Fully scalable solver for frequency-domain visco-elastic wave equations in 3D heterogeneous media: A controllability approach

Tang, Jet Hoe; Brossier, Romain; Métivier, Ludovic

doi:10.1016/j.jcp.2022.111514

Cited by 4 publications

(2 citation statements)

References 61 publications

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“…( 2) with a classic weak-form based spectral-element method (SEM) to match all the strong discontinuities in the media. However, regarding the solution of the resulting discrete system, instead of using a direct solver such as PARDISO or MUMPS, we consider applying a parallel iterative solver that is relatively cheap in terms of complexity and storage and can also overcome the weak scalability and load balancing issues in the state-of-the-art parallel direct solvers (Tang et al, 2022). To guarantee the convergence, we impose homogeneous Dirichlet boundary conditions instead of periodic boundary conditions, and together with the symmetry of elasticity tensor C, this makes the stiffness matrix K symmetric positive definite.…”

Section: D Non-periodic Homogenization With the Conjugate Gradient Me...mentioning

confidence: 99%

A fully scalable 3D non-periodic homogenization method to upscale elastic media

Brossier

Capdeville

Métivier

et al. 2023

84th EAGE Annual Conference &Amp; Exhibition

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Full waveform modelling and inversion are essential tools commonly used in seismic imaging. Due to the restrictions from instruments and computing resources, the seismic data are usually frequency-band limited. Thus, the resulting imaging result is a smooth version of the true Earth with the lack of scales smaller than the minimum propagating wavelength. The non-periodic homogenization technique allows for building a long-wave equivalent medium to account for wave interactions with small geological structures and producing similar waveforms as for the original medium at a controlled accuracy. The current non-periodic homogenization implementation is memory and time consuming even with parallel computing techniques. To boost its applicability on large-scale 3D problems, we propose a fully scalable non-periodic homogenization implementation. As the core of the homogenization process, the solution of elastostatic equations and the low-pass filtering operations are formulated as the linear system solution with a matrix-free conjugate-gradient algorithm to exploit highly optimized matrix-vector-product routines developed in our elastic wave modelling and inversion parallel code SEM46. For the algorithm consistency, an approximated Gaussian low-pass filtering is introduced by a cascade of PDE-defined Bessel filters without sacrificing the effectiveness. All these improvements enhance the efficiency, scalability and robustness of the non-periodic homogenization process.

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Section: D Non-periodic Homogenization With the Conjugate Gradient Me...mentioning

confidence: 99%

A fully scalable 3D non-periodic homogenization method to upscale elastic media

Brossier

Capdeville

Métivier

et al. 2023

84th EAGE Annual Conference &Amp; Exhibition

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“…The exact controllability approach was extensively studied in the late 2000s and early 2010s by Mönkölä et al In particular, higher-order spectral element discretizations and fluid-structure interaction problems were considered in [34][35][36]. The approach was recently extended to threedimensional visco-elastic equations [37]. Essentially, the approach is a controlled variation of the asymptotic approach with periodic constraints, in which the time-dependent equation is simulated in time until the time-harmonic solution is reached.…”

Section: Introductionmentioning

confidence: 99%

Time-harmonic electromagnetics with exact controllability and discrete exterior calculus

Mönkölä,

Räbinä,

Rossi

2024

Comptes Rendus. Mécanique

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In this paper, we apply the exact controllability concept for time-harmonic electromagnetic scattering. The problem is presented in terms of the differential forms, and the discrete exterior calculus is utilized for spatial discretization. Accordingly, the physical properties of the problem are maintained. Despite we consider time-harmonic problems, we concentrate on transient wave equations treated by the exact controllability approach. Essentially, we use a controlled variation of the asymptotic approach with periodic constraints, in which the time-dependent equation is simulated in time, until the time-harmonic solution is reached.Résumé. Dans cet article, nous appliquons le concept de contrôlabilité exacte à la dispersion électromagnétique temporelle. Le problème est présenté en termes de formes différentielles et le calcul extérieur discret est utilisé pour la discrétisation spatiale. En conséquence, les propriétés physiques du problème sont maintenues. Bien que nous considérions des problèmes harmoniques temporels, nous nous concentrons sur les équations d'ondes transitoires traitées par l'approche de contrôlabilité exacte. Essentiellement, nous utilisons une variation contrôlée de l'approche asymptotique avec des contraintes périodiques, dans laquelle l'équation dépendant du temps est simulée dans le temps, jusqu'à ce que la solution harmonique temporelle soit atteinte.

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