An efficient preconditioner for adaptive Fast Multipole accelerated Boundary Element Methods to model time-harmonic 3D wave propagation

International audienceThis paper presents an efficient algebraic preconditioner to speed up the convergence of Fast Multipole accelerated Boundary Element Methods (FM-BEMs) in the context of time-harmonic 3D wave propagation problems and in particular the case of highly non-uniform discretizations. Such configurations are produced by a recently-developed anisotropic mesh adaptation procedure that is independent of partial differential equation and integral equation. The new preconditioning methodology exploits a complement between fast BEMs by using two nested GMRES algorithms and rapid matrix-vector calculations. The fast inner iterations are evaluated by a coarse hierarchical matrix (H-matrix) representation of the BEM system. These inner iterations produce a preconditioner for FM-BEM solvers. It drastically reduces the number of outer GMRES iterations. Numerical experiments demonstrate significant speedups over non-preconditioned solvers for complex geometries and meshes specifically adapted to capture anisotropic features of a solution, including discontinuities arising from corners and edges

Transient Propagation and Scattering of Quasi-Rayleigh Waves in Plates: Quantitative comparison between Pulsed TV-Holography Measurements and FC(Gram) elastodynamic simulations

We study the scattering of transient, high-frequency, narrow-band quasi-Rayleigh elastic waves by through-thickness holes in aluminum plates, in the framework of ultrasonic nondestructive testing (NDT) based on full-field optical detection. Sequences of the instantaneous two-dimensional (2-D) out-of-plane displacement scattering maps are measured with a self-developed PTVH system. The corresponding simulated sequences are obtained by means of an FC(Gram) elastodynamic solver introduced recently, which implements a full three-dimensional (3D) vector formulation of the direct linear-elasticity scattering problem. A detailed quantitative comparison between these experimental and numerical sequences, which is presented here for the first time, shows very good agreement both in the amplitude and the phase of the acoustic field in the forward, lateral and backscattering areas. It is thus suggested that the combination of the PTVH system and the FC(Gram) elastodynamic solver provides an effective ultrasonic inspection tool for plate-like structures, with a significant potential for ultrasonic NDT applications.Comment: 46 pages, 16 figures, corresponding author Jos\'e Carlos L\'opez-V\'azquez, [email protected]. Changes: 1st, 4th, 5th paragraphs (intro), 3rd, 4th paragraphs (sec. 4); [59-60] cited only in appendixes; old ref. [52] removed; misprints corrected in the uncertainty of c_L (subsec. 3.1), citation to fig. 10 (sec. 4), size of images (caption fig.15); reference to Lam\'e constants removed in subsec. 3.

Numerical modeling and measurement by pulsed television holography of ultrasonic displacement maps in plates with through-thickness defects

We present a novel numerical modeling of ultrasonic Lamb and Rayleigh wave propagation and scattering by through-thickness defects like holes and slots in homogeneous plates, and its experimental verification in both near and far field by a self-developed pulsed TV holography system. In contrast to rigorous vectorial formulation of elasticity theory, our model is based on the 2-D scalar wave equation over the plate surface, with specific boundary conditions in the defects and plate edges. The experimental data include complex amplitude maps of the out-of-plane displacements of the plate surface, obtained by a two-step spatiotemporal Fourier transform method. We find a fair match between the numerical and experimental results, which allows for quantitative characterization of the defects

3D metric-based anisotropic mesh adaptation for the fast multipole accelerated boundary element method in acoustics

International audienceWe introduce a metric-based anisotropic mesh adaptation strategy for the fast multipole accelerated boundary element method (FM-BEM) applied to exterior boundary value problems of the three-dimensional Helmholtz equation. The present methodology is independent of discretiz-ation technique and iteratively constructs meshes refined in size, shape and orientation according to an " optimal " metric reliant on a reconstructed Hessian of the boundary solution. The resulting adaptation is anisotropic in nature and numerical examples demonstrate optimal convergence rates for domains that include geometric singularities such as corners and ridges

Modelling for characterizing defects in plates using two-dimensional maps of instantaneous ultrasonic out-of-plane displacement obtained by pulsed TV-holography

It has been demonstrated that non-destructive inspection of plates can be performed by using two-dimensional maps of instantaneous out-of-plane displacements obtained with a self-developed pulsed TV-holography system. Specifically, the interaction of guided elastic waves with defects produces scattering patterns that contain information about the defects (position, dimensions, orientation, etc.). For quantitative characterization on this basis, modeling of the wave propagation and interaction with the defects is necessary. In fact, the development of models for scattering of waves in plates is yet an active research field in which the most reliable approach is usually based on the rigorous formulation of elasticity theory. By contrast, in this work the capability of a simple two-dimensional scalar model for obtaining a quantitative description of the output two-dimensional maps associated to artificial defects in plates is studied. Some experiments recording the interaction of narrowband Rayleigh waves with artificial defects in aluminum plates are presented, in which the acoustic field is obtained from the TV-holography optical phase-change maps by means of a specially developed two-step spatio-temporal Fourier transform method. For the modeling, harmonic regime and free-stress boundary conditions are assumed. Comparisons between experimental and simulated maps are included for defects with different shapes

Transient Propagation and Scattering of Quasi-Rayleigh Waves in Plates: Quantitative comparison between Pulsed TV-Holography Measurements and FC(Gram) elastodynamic simulations

We study the scattering of transient, high-frequency, narrow-band quasi-Rayleigh elastic waves by through-thickness holes in aluminum plates, in the framework of ultrasonic nondestructive testing (NDT) based on full-field optical detection. Sequences of the instantaneous two-dimensional (2-D) out-of-plane displacement scattering maps are measured with a self-developed PTVH system. The corresponding simulated sequences are obtained by means of an FC(Gram) elastodynamic solver introduced recently, which implements a full three-dimensional (3D) vector formulation of the direct linear-elasticity scattering problem. A detailed quantitative comparison between these experimental and numerical sequences, which is presented here for the first time, shows very good agreement both in the amplitude and the phase of the acoustic field in the forward, lateral and backscattering areas. It is thus suggested that the combination of the PTVH system and the FC(Gram) elastodynamic solver provides an effective ultrasonic inspection tool for plate-like structures, with a significant potential for ultrasonic NDT applications

A New High-Order Fourier Continuation-Based Elasticity Solver for Complex Three-Dimensional Geometries

This thesis presents a new approach for the numerical solution of three-dimensional problems in elastodynamics. The new methodology, which is based on a recently introduced Fourier continuation (FC) algorithm for the solution of Partial Differential Equations on the basis of accurate Fourier expansions of possibly non-periodic functions, enables fast, high-order solutions of the time-dependent elastic wave equation in a nearly dispersionless manner, and it requires use of CFL constraints that scale only linearly with spatial discretizations. A new FC operator is introduced to treat Neumann and traction boundary conditions, and a block-decomposed (sub-patch) overset strategy is presented for implementation of general, complex geometries in distributed-memory parallel computing environments. Our treatment of the elastic wave equation, which is formulated as a complex system of variable-coefficient PDEs that includes possibly heterogeneous and spatially varying material constants, represents the first fully-realized three-dimensional extension of FC-based solvers to date. Challenges for three-dimensional elastodynamics simulations such as treatment of corners and edges in three-dimensional geometries, the existence of variable coefficients arising from physical configurations and/or use of curvilinear coordinate systems and treatment of boundary conditions, are all addressed. The broad applicability of our new FC elasticity solver is demonstrated through application to realistic problems concerning seismic wave motion on three-dimensional topographies as well as applications to non-destructive evaluation where, for the first time, we present three-dimensional simulations for comparison to experimental studies of guided-wave scattering by through-thickness holes in thin plates