Isogeometric multilevel quadrature for forward and inverse random acoustic scattering

Dölz, Jürgen; Harbrecht, Helmut; Jerez-Hanckes, Carlos; Multerer, Michael

doi:10.1016/j.cma.2021.114242

Cited by 11 publications

(5 citation statements)

References 66 publications

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“…The (known) right hand side vector b contains not only the vector y but also the products of the terms in ũ and t that are prescribed boundary conditions and the corresponding columns of H and G. By solving the linear system in (43), all the unknown coefficients of temperature and heat flux can be obtained. The temperature and flux density distributions around the boundary can then be recovered from ( 23) and (24). As a postprocessing step, the temperature at any interior point P can be simply computed by the BIE for interior point in equation (44).…”

Section: Implementation Of Current Isogeometric Boundary Element Methodsmentioning

confidence: 99%

“…Based on the IGA and scaled boundary element method Zang et al [14] developed a numerical scheme to solve the static bending and free vibration problems of functionally graded material plates. Actually, IGA has attracted a large research community and been successfully applied in elasticity problems [15][16][17], electromagnetics [18][19][20], fluids problems [21,22], accoustic problems [23,24], wave problems [25], contact problems [26], vibration analysis [27][28][29], cracks [30][31][32][33][34], optimization problems [35][36][37], material uncertainty [38], thermal buckling [39], poroelastic material [40], etc. Since the initial IGA was based on NURBS [6] which contains a tensor product form, the uniform NURBS-based refinement scheme is difficult to capture local features of interest.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources

Gong

Qin

Dong

et al. 2022

Applied Mathematical Modelling

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Section: Implementation Of Current Isogeometric Boundary Element Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources

Gong

Qin

Dong

et al. 2022

Applied Mathematical Modelling

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“…For the numerical computation of the Karhunen–Loève expansion, it is sufficient to know the expectation and the covariance at

\sum_{ref} \times ([], 0, T)

, see Reference 36. In our concrete case, it is even sufficient to only compute the Karhunen–Loève expansion in the space–time collocation points.…”

Section: Uncertainty Quantificationmentioning

confidence: 99%

Space–time shape uncertainties in the forward and inverse problem of electrocardiography

Gander

Krause

Multerer

et al. 2021

Numer Methods Biomed Eng

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In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty may be perpetuated in the inverse reconstruction. The purpose of this work is to study the effect of shape uncertainty on the forward and the inverse problem of electrocardiography. To this aim, the problem is first recast into a boundary integral formulation and then discretised with a collocation method to achieve high convergence rates and a fast time to solution. The shape uncertainty of the domain is represented by a random deformation field defined on a reference configuration. We propose a periodic-in-time covariance kernel for the random field and approximate the Karhunen-Loève expansion using low-rank techniques for fast sampling. The space-time uncertainty in the expected potential and its variance is evaluated with an anisotropic sparse quadrature approach and validated by a quasi-Monte Carlo method. We present several numerical experiments on a simplified but physiologically grounded two-dimensional geometry to illustrate the validity of the approach. The tested parametric dimension ranged from 100 up to 600. For the forward problem, the sparse quadrature is very effective. In the inverse problem, the sparse quadrature and the quasi-Monte Carlo method perform as expected, except for the total variation regularisation, where convergence is limited by lack of regularity. We finally investigate an H 1=2 regularisation, which naturally stems from the boundary integral formulation, and compare it to more classical approaches.

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“…For the numerical computation of the Karhunen-Loéve expansion at is sufficient to know the expectation and the covariance at Σ ref , see [29]. In our concrete case, it is even sufficient to only compute the Karhunen-Loéve expansion in the collocation points.…”

Section: Modeling Time-dependent Shape Uncertaintymentioning

confidence: 99%

Space-time shape uncertainties in the forward and inverse problem of electrocardiography

Gander¹,

Krause²,

Multerer³

et al. 2020

Preprint

Self Cite

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In electrocardiography, the "classic" inverse problem consists of finding electric potentials on a surface enclosing the heart from remote recordings on the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty may be perpetuated in the inverse reconstruction.The purpose of this work is to study the effect of shape uncertainty on the forward and the inverse problem of electrocardiography. To this aim, the problem is first recast into a boundary integral formulation and then discretised with a collocation method to achieve high convergence rates and a fast time to solution. The shape uncertainty of the domain is represented by a random deformation field defined on a reference configuration. We propose a periodic-in-time covariance kernel for the random field and approximate the Karhunen-Loève expansion using low-rank techniques for fast sampling. The space-time uncertainty in the expected potential and its variance is evaluated with an anisotropic sparse quadrature approach and validated by a quasi-Monte Carlo method.We present several examples to illustrate the validity of the approach with parametric dimension up to 600. For the forward problem the sparse quadrature is very effective. In the inverse problem, the sparse quadrature and the quasi-Monte Carlo methods perform as expected except with total variation regularisation, in which convergence is limited by lack of regularity. We finally investigate an H 1/2 -Tikhonov regularisation, which naturally stems from the boundary integral formulation, and compare it to more classical approaches.

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Isogeometric multilevel quadrature for forward and inverse random acoustic scattering

Cited by 11 publications

References 66 publications

An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources

An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources

Space–time shape uncertainties in the forward and inverse problem of electrocardiography

Space-time shape uncertainties in the forward and inverse problem of electrocardiography

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