2. Parallel adaptive discontinuous Galerkin discretizations in space and time for linear elastic and acoustic waves

Dörfler, Willy; Findeisen, Stefan; Wieners, Christian; Ziegler, Daniel

doi:10.1515/9783110548488-002

Cited by 11 publications

(3 citation statements)

References 28 publications

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“…• adaptive space-time discontinuous Galerkin methods for linear hyperbolic systems with multilevel preconditioning (Dörfler et al (2016)) and with applications to acoustic, elastic and visco-elastic waves (Dörfler et al (2019)).…”

Section: Further Applications and Outlookmentioning

confidence: 99%

The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods

Baumgarten

Wieners

2021

Computers & Mathematics with Applications

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We present a parallel data structure for the discretization of partial differential equations which is based on distributed point objects and which enables the flexible, transparent, and efficient realization of conforming, nonconforming, and mixed finite elements. This concepts is realized for elliptic, parabolic and hyperbolic model problems, and sample applications are provided by a tutorial complementing a lecture on scientific computing. The corresponding open-source software is based on this parallel data structure, and it supports multilevel methods on nested meshes and 2D and 3D as well as in space-time. Here, we present generic results on porous media applications including multilevel preconditioning and multilevel Monte Carlo methods for uncertainty quantification.

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Section: Further Applications and Outlookmentioning

confidence: 99%

The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods

Baumgarten

Wieners

2021

Computers & Mathematics with Applications

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“…A more detailed version can be found in [6]. This discretization is applied to the acoustic and elastic wave equation in [9]. A discretization using discontinuous ansatz functions in space and time is presented in [12] and applied to the visco-acoustic and visco-elastic wave equation.…”

Section: Solving the Visco-elastic Wave Equation In Space And Timementioning

confidence: 99%

Parallel Space-Time Solutions for the Linear Visco-Acoustic and Visco-Elastic Wave Equation

Dörfler¹,

Wieners²,

Ziegler³

2021

High Performance Computing in Science and Engineering '19

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We present parallel adaptive results for a discontinuous Galerkin spacetime discretization for acoustic and elastic waves with attenuation. The method is based on p-adaptive polynomial discontinuous ansatz and test spaces and a first-order formulation with full upwind fluxes. Adaptivity is controlled by dual-primal error estimation, and the full linear system is solved by a Krylov method with space-time multilevel preconditioning. The discretization and solution method is introduced in Dörfler-Findeisen-Wieners (Comput. Meth. Appl. Math. 2016) for general linear hyperbolic systems and applied to acoustic and elastic waves in Dörfler-Findeisen-Wieners-Ziegler (Radon Series Comp. Appl. Math. 2019); attenuation effects were included in Ziegler (PhD thesis 2019, Karlsruhe Institute of Technology). Here, we consider the evaluation of this method for a benchmark configuration in geophysics, where the convergence is tested with respect to seismograms. We consider the scaling on parallel machines and we show that the adaptive method based on goal-oriented error estimation is able to reduce the computational effort substantially.

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“…depending on a density distribution ρ > 0 and bulk modulus κ > 0 (see [8,Sect. 2] for more details on this model and the relation to elastic waves).…”

Section: Linear Acoustic Wavesmentioning

confidence: 99%

3. A space-time discontinuous Petrov–Galerkin method for acoustic waves

Ernesti¹,

Wieners²

2019

Space-Time Methods

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We apply the discontinuous Petrov-Galerkin (DPG) method to linear acoustic waves in space and time using the framework of first-order Friedrichs systems. Based on results for operators and semigroups of hyperbolic systems, we show that the ideal DPG method is wellposed. The main task is to avoid the explicit use of traces, which are difficult to define in Hilbert spaces with respect to the graph norm of the space-time differential operator. Then, the practical DPG method is analyzed by constructing a Fortin operator numerically. For our numerical experiments we introduce a simplified DPG method with discontinuous ansatz functions on the faces of the space-time skeleton, where the error is bounded by an equivalent conforming DPG method. Examples for a plane wave configuration confirms the numerical analysis, and the computation of a diffraction pattern illustrates a first step to applications.

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2. Parallel adaptive discontinuous Galerkin discretizations in space and time for linear elastic and acoustic waves

Cited by 11 publications

References 28 publications

The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods

The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods

Parallel Space-Time Solutions for the Linear Visco-Acoustic and Visco-Elastic Wave Equation

3. A space-time discontinuous Petrov–Galerkin method for acoustic waves

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