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Gabard G.,University of Southampton | Gamallo P.,University of Vigo | Huttunen T.,University of Eastern Finland | Huttunen T.,Kuava Ltd
International Journal for Numerical Methods in Engineering | Year: 2011

Several numerical methods using non-polynomial interpolation have been proposed for wave propagation problems at high frequencies. The common feature of these methods is that in each element, the solution is approximated by a set of local solutions. They can provide very accurate solutions with a much smaller number of degrees of freedom compared to polynomial interpolation. There are however significant differences in the way the matching conditions enforcing the continuity of the solution between elements can be formulated. The similarities and discrepancies between several non-polynomial numerical methods are discussed in the context of the Helmholtz equation. The present comparison is concerned with the ultra-weak variational formulation (UWVF), the least-squares method (LSM) and the discontinuous Galerkin method with numerical flux (DGM). An analysis in terms of Trefftz methods provides an interesting insight into the properties of these methods. Second, the UWVF and the LSM are reformulated in a similar fashion to that of the DGM. This offers a unified framework to understand the properties of several non-polynomial methods. Numerical results are also presented to put in perspective the relative accuracy of the methods. The numerical accuracies of the methods are compared with the interpolation errors of the wave bases. © 2010 John Wiley & Sons, Ltd.

Lahivaara T.,University of Eastern Finland | Dudley Ward N.F.,University of Canterbury | Huttunen T.,University of Eastern Finland | Huttunen T.,Kuava Ltd | And 3 more authors.
Geophysical Journal International | Year: 2014

Small magnitude seismic activity has recently been considered for the assessment of aquifer properties and state. Since the aquifers are modelled as poroelastic, the computational resources needed to simulate the related wave propagation accurately can prove to be impracticable for field studies. Furthermore, the related parameter estimation problem poses significantly higher requirements. In this paper, we investigate model reduction and the Bayesian approximation error (BAE) approach under additional model uncertainties, and establish its feasibility for the estimation of aquifer geometry. The main model approximation is the use of an elastic model in lieu of a poroelastic model. However, the use of an elastic model alone results in a posterior distribution that does not capture the actual parameters. We use the BAE to recover from the model errors. The main uncertainties on which we focus here are related to the unknown material properties and the earthquake itself, including the location and moments. In this feasibility study, we show that the overall approach is able to provide posterior models that capture the actual parameters. © The Authors 2015. Published by Oxford University Press on behalf of The Royal Astronomical Society.

Lahivaara T.,University of Eastern Finland | Huttunen T.,University of Eastern Finland | Huttunen T.,Kuava Ltd
ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers | Year: 2012

The numerical modeling of coupled elastic-acoustic wave problems is a topic of increasing interest in many fields of computational physics and engineering. However, the modeling of wave propagation in complex geometries is a difficult task. Promising candidates for accurately approximating underwater acoustic problems with a reduced computational cost are studied in this work. Namely these methods are the high-order discontinuous Galerkin with the low-storage Runge-Kutta time-stepping scheme for the time-domain problems and the ultra weak variational formulation for the approximations that are computed in the frequency-domain. As the numerical experiment, we study acoustic scattering from cylindrical shaped elastic objects placed on the water/sediment interface.

Simonaho S.-P.,University of Eastern Finland | Lahivaara T.,University of Eastern Finland | Huttunen T.,University of Eastern Finland | Huttunen T.,Kuava Ltd
Applied Acoustics | Year: 2012

Simulations of acoustic wave propagation in time-domain are presented. In the simulations, the discontinuous Galerkin method for spatial derivatives and the low-storage Runge-Kutta approach for time derivatives are used. Three different simulation cases are studied. First, the directivity of loudspeaker is simulated. In the second case, acoustic wave propagation in free space is studied using a short pulse. In the last case, acoustic wave scattering from a metallic cylinder is simulated. All simulation results are compared with measurement results. The measurements for the acoustic wave scattering from the metallic cylinder are made in 2D planes using an automated measurement system. Comparison between the simulation and measurement results are made both temporally and spatially and a good agreement between the simulation and measurement results is found. The results suggest that the discontinuous Galerkin method coupled with the low-storage Runge-Kutta approach is a viable tool for modeling acoustic wave propagation in the time-domain. © 2011 Elsevier Ltd. All rights reserved.

Lahivaara T.,University of Eastern Finland | Dudley Ward N.F.,Otago Computational Modelling Group Ltd | Huttunen T.,University of Eastern Finland | Huttunen T.,Kuava Ltd | And 4 more authors.
Inverse Problems | Year: 2014

We study the inverse problem of estimating the pipeline location from ground-penetrating radar data in the context of Bayesian inversion. Maxwells equations are used to model the electromagnetic wave propagation, and are solved using a high-order discontinuous Galerkin method. The uncertainties related to the wave propagation in inhomogeneous background are taken into account by the Bayesian approximation error (BAE) approach. The inverse problem is solved using the full waveform data. Numerical simulations suggest that by using the BAE the model uncertainties can be taken satisfactorily into account, while at the same time making a significant reduction in the computational burden. Furthermore, the estimates for the location of the pipeline are feasible in the sense that the posterior model supports the actual location. © 2014 IOP Publishing Ltd.

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