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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.

Lahivaara T.,University of Eastern Finland | Ward N.F.D.,Otago Computational Modelling Group Ltd | Huttunen T.,University of Eastern Finland | Huttunen T.,Kuava Ltd | And 3 more authors.
Inverse Problems | Year: 2014

Recently, it has been proposed that spontaneous seismic activity could be used in the estimation of hydrological parameters of aquifers such as permeability and storage. Approximate wave propagation models such as ray tracing, which are commonly used in hydrological parameter estimation with active sources and backscattering geometry, are not feasible with passive seismological imaging. With respect to full wave propagation models, the most accurate known model for aquifers is the poroelastic model while bedrock is usually modelled as an elastic medium. Using a poroelastic model in the forward model can be a computationally impractical choice. In this paper, we carry out a feasibility study in which we attempt to estimate the aquifer depth and water table using a highly approximate elastic model also for the aquifer. We adopt the Bayesian approximation error approach in which a statistical model is constructed for the errors that are induced by using model approximations such as sparse meshing and simplified physical models. We consider the problem in a simple two-dimensional geometry and show that straightforward adoption of approximate models leads to inconsistent parameter estimates, that is, the true parameters have essentially vanishing posterior density. On the other hand, using the Bayesian approximation error approach, the parameter estimates are consistent. © 2014 IOP Publishing 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.

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 | 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.

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.

Huttunen T.,Kuava Ltd.
Proceedings of Meetings on Acoustics | Year: 2013

Due to the complexity of measurements for obtaining individual head-related transfer functions (HRTFs), numerical simulations offer an attractive alternative for generating large HRTF data bases. In this study, HRTFs are simulated using a fast multipole boundary element method (BEM). The BEM is well suited for the HRTF simulations. Namely, only the surface of the model geometry is discretized which simplifies the pre-processing compared to other full-wave simulation methods (such as finite element and finite difference methods). The BEM is formulated in frequency domain and the model is solved separately for each frequency. Since a large number of frequencies is needed in wide-band HRTF simulations, the BEM simulation greatly benefits from distributed (or parallel) computing. That is, a single computing unit takes care of a single frequency. In this study, a distributed BEM using cloud computing is introduced. Simulations are computed in a public cloud (Amazon EC2) using a realistic head and torso geometry (3D laser scanned geometry of Bruel & Kjaer HATS 4128 mannequin). The frequency range of the simulations is from 20 to 20000 Hz. The feasibility of cloud computing for simulating HRTFs is examined and first analysis results for the simulated HRTFs are shown. © 2013 Acoustical Society of America.

Lahivaara T.,University of Eastern Finland | Huttunen T.,University of Eastern Finland | Huttunen T.,Kuava Ltd.
Journal of Computational Physics | Year: 2010

In this study a discontinuous Galerkin method (DG) for solving the three-dimensional time-dependent dissipative wave equation is investigated. In the case of unbounded problems, the perfectly matching layer (PML) is used to truncate the computational domain. The aim of this work is to investigate a simple selection method for choosing the basis order for elements in the computational mesh in order to obtain a predetermined error level. The selection method studied here relies on the error estimates provided by Ainsworth [M. Ainsworth, Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods, Journal of Computational Physics 198(1) (2004) 106-130]. The performance of the non-uniform basis is examined using numerical experiments. In the simulated model problems, a feasible method choosing the basis order for arbitrary sized elements is achieved. In simulations, the effect of dissipation and the choices of the PML parameters on the performance of the DG method are also investigated. © 2010 Elsevier Inc.

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