Seismic soil-structure interaction analysis by direct boundary element methods

Pak, Ronald Y. S.; Guzina, Bojan B.

doi:10.1016/s0020-7683(98)00263-7

Cited by 71 publications

(77 citation statements)

References 28 publications

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“…Let U (x, ξ) and T (x, ξ) denote the (half-space) elastodynamic Green's tensors, defined such that U iℓ and T iℓ (i, ℓ = 1, 2, 3) respectively denote the ith component of the displacement and traction at ξ ∈ Ω resulting from a unit time-harmonic point force applied at x ∈ Ω in the ℓth direction, with T iℓ vanishing identically on S. Similarly, letÛ (x, ξ) and T (x, ξ) denote the (full-space) elastodynamic Green's tensors corresponding to the material properties of the inclusion. With these definitions, the forward problem (4)-(6) for a semi-infinite solid can be reformulated in terms of a pair of regularized boundary integral equations [11,36]:…”

Section: Direct and Inverse Scattering By Elastic Inclusionsmentioning

confidence: 99%

“…Owing to the high computational cost commonly associated with 3D inverse scattering, regularized boundary integral treatment [36] of the primary, ad- joint, and material-sensitivity problems in (53a-c) is implemented, together with formulas (38) and (44) for • J and J ′ , in a data parallel code using the message-passing interface (MPI) [35]. Data-type parallelism normally applies when identical operations are performed concurrently on multiple data items.…”

Section: Parallel Computationmentioning

confidence: 99%

“…. , 9) stemming from (38) and (44) their central difference approximations computed using the boundary integral approach of [36] and a surface mesh with 650 eight-noded quadrangular elements. The comparison is performed at a = (.1, .1, 3; .5, .5, .5; 2, .35, .9) for a "true" ellipsoid given by a true = (0, 0, 3; .5, .5, .5; 5, .25, 1), assuming an infinite reference domain Ω = R 3 to ensure maximum accuracy for the Green's functions and focus on the performance of the proposed computation scheme.…”

Section: Sensitivity Evaluationmentioning

confidence: 99%

“…For identificatiom purposes, the inverse problem is reduced to the minimization of a cost functional representing the misfit between experimental observations (values of displacements at sensor locations) and their simulations for an assumed inclusion configuration. The latter are based on a coupled system of regularized boundary integral equations [11,36]. For computational efficiency of the gradient search technique employed by the inverse solution, the shape sensitivity of the featured cost functional is evaluated via an adjoint field approach which, besides the matter of elegance, is computationally much more efficient than finitedifference evaluations.…”

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confidence: 99%

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Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework

Bonnet

Guzina

2009

Journal of Computational Physics

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This study deals with elastic-wave identification of discrete heterogeneities (inclusions) in an otherwise homogeneous "reference" solid from limited-aperture waveform measurements taken on its surface. On adopting the boundary integral equation (BIE) framework for elastodynamic scattering, the inverse query is cast as a minimization problem involving experimental observations and their simulations for a trial inclusion that is defined through its boundary, elastic moduli, and mass density. For an optimal performance of the gradient-based search methods suited to solve the problem, explicit expressions for the shape (i.e. boundary) and material sensitivities of the misfit functional are obtained via the adjoint field approach and direct differentiation of the governing BIEs. Making use of the message-passing interface, the proposed sensitivity formulas are implemented in a data-parallel code and integrated into a nonlinear optimization framework based on the direct BIE method and an augmented Lagrangian whose inequality constraints are employed to avoid solving forward scattering problems for physically inadmissible (or overly distorted) trial inclusion configurations. Numerical results for the reconstruction of an ellipsoidal defect in a semi-infinite solid show the effectiveness of the proposed shape-material sensitivity formulation, which constitutes an essential computational component of the defect identification algorithm.

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Section: Direct and Inverse Scattering By Elastic Inclusionsmentioning

confidence: 99%

Section: Parallel Computationmentioning

confidence: 99%

Section: Sensitivity Evaluationmentioning

confidence: 99%

mentioning

confidence: 99%

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Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework

Bonnet

Guzina

2009

Journal of Computational Physics

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“…Its numerical evaluation is therefore complex and time-consuming [21,28]. Singularity and regularization issues for the half-space Green's tensor are addressed in [32], and also [1,30] for layered half-spaces, with applications to soil-structure interaction. Formulations based on full-space and half-space Green's tensors are compared in [31], the latter being found therein to entail prohibitive computational costs.…”

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confidence: 99%

A new Fast Multipole formulation for the elastodynamic half-space Greenʼs tensor

Chaillat

Bonnet

2014

Journal of Computational Physics

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Abstract. In this article, a version of the frequency-domain elastodynamic Fast Multipole-Boundary Element Method (FM-BEM) for semi-infinite media, based on the half-space Green's tensor (and hence avoiding any discretization of the planar traction-free surface), is presented. The half-space Green's tensor is often used (in non-multipole form until now) for computing elastic wave propagation in the context of soil-structure interaction, with applications to seismology or civil engineering. However, unlike the fullspace Green's tensor, the elastodynamic half-space Green's tensor cannot be expressed using derivatives of the Helmholtz fundamental solution. As a result, multipole expansions of that tensor cannot be obtained directly from known expansions, and are instead derived here by means of a partial Fourier transform with respect to the spatial coordinates parallel to the free surface. The obtained formulation critically requires an efficient quadrature for the Fourier integral, whose integrand is both singular and oscillatory. Under these conditions, classical Gaussian quadratures would perform poorly, fail or require a large number of points. Instead, a version custom-tailored for the present needs of a methodology proposed by Rokhlin and coauthors, which generates generalized Gaussian quadrature rules for specific types of integrals, has been implemented. The accuracy and efficiency of the proposed formulation is demonstrated through numerical experiments on single-layer elastodynamic potentials involving up to about N = 6×10 5 degrees of freedom. In particular, a complexity significantly lower than that of the non-multipole version is shown to be achieved. IntroductionThe main advantage of the boundary element method (BEM) is that only the domain boundaries (and possibly interfaces) are discretized, leading to a reduction of the number of degrees of freedom (DOFs) relative to domain-discretization methods. Moreover, elastodyamic field equations and radiation conditions are exactly satisfied by the formulation [26], which avoids cumulative effects of grid dispersion and makes the BEM well suited for modeling wave propagation in unbounded domains. However, the standard BEM [3] leads to fully-populated matrices, which results in high computational complexity (O(N 2 ) per iteration using an iterative solver such as GMRES, where N denotes the number of boundary degrees of freedom (DOFs) of the BE model) and severe problem size limitations induced by the O(N 2 ) size of the influence matrix.The advent of accelerated BE methodologies has dramatically improved the capabilities of BEMs for many areas of application, in a large part owing to the rapid development of the Fast Multipole Method (FMM) over the last 15-20 years [29]. Such approaches have resulted in considerable solution speedup, memory reduction and model size increase. The FMM inherently relies on iterative solvers (usually GMRES), so as to avoid actual computation and storage of the fully-populated influence matrix, and is known to require O(N log N )...

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Dynamisch belastete starre Fundamente

2018

Empfehlungen Des Arbeitskreises Baugrunddynamik

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Seismic soil-structure interaction analysis by direct boundary element methods

Cited by 71 publications

References 28 publications

Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework

Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework

A new Fast Multipole formulation for the elastodynamic half-space Greenʼs tensor

Dynamisch belastete starre Fundamente

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