A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: Penalty fluxes and micro-heterogeneities

Shukla, K. K.; Chan, Jesse; Hoop, Maarten V. de; Jaiswal, Priyank

doi:10.1016/j.jcp.2019.109061

Cited by 23 publications

(17 citation statements)

References 48 publications

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“…Compared to the direct implementation that is briefly described above, the proposed method reduces the memory requirement to 15KPML × Nq, where Nq ∼ Np, while maintaining the PML performance. It should be noted here that the WAA has been proved to be energy-stable and preserve the high-order convergence of DGTD [20]- [22]. Indeed, numerical examples presented here also show the proposed method maintains the higher-order accuracy of the solution.…”

Section: Introductionsupporting

confidence: 51%

“…To reduce the memory requirement of implementing (15) with αuu(r) allowed to vary inside the elements, WAA [20] is used. It has been shown that with this approximation DGTD retains provable energy-stability and high-order accuracy [20]- [22]. Note that in the above SC-PML formulation, directly multiplying (5) and 6witḧ a −1 on both sides reduces the number of element-dependent mass matrices to 4.…”

Section: A Waa-dgtd For Sc-pmlmentioning

confidence: 97%

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A Memory-Efficient Implementation of Perfectly Matched Layer With Smoothly Varying Coefficients in Discontinuous Galerkin Time-Domain Method

Chen¹,

Ozakin²,

Ahmed³

et al. 2021

IEEE Trans. Antennas Propagat.

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Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a smoothlyincreasing attenuation coefficient to increase the absorption for a given layer thickness, and, at the same time, to reduce the numerical reflection from the interface between the computation domain and the PML. In discontinuous Galerkin time-domain (DGTD) methods, using a PML coefficient that varies within a mesh element requires a different mass matrix to be stored for every element and therefore significantly increases the memory footprint. In this work, this bottleneck is addressed by applying a weight-adjusted approximation to these mass matrices. The resulting DGTD scheme has the same advantages as the scheme that stores individual mass matrices, namely higher accuracy (due to reduced numerical reflection) and increased meshing flexibility (since the PML does not have to be defined layer by layer) but it requires significantly less memory.

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Section: Introductionsupporting

confidence: 51%

Section: A Waa-dgtd For Sc-pmlmentioning

confidence: 97%

A Memory-Efficient Implementation of Perfectly Matched Layer With Smoothly Varying Coefficients in Discontinuous Galerkin Time-Domain Method

Chen¹,

Ozakin²,

Ahmed³

et al. 2021

IEEE Trans. Antennas Propagat.

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“…Besides, it is noteworthy that penalty fluxes, an alternative to upwind fluxes for dG methods, have also been developed in the literature [11,12,13,14]. To derive numerical fluxes, the penalty method is energy stable and significantly less complicated.…”

Section: Introductionmentioning

confidence: 99%

Systematic development of upwind numerical fluxes for the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media with physical interfaces

Tié

Mouronval

2020

Computer Methods in Applied Mechanics and Engineering

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This research work presents, within a unified and wave oriented variational framework, systematic development of upwind numerical fluxes for the space discontinuous Galerkin methods to model elastic wave propagation in multidimensional anisotropic media with discontinuous material properties. Both first-order velocity-stress and velocity-strain wave formulations are considered. The proposed approach allows the derivation of upwind numerical fluxes in a well structured and hierarchical way according to the degree of inhomogeneity across a physical interface. The numerical fluxes that are exact solutions of a relevant Riemann problem defined at a physical interface are obtained. The developed explicit and intrinsic tensorial expressions of upwind numerical fluxes in multidimensional case allow a better understanding and analysis of the physical meaning of involved terms. As numerical applications, an example with a physical interface separating two materials, one anisotropic and the other isotropic, and an example of polycrystalline material that presents a particular case with a larger number of physical interfaces, are considered. The proposed numerical fluxes are numerically investigated and validated.

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“…Background information and references on numerical approaches to solving the poroelastic wave equation are given in [12] and is not repeated here. More recent work on numerical approaches to the poroelastic wave equation in the DF framework in three dimensions can be found in [25,30,31]. We also provided background on our motivation for studying poroelatic wave problems and the application to delineating aquifers from ground motion data.…”

Section: Introductionmentioning

confidence: 99%

A Discontinuous Galerkin method for three-dimensional elastic and poroelastic wave propagation: forward and adjoint problems

Ward,

Eveson,

Lahivaara

2020

Preprint

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We develop a numerical solver for three-dimensional wave propagation in coupled poroelastic-elastic media, based on a high-order discontinuous Galerkin (DG) method, with the Biot poroelastic wave equation formulated as a first order conservative velocity/strain hyperbolic system. To derive an upwind numerical flux, we find an exact solution to the Riemann problem, including the poroelastic-elastic interface; we also consider attenuation mechanisms both in Biot's low-and high-frequency regimes. Using either a low-storage explicit or implicit-explicit (IMEX) Runge-Kutta scheme, according to the stiffness of the problem, we study the convergence properties of the proposed DG scheme and verify its numerical accuracy. In the Biot low frequency case, the wave can be highly dissipative for small permeabilities; here, numerical errors associated with the dissipation terms appear to dominate those arising from discretisation of the main hyperbolic system.We then implement the adjoint method for this formulation of Biot's equation. In contrast with the usual second order formulation of the Biot equation, we are not dealing with a self-adjoint system but, with an appropriate inner product, the adjoint may be identified with a non-conservative velocity/stress formulation of the Biot equation. We derive dual fluxes for the adjoint and present a simple but illuminating example of the application of the adjoint method.

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A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: Penalty fluxes and micro-heterogeneities

Cited by 23 publications

References 48 publications

A Memory-Efficient Implementation of Perfectly Matched Layer With Smoothly Varying Coefficients in Discontinuous Galerkin Time-Domain Method

A Memory-Efficient Implementation of Perfectly Matched Layer With Smoothly Varying Coefficients in Discontinuous Galerkin Time-Domain Method

Systematic development of upwind numerical fluxes for the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media with physical interfaces

A Discontinuous Galerkin method for three-dimensional elastic and poroelastic wave propagation: forward and adjoint problems

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