Full-anisotropic poroelastic wave modeling: A discontinuous Galerkin algorithm with a generalized wave impedance

Zhan, Qiwei; Zhuang, Mingwei; Fang, Yuan; Hu, Yunxiang; Mao, Yiqian; Huang, Wei‐Feng; Zhang, Runren; Wang, Dezhi; Liu, Qing

doi:10.1016/j.cma.2018.12.003

Cited by 16 publications

(8 citation statements)

References 48 publications

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“…Also, the DG framework has been used to solve the governing equations of poroelasticity [9,39,40,41]. de la Puente et al [9] combine ADER time stepping with the DG method using modal basis functions (using a deprecated version of SeisSol).…”

Section: Related Workmentioning

confidence: 99%

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An Efficient ADER-DG Local Time Stepping Scheme for 3D HPC Simulation of Seismic Waves in Poroelastic Media

Wolf,

Galis,

Uphoff

et al. 2021

Preprint

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Many applications from the fields of seismology and geoengineering require simulations of seismic waves in porous media. Biot's theory of poroelasticity describes the coupling between solid and fluid phases and introduces a stiff reactive source term (Darcy's Law) into the elastodynamic wave equations, thereby increasing computational cost of respective numerical solvers and motivating efficient methods utilising High-Performance Computing.We present a novel realisation of the discontinuous Galerkin scheme with Arbitrary High-Order DERivative time stepping (ADER-DG) that copes with stiff source terms. To integrate this source term with a reasonable time step size, we utilise an element-local space-time predictor, which needs to solve medium-sized linear systems -each with 1,000 to 10,000 unknowns -in each element update (i.e., billions of times). We present a novel block-wise back-substitution algorithm for solving these systems efficiently, thus enabling large-scale 3D simulations. In comparison to LU decomposition, we reduce the number of floating-point operations by a factor of up to 25, when using polynomials of degree 6. The block-wise back-substitution is mapped to a sequence of small matrix-matrix multiplications, for which code generators are available to generate highly optimised code.We verify the new solver thoroughly against analytical and semi-analytical reference solutions in problems of increasing complexity. We demonstrate high-order convergence of the scheme for 3D problems. We verify the correct treatment of point sources and boundary conditions, including homogeneous and heterogeneous full space problems as well as problems with traction-free boundary conditions. In addition, we compare against a finite difference solution for a newly defined 3D layer over half-space problem containing an internal material interface and free surface. We find that extremely high accuracy is required to accurately resolve the slow, diffusive P-wave at a or near a free surface, while we also demonstrate that solid particle velocities are not affected by coarser resolutions. We demonstrate that by using a clustered local time stepping scheme, time to solution is reduced by a factor of 6 to 10 compared to global time stepping. We conclude our study with a scaling and performance analysis on the SuperMUC-NG supercomputer, demonstrating our implementation's high computational efficiency and its potential for extreme-scale simulations.

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Section: Related Workmentioning

confidence: 99%

“…Zhang et al [39] use ADER time stepping similar to SeisSol and focus on the coupling between wave propagation in elastic and poroelastic materials. Zhan et al [41] also combine the DG method with Runge Kutta time stepping. However, they omit the stiff source term, by only considering inviscid fluids.…”

Section: Related Workmentioning

confidence: 99%

An Efficient ADER-DG Local Time Stepping Scheme for 3D HPC Simulation of Seismic Waves in Poroelastic Media

Wolf,

Galis,

Uphoff

et al. 2021

Preprint

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“…The differences between the quantities are the corresponding eigenvectors. A detailed derivation can be found in [23,26].…”

Section: Flux and Boundary Conditionsmentioning

confidence: 99%

“…Anisotropic material behavior has been successfully included in Finite Difference schemes [11,22], pseudo-spectral methods [5], Spectral Element codes [13] and Discontinuous Galerkin (DG) schemes for the velocity-stress formulation [20] and for the velocity-strain formulation [26]. Only few open-source codes exist which are able to simulate seismic wave propagation in anisotropic materials and which are also tailored to run efficiently on supercomputers.…”

Section: Introductionmentioning

confidence: 99%

Optimization and Local Time Stepping of an ADER-DG Scheme for Fully Anisotropic Wave Propagation in Complex Geometries

Wolf

Gabriel

Bäder

2020

Lecture Notes in Computer Science

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We present an extension of the earthquake simulation software SeisSol to support seismic wave propagation in fully triclinic anisotropic materials. To our best knowledge, SeisSol is one of the few opensource codes that offer this feature for simulations at petascale performance and beyond. We employ a Discontinuous Galerkin (DG) method with arbitrary high-order derivative (ADER) time stepping. Here, we present a novel implementation of fully physical anisotropy with a twosided Godunov flux and local time stepping. We validate our implementation on various benchmarks and present convergence analysis with respect to analytic solutions. An application example of seismic waves scattering around the Zugspitze in the Bavarian Alps demonstrates the capabilities of our implementation to solve geophysics problems fast.

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“…A detailed review of early studies is given in Carcione et al (2010). Different methods have been used, based on combined finite-volumes/differences on structured grids (Blanc et al, 2013;Carcione & Quiroga-Goode, 1995;Chiavassa et al, 2010;Chiavassa & Lombard, 2011;Dai et al, 1995;Masson et al, 2006;Özdenvar & McMechan, 1997;Wenzlau & Müller, 2009;Zeng et al, 2001;Zhu & McMechan, 1991), pseudo-spectral methods (Özdenvar & McMechan, 1997), discontinuous Galerkin methods (de la Puente et al, 2008;Dupuy et al, 2011;Shukla et al, 2019Shukla et al, , 2020Ward et al, 2017;Zhan et al, 2019), spectral element methods (Morency & Tromp, 2008), and finite-volume methods (Lemoine, 2016;Lemoine et al, 2013). Most of these studies implemented the corresponding equations as a first-order hyperbolic system and used explicit time integration schemes as it is convenient for the elastic wave propagation, except for (Morency & Tromp, 2008;Özdenvar & McMechan, 1997), where a ALKHIMENKOV ET AL.…”

mentioning

confidence: 99%

Resolving Wave Propagation in Anisotropic Poroelastic Media Using Graphical Processing Units (GPUs)

et al. 2021

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Majority of the most powerful supercomputers on the world host hardware accelerators to sustain calculations at the petascale level and beyond. Graphical processing units (GPUs) are amongst widely employed hardware accelerators, initiating a revolution in high-performance computing (HPC) in the last decade. The three-dimensional calculations targeting billions of grid cells -technically impossible resolutions decades ago -became reality. This major breakthrough in HPC and supercomputing comes however with the cost of developing and reengineering scientific codes to efficiently utilize the available computing power. Increasing the low-level parallelism is the key. In Earth sciences, HPC and GPU-accelerated applications target in particular forward and inverse seismic modeling and geodynamics -fields where high spatial and temporal resolutions as well as large spatial domains are required. We here develop a multi-GPU implementation for applications in seismic modeling in porous media.Understanding seismic wave propagation in fluid-saturated porous media enables more accurate interpretation of seismic signals in Earth sciences. The two phase medium is represented by an elastic solid matrix (skeleton) saturated with a compressible viscous fluid. The dynamic response of such an isotropic two phase medium results in two longitudinal waves and one shear wave, as predicted by Frenkel (1944) (see also Pride and Garambois (2005)). The wave of the first kind (fast wave) is a true longitudinal wave where the solid matrix motion and the fluid velocity vector fields are in-phase. The wave of the second kind (slow wave) is a highly attenuated wave where the solid matrix motion and the fluid velocity vector fields are

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Full-anisotropic poroelastic wave modeling: A discontinuous Galerkin algorithm with a generalized wave impedance

Cited by 16 publications

References 48 publications

An Efficient ADER-DG Local Time Stepping Scheme for 3D HPC Simulation of Seismic Waves in Poroelastic Media

An Efficient ADER-DG Local Time Stepping Scheme for 3D HPC Simulation of Seismic Waves in Poroelastic Media

Optimization and Local Time Stepping of an ADER-DG Scheme for Fully Anisotropic Wave Propagation in Complex Geometries

Resolving Wave Propagation in Anisotropic Poroelastic Media Using Graphical Processing Units (GPUs)

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