ESAIM: Mathematical Modelling and Numerical Analysis. 47(1): 183-211, 2013.


G. Gabard, P. Gamallo and T. Huttunen
A comparison of wave-based discontinuous Galerkin, ultra-weak and least-square methods for wave problems
Int. J. Numer. Meth. Engng, 85:380–402, 2011


S.-P. Simonaho, T. Lähivaara, T. Huttunen
Modeling of acoustic wave propagation in time-domain using the discontinuous Galerkin method – A comparison with measurements
Applied Acoustics, 73(2):173-183, 2011.


T. Lähivaara, T. Huttunen
A non-uniform basis order for the discontinuous Galerkin method of the 3D dissipative wave equation with perfectly matched layer
Journal of Computational Physics 229(13): 5144-5160, 2010.


T. Lähivaara, T. Huttunen
A non-uniform basis order for the discontinuous Galerkin method of the acoustic and elastic wave equations
Applied numerical mathematics, 61(4): 473–486, 2010.

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