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Python Framework for HP Adaptive Discontinuous Galerkin Method for Two Phase Flow in Porous Media [article]

Andreas Dedner, Birane Kane, Robert Klöfkorn, Martin Nolte
2018 arXiv   pre-print
In this paper we present a framework for solving two phase flow problems in porous media.  ...  The implementation of the discretization is very flexible allowing for test different formulations of the two phase flow model and adaptation strategies.  ...  Conclusion We have presented a framework that allows to study hp-adaptive schemes for two-phase flow in porous media.  ... 
arXiv:1805.00290v1 fatcat:i6jtzkt2wnf7lmrtlrcibrr5sq

Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Method [article]

Andreas Dedner, Robert Klöfkorn
2021 arXiv   pre-print
This paper discusses a Python interface for the recently published DUNE-FEM-DG module which provides highly efficient implementations of the Discontinuous Galerkin (DG) method for solving a wide range  ...  The Python interfaces are demonstrated for both parabolic and first order hyperbolic PDEs.  ...  Conclusion and outlook In this paper we presented a comprehensive framework for the Discontinuous Galerkin (DG) method with an easy to use Python interface for model description and solver configuration  ... 
arXiv:2009.13416v2 fatcat:uzzbg2acvjehnmsyi3j7jbsvem

The deal.II Library, Version 9.0

Giovanni Alzetta, Daniel Arndt, Wolfgang Bangerth, Vishal Boddu, Benjamin Brands, Denis Davydov, Rene Gassmöller, Timo Heister, Luca Heltai, Katharina Kormann, Martin Kronbichler, Matthias Maier (+3 others)
2018 Journal of Numerical Mathematics  
Discontinuous Galerkin operators are implemented defining two face functions, one for interior and one for boundary faces, in addition to the cell function.  ...  implementation of the Local Discontinuous Galerkin (LDG) method applied to the Poisson equation.  ... 
doi:10.1515/jnma-2018-0054 fatcat:mwyqwwpzajgadktrpcw2rdpiye

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
2010 Numerical Mathematics and Advanced Applications 2009  
The resulting linear systems are solved alternatively by the Multigrid method and Krylov subspace methods. We treat two types of boundary conditions: Dirichlet and natural boundary condition.  ...  We develop a mathematical model of air flow and pollution transport in 2D street canyon.  ...  Examples are given where these methods are applied to compressible two-phase flow problems in porous media, including gravity.  ... 
doi:10.1007/978-3-642-11795-4_6 fatcat:nx4nvuxaxfbcdjknopny53ck5e

The DUNE Framework: Basic Concepts and Recent Developments [article]

Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, Oliver Sander
2020 arXiv   pre-print
and node level performance, non-smooth multigrid methods, and multiscale methods.  ...  A brief discussion on current and future development directions of the framework concludes the paper.  ...  Acknowledgements We thank the Dune users and contributors for their continuous support, as only a vivid community unfolds the power of open source.  ... 
arXiv:1909.13672v3 fatcat:hc5a7al4xvhahdp7fs7f55cwg4

The Dune framework: Basic concepts and recent developments

Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, Oliver Sander
2020 Computers and Mathematics with Applications  
Examples are the porous media simulators OPM [14] and DuMu x [15], the FEM toolbox KASCADE7 [16], and the reduced basis method module Dune-RB [17] .  ...  Examples currently are Python bindings, a generic implementation of grid functions, and support for system testing. Application modules provide frameworks for applications.  ...  A number of applications focus on hp-adaptive schemes, e.g. for continuous Galerkin approximations of Poisson type problems [63] , or discontinuous Galerkin approximations of two-phase flow in porous  ... 
doi:10.1016/j.camwa.2020.06.007 fatcat:37m6di54rbgo3m2y5y5m2hd234

Proceedings of the FEniCS Conference 2017

Jack S. Hale
2017 Figshare  
Proceedings of the FEniCS Conference 2017 that took place 12-14 June 2017 at the University of Luxembourg, Luxembourg.You can cite individual articles in the proceedings using the following bibtex as a  ...  Acknowledgements This work was supported in part by the Belgian Science Policy Office under grant IAP P7/02 and the Walloon Region under grant WIST3 DOMHEX. N.  ...  The FEniCS project has embraced the use of containers for Continuous Integration, and for distribution of pre-configured images for users.  ... 
doi:10.6084/m9.figshare.5086369.v1 fatcat:siyz4enqijbp5byzmdrvi75owm

A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model [article]

M. S. Joshaghani, S. H. S. Joodat, K. B. Nakshatrala
2018 arXiv   pre-print
We present a stable mixed discontinuous Galerkin (DG) formulation for the DPP model. The formulation enjoys several attractive features.  ...  Herein, we consider the double porosity/permeability (DPP) model, which describes the flow of a single-phase incompressible fluid through a porous medium exhibiting two dominant pore-networks with a possibility  ...  The DPP model describes the flow of a single-phase incompressible fluid in a rigid porous medium with two distinct pore-networks with possible mass transfer across them.  ... 
arXiv:1805.01389v2 fatcat:l5v3ec5i6vf7hmbxgnjmais4ki

Composable block solvers for the four-field double porosity/permeability model

M.S. Joshaghani, J. Chang, K.B. Nakshatrala, M.G. Knepley
2019 Journal of Computational Physics  
The DPP model, which is a four-field mathematical model, describes the flow of a single-phase incompressible fluid in a porous medium with two distinct pore-networks and with a possibility of mass transfer  ...  mixed formulation, and stabilized discontinuous Galerkin mixed formulation) for the DPP model.  ...  The DG method supports non-matching grids and hanging nodes, and hence ideal for hp adaptivity [Cockburn et al., 2000] .  ... 
doi:10.1016/j.jcp.2019.02.020 fatcat:2bjez3djfbbkzgqqhpq543xawi

Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next [article]

Salvatore Cuomo, Vincenzo Schiano di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, Francesco Piccialli
2022 arXiv   pre-print
Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method  ...  This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual.  ...  the two temperature distributions of the phases.  ... 
arXiv:2201.05624v4 fatcat:rezb3ctw3bamtfrswcwxlc2cvy

FEMPAR: An Object-Oriented Parallel Finite Element Framework

Santiago Badia, Alberto F. Martín, Javier Principe
2017 Archives of Computational Methods in Engineering  
FEMPAR includes a rich set of algorithms for the discretization step, namely (arbitrary-order) grad, div, and curl-conforming finite element methods, discontinuous Galerkin methods, B-splines, and unfitted  ...  But it is also a framework for researchers that want to experience with new algorithms and solvers, by providing a highly extensible framework.  ...  The extension of FE methods to other applications, like porous media flow or electromagnetism, motivated the design of more complex bases and require different mappings from the reference to the physical  ... 
doi:10.1007/s11831-017-9244-1 pmid:29962831 pmcid:PMC6003441 fatcat:ighq7azdkvfsripfpsqvq5rwtm

FEMPAR: An object-oriented parallel finite element framework [article]

Santiago Badia, Alberto F. Martín, Javier Principe
2017 arXiv   pre-print
FEMPAR includes a rich set of algorithms for the discretization step, namely (arbitrary-order) grad, div, and curl-conforming finite element methods, discontinuous Galerkin methods, B-splines, and unfitted  ...  But it is also a framework for researchers that want to experience with new algorithms and solvers, by providing a highly extensible framework.  ...  The extension of FE methods to other applications, like porous media flow or electromagnetism, motivated the design of more complex bases and require different mappings from the reference to the physical  ... 
arXiv:1708.01773v3 fatcat:spquy7jgmfayrk4m22kphokfam

The neural bases of normalising for accented speech: A repetition suppression functional magnetic resonance imaging study

Patti Adank, Peter Hagoort
2008 Journal of the Acoustical Society of America  
Presence vs. absence of a dip in intensity, duration of that dip, and degree of that dip in decibels are manipulated.  ...  indicate that all three of these characteristics do affect listeners' percept of a consonant, but not sufficiently to completely account for the percept.  ...  Whereas this method is accurate for a weakly heterogeneous moving medium, it degenerates for media with discontinuous properties.  ... 
doi:10.1121/1.2934685 fatcat:qqmjcl5gjzcj7kssv2pi6efwti

Speaker comfort and increase of voice level in lecture rooms

Jonas Brunskog, Anders C. Gade, Gaspar Payà Bellester, Lilian Reig Calbo
2008 Journal of the Acoustical Society of America  
Presence vs. absence of a dip in intensity, duration of that dip, and degree of that dip in decibels are manipulated.  ...  indicate that all three of these characteristics do affect listeners' percept of a consonant, but not sufficiently to completely account for the percept.  ...  Whereas this method is accurate for a weakly heterogeneous moving medium, it degenerates for media with discontinuous properties.  ... 
doi:10.1121/1.2934367 fatcat:xr6gp4ldo5bylnxytx2iumrdmi

Fine‐structure processing, frequency selectivity and speech perception in hearing‐impaired listeners

Olaf Strelcyk, Torsten Dau
2008 Journal of the Acoustical Society of America  
Presence vs. absence of a dip in intensity, duration of that dip, and degree of that dip in decibels are manipulated.  ...  indicate that all three of these characteristics do affect listeners' percept of a consonant, but not sufficiently to completely account for the percept.  ...  Whereas this method is accurate for a weakly heterogeneous moving medium, it degenerates for media with discontinuous properties.  ... 
doi:10.1121/1.2935148 fatcat:nqyyia5pubamnhqgonegghrudm
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