Bernstein-Bézier weight-adjusted discontinuous Galerkin methods for wave propagation in heterogeneous media

Guo, Kaihang; Chan, Jesse

doi:10.1016/j.jcp.2019.108971

Cited by 6 publications

(5 citation statements)

References 30 publications

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“…The right hand side of (7) is equivalent to the discretization of a constant coefficient system. This provides additional advantages in that the right hand side can be evaluated using efficient techniques for DG discretizations of constant-coefficient problems [38,39].…”

Section: Energy Stabilitymentioning

confidence: 99%

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

Shukla

Chan

Hoop

et al. 2020

Journal of Computational Physics

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We introduce a high-order weight-adjusted discontinuous Galerkin (WADG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in anisotropic porous media. We use a coupled first-order symmetric stress-velocity formulation [1,2]. Careful attention is directed at (a) the derivation of an energy-stable penalty-based numerical flux, which offers high-order accuracy in presence of material discontinuities, and (b) proper treatment of micro-heterogeneities (sub-element variations) in the numerical scheme. The use of a penalty-based numerical flux avoids the diagonalization of Jacobian matrices into polarized wave constituents necessary when solving element-wise Riemann problems. Micro-heterogeneities are accurately and stably incorporated in the numerical scheme using easily-invertible weight-adjusted mass matrices [3]. The convergence of the proposed numerical scheme is proven and verified by using convergence studies against analytical plane wave solutions. The proposed method is also compared against an existing implementation using the spectral element method to solve the poroelastic wave equation [4].

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Section: Energy Stabilitymentioning

confidence: 99%

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

Shukla

Chan

Hoop

et al. 2020

Journal of Computational Physics

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“…Here,Pq =M −1V T qwq is introduced to simplify the implementation. In (21),Pq andVq are defined on the reference element, andM −1 k is a scaled version of the reference matrix,…”

Section: A Waa-dgtd For Sc-pmlmentioning

confidence: 99%

“…where (21) is used for α = a and (20) is used for α ∈ {b, c, d, 1/κ}. These operators can be directly used on the right hand sides of (10)- (13).…”

Section: A Waa-dgtd For Sc-pmlmentioning

confidence: 99%

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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“…In this case, we must construct and invert a high order weighted mass matrix on each element at every time step. In order to reduce the computational cost, we build upon a weight‐adjusted DG (WADG) formulation, 18 which is low storage, energy stable, and high order accurate for static heterogeneous media 18,19 and curvilinear meshes 20,21 . We then extend this WADG formulation to moving curved meshes and prove that it is energy stable up to a term that converges to zero with the same rate as the optimal

L^{2}

error estimate.…”

Section: Introductionmentioning

confidence: 99%

High order weight‐adjusted discontinuous Galerkin methods for wave propagation on moving curved meshes

Guo

Chan

2021

Numerical Meth Engineering

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This article presents high order accurate discontinuous Galerkin (DG) methods for wave problems on moving curved meshes with general choices of basis and quadrature. The proposed method adopts an arbitrary Lagrangian–Eulerian formulation to map the wave equation from a time‐dependent moving physical domain onto a fixed reference domain. For moving curved meshes, weighted mass matrices must be assembled and inverted at each time step when using explicit time‐stepping methods. We avoid this step by utilizing an easily invertible weight‐adjusted approximation. The resulting semi‐discrete weight‐adjusted DG scheme is provably energy stable up to a term that (for a fixed time interval) converges to zero with the same rate as the optimal L2 error estimate. Numerical experiments using both polynomial and B‐spline bases verify the high order accuracy and energy stability of proposed methods.

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Bernstein-Bézier weight-adjusted discontinuous Galerkin methods for wave propagation in heterogeneous media

Cited by 6 publications

References 30 publications

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

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

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

High order weight‐adjusted discontinuous Galerkin methods for wave propagation on moving curved meshes

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