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Relevant bibliographies by topics / ADER-DG

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Academic literature on the topic 'ADER-DG'

Author: Grafiati

Published: 10 March 2023

Last updated: 31 July 2025

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Journal articles on the topic "ADER-DG"

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Dumbser, Michael, Francesco Fambri, Maurizio Tavelli, Michael Bader, and Tobias Weinzierl. "Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine." Axioms 7, no. 3 (2018): 63. http://dx.doi.org/10.3390/axioms7030063.

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In this paper we discuss a new and very efficient implementation of high order accurate arbitrary high order schemes using derivatives discontinuous Galerkin (ADER-DG) finite element schemes on modern massively parallel supercomputers. The numerical methods apply to a very broad class of nonlinear systems of hyperbolic partial differential equations. ADER-DG schemes are by construction communication-avoiding and cache-blocking, and are furthermore very well-suited for vectorization, and so they appear to be a good candidate for the future generation of exascale supercomputers. We introduce the

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Wenk, S., C. Pelties, H. Igel, and M. Käser. "Regional wave propagation using the discontinuous Galerkin method." Solid Earth Discussions 4, no. 2 (2012): 1129–64. http://dx.doi.org/10.5194/sed-4-1129-2012.

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Abstract. We present an application of the discontinuous Galerkin (DG) method to regional wave propagation. The method makes use of unstructured tetrahedral meshes, combined with a time integration scheme solving the arbitrary high-order derivative (ADER) Riemann problem. The ADER-DG method is high-order accurate in space and time, beneficial for reliable simulations of high-frequency wavefields over long propagation distances. Due to the ease with which tetrahedral grids can be adapted to complex geometries, undulating topography of the Earth's surface and interior interfaces can be readily i

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Wenk, S., C. Pelties, H. Igel, and M. Käser. "Regional wave propagation using the discontinuous Galerkin method." Solid Earth 4, no. 1 (2013): 43–57. http://dx.doi.org/10.5194/se-4-43-2013.

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Abstract. We present an application of the discontinuous Galerkin (DG) method to regional wave propagation. The method makes use of unstructured tetrahedral meshes, combined with a time integration scheme solving the arbitrary high-order derivative (ADER) Riemann problem. This ADER-DG method is high-order accurate in space and time, beneficial for reliable simulations of high-frequency wavefields over long propagation distances. Due to the ease with which tetrahedral grids can be adapted to complex geometries, undulating topography of the Earth's surface and interior interfaces can be readily

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Pelties, C., A. A. Gabriel, and J. P. Ampuero. "Verification of an ADER-DG method for complex dynamic rupture problems." Geoscientific Model Development 7, no. 3 (2014): 847–66. http://dx.doi.org/10.5194/gmd-7-847-2014.

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Abstract. We present results of thorough benchmarking of an arbitrary high-order derivative discontinuous Galerkin (ADER-DG) method on unstructured meshes for advanced earthquake dynamic rupture problems. We verify the method by comparison to well-established numerical methods in a series of verification exercises, including dipping and branching fault geometries, heterogeneous initial conditions, bimaterial interfaces and several rate-and-state friction laws. We show that the combination of meshing flexibility and high-order accuracy of the ADER-DG method makes it a competitive tool to study

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Pelties, C., A. A. Gabriel, and J. P. Ampuero. "Verification of an ADER-DG method for complex dynamic rupture problems." Geoscientific Model Development Discussions 6, no. 4 (2013): 5981–6034. http://dx.doi.org/10.5194/gmdd-6-5981-2013.

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Abstract. We present thorough benchmarking of an arbitrary high-order derivative Discontinuous Galerkin (ADER-DG) method on unstructured meshes for advanced earthquake dynamic rupture problems. We validate the method in comparison to well-established numerical methods in a series of verification exercises, including dipping and branching fault geometries, heterogeneous initial conditions, bi-material cases and several rate-and-state friction constitutive laws. We show that the combination of meshing flexibility and high-order accuracy of the ADER-DG method makes it a competitive tool to study

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Gaburro, Elena, Philipp Öffner, Mario Ricchiuto, and Davide Torlo. "High order entropy preserving ADER-DG schemes." Applied Mathematics and Computation 440 (March 2023): 127644. http://dx.doi.org/10.1016/j.amc.2022.127644.

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Zhao, Xiaoxu, Baining Wang, Gang Li, and Shouguo Qian. "A Path-Conservative ADER Discontinuous Galerkin Method for Non-Conservative Hyperbolic Systems: Applications to Shallow Water Equations." Mathematics 12, no. 16 (2024): 2601. http://dx.doi.org/10.3390/math12162601.

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In this article, we propose a new path-conservative discontinuous Galerkin (DG) method to solve non-conservative hyperbolic partial differential equations (PDEs). In particular, the method here applies the one-stage ADER (Arbitrary DERivatives in space and time) approach to fulfill the temporal discretization. In addition, this method uses the differential transformation (DT) procedure rather than the traditional Cauchy–Kowalewski (CK) procedure to achieve the local temporal evolution. Compared with the classical ADER methods, the current method is free of solving generalized Riemann problems

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Guerrero Fernández, Ernesto, Cipriano Escalante, and Manuel J. Castro Díaz. "Well-Balanced High-Order Discontinuous Galerkin Methods for Systems of Balance Laws." Mathematics 10, no. 1 (2021): 15. http://dx.doi.org/10.3390/math10010015.

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This work introduces a general strategy to develop well-balanced high-order Discontinuous Galerkin (DG) numerical schemes for systems of balance laws. The essence of our approach is a local projection step that guarantees the exactly well-balanced character of the resulting numerical method for smooth stationary solutions. The strategy can be adapted to some well-known different time marching DG discretisations. Particularly, in this article, Runge–Kutta DG and ADER DG methods are studied. Additionally, a limiting procedure based on a modified WENO approach is described to deal with the spurio

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Popov, I. S. "Space–time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation." Computers & Fluids 284 (November 2024): 106425. http://dx.doi.org/10.1016/j.compfluid.2024.106425.

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Castro, C. E., J. Behrens, and C. Pelties. "CUDA-C implementation of the ADER-DG method for linear hyperbolic PDEs." Geoscientific Model Development Discussions 6, no. 3 (2013): 3743–86. http://dx.doi.org/10.5194/gmdd-6-3743-2013.

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Abstract. We implement the ADER-DG numerical method using the CUDA-C language to run the code in a Graphic Processing Unit (GPU). We focus on solving linear hyperbolic partial differential equations where the method can be expressed as a combination of precomputed matrix multiplications becoming a good candidate to be used on the GPU hardware. Moreover, the method is arbitrarily high-order involving intensive work on local data, a property that is also beneficial for the target hardware. We compare our GPU implementation against CPU versions of the same method observing similar convergence pro

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Dissertations / Theses on the topic "ADER-DG"

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Hermann, Verena. "ADER-DG - Analysis, further Development and Applications." Diss., lmu, 2011. http://nbn-resolving.de/urn:nbn:de:bvb:19-125403.

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Chiocchetti, Simone. "High order numerical methods for a unified theory of fluid and solid mechanics." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/346999.

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This dissertation is a contribution to the development of a unified model of continuum mechanics, describing both fluids and elastic solids as a general continua, with a simple material parameter choice being the distinction between inviscid or viscous fluid, or elastic solids or visco-elasto-plastic media. Additional physical effects such as surface tension, rate-dependent material failure and fatigue can be, and have been, included in the same formalism. The model extends a hyperelastic formulation of solid mechanics in Eulerian coordinates to fluid flows by means of stiff algebrai

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Hermann, Verena [Verfasser]. "ADER-DG : analysis, further development and applications / vorgelegt von Verena Hermann." 2010. http://d-nb.info/1010536419/34.

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Molinari, Irene. "Modeling the European crust for seismic wave propagation." Thesis, 2011. http://hdl.handle.net/2122/7188.

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Looking into the structure, composition and behaviour of the Earth is one of the main goals of the seismic studies. Many geophysical problems — such as surface wave, group velocity and full waveform tomography , determination of mantle flows, gravity studies, source inversion — need plausible models as starting point for such studies. Crustal structure varies greatly over small scale length and has a strong effects on seismic waves. A priori models of the crust are thus often used to model seismic wave propagation at large distance and to account for shallow structure when imaging upper m

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Book chapters on the topic "ADER-DG"

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Castro, Cristóbal E., and Eleuterio F. Toro. "ADER DG and FV Schemes for Shallow Water Flows." In Progress in Industrial Mathematics at ECMI 2006. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-71992-2_49.

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Breuer, Alexander, Alexander Heinecke, Leonhard Rannabauer, and Michael Bader. "High-Order ADER-DG Minimizes Energy- and Time-to-Solution of SeisSol." In Lecture Notes in Computer Science. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20119-1_25.

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Wolf, Sebastian, Alice-Agnes Gabriel, and Michael Bader. "Optimization and Local Time Stepping of an ADER-DG Scheme for Fully Anisotropic Wave Propagation in Complex Geometries." In Lecture Notes in Computer Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50420-5_3.

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Conference papers on the topic "ADER-DG"

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Breuer, Alexander, Alexander Heinecke, and Michael Bader. "Petascale Local Time Stepping for the ADER-DG Finite Element Method." In 2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS). IEEE, 2016. http://dx.doi.org/10.1109/ipdps.2016.109.

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В. Подгорнова, О., та И. Л. Софронов. "Моделирование динамической упругости алгоритмами высокого порядка точности на основе подхода ADER-DG". У Geomodel 2008 - 10th EAGE science and applied research conference on oil and gas geological exploration and development. European Association of Geoscientists & Engineers, 2008. http://dx.doi.org/10.3997/2214-4609.201404440.

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Breuer, Alexander, and Alexander Heinecke. "Next-Generation Local Time Stepping for the ADER-DG Finite Element Method." In 2022 IEEE International Parallel and Distributed Processing Symposium (IPDPS). IEEE, 2022. http://dx.doi.org/10.1109/ipdps53621.2022.00046.

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Amler, Thomas G., Ibrahim Hoteit, and Tariq A. Alkhalifah. "A combined ADER-DG and PML approach for simulating wave propagation in unbounded domains." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756380.

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He, Yangyang, Jinghuai Gao, Wei Wang, Xiaokai Wang, and Yicheng Ma. "Elastic wave modeling with high dominant frequency directional point source using ADER‐DG FE scheme." In SEG Technical Program Expanded Abstracts 2009. Society of Exploration Geophysicists, 2009. http://dx.doi.org/10.1190/1.3255404.

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