Multipoint flux approximation methods for quadrilateral grids. 9th International Forum on Reservoir Simulation, 2007. ,
, Discretization on non-orthogonal, curvilinear grids for multi-phase flow. 4th European Conference on the Mathematics of Oil Recovery, vol.06, 1994.
Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media, J. Comp. Phys, vol.127, issue.1, pp.2-14, 1996. ,
Analysis of a new nonlinear subdivision scheme. applications in image processing, Found. Comput. Math, pp.193-225, 2006. ,
On the stability of the pph nonlinear multiresolution, Appl. Comput. Harm. Anal, vol.18, pp.198-206, 2005. ,
A review on the piecewise polynomial harmonic interpolation, Appl. Numer. Math, vol.58, pp.1168-1185, 2008. ,
Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow, part i, J. Comp. Phys, vol.135, pp.103-114, 1997. ,
Comparison of different interpolation operators including nonlinear subdivision schemes in the simulation of particle trajectories, J. Comp. Phys, vol.236, pp.346-366, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01464719
A multigrid tutorial, 2000. ,
A control volume finite-element method for two-dimensional fluid flow and heat transfer, Num. Heat Transfer, vol.6, pp.245-261, 1983. ,
Transport process in a plasma, Rev. in Plasma Physics, vol.1, pp.205-311, 1965. ,
On locking and robustness in the finite element method, J. Comp. Phys, vol.29, issue.5, pp.1261-1293, 1992. ,
Analysis of variable-degree hdg methods for convection-diffusion equations. part i: General nonconforming meshes ,
, IMA J Numer Anal, vol.32, pp.1267-1293, 2012.
Analysis of variable-degree hdg methods for convection-diffusion equations. part ii: Semimatching nonconforming meshes, Mathematics of Computation, vol.83, pp.87-111, 2014. ,
A superconvergent ldghybridizable galerkin method for second-order elliptic problems, Math. Comput, vol.77, pp.1887-1916, 2008. ,
Unified hybridization of discontinuous galerkin, mixed, and continuous galerkin methods for second order elliptic problems, SIAM Journal on Numerical Analysis, vol.47, issue.2, pp.1319-1365, 2006. ,
A fast l-h bifurcation dynamics in a tokamak edge plasma gyrokinetic simulation, APS Division of Plasma Physics Meeting, vol.3, pp.2767-2782, 1991. ,
Turbulent transport modelling in the edge plasma of tokamaks: Verification, validation, simulation and synthetic diagnostics. PhD thesis, 2015. ,
The local discontinuous galerkin method for time-dependent convection-diffusion systems, SIAM Journal on Numerical Analysis, vol.35, pp.2440-2463, 1997. ,
An introduction to magnetohydrodynamics, 2001. ,
Algorithm 832: UMFPACK v4.3-an Unsymmetricpattern Multifrontal Method, ACM Trans. Math. Softw, vol.30, issue.2, pp.196-199, 2004. ,
Local and nonlocal parallel heat transport in general magnetic fields, Physical review letters, vol.106, 2011. ,
Duality-based asymptotic-preserving method for highly anisotropic diffusion equations, Commun. Math. Sci, vol.10, issue.1, pp.1-31, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00876538
An asymptotic preserving scheme for anisotropic elliptic problems, Multiscale Model. Simul, vol.8, pp.645-666, 2010. ,
Applied numerical linear algebra, 1997. ,
Ballooning mode spectrum in general toroidal systems, Phys. of Fluids, vol.26, issue.10, pp.3038-3052, 1983. ,
An asymptoticpreserving method for highly anisotropic elliptic equations based on a micro-macro decomposition, J. Comp. Phys, vol.231, pp.2724-2740, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00933503
Finite volume schemes for diffusion equations: Introduction to and review of modern methods, Mathematical Models and Methods in Applied Sciences, vol.24, issue.08, p.4, 2011. ,
Recent developements in discontinous galerkin finite element methods for partial differential equations ,
, , vol.157, 2013.
Plasma physics and fusion energy, 2007. ,
A control volume finite element numerical simulation of the drying of spruce, J. Comp. Phys, vol.125, issue.79, pp.59-70, 1996. ,
Instabilities, turbulence et transport dans un plasma magnetisé, 2001. ,
A hybrid discontinuous galerkin method for tokamak edge plasma simulations in global realistic geometry, J. Comp. Phys, vol.374, pp.515-532, 2014. ,
Optimized schwarz methods for anisotropic diffusion with discrete duality finite volume discretizations, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01782357
A comparison of preconditioned krylov subspace methods for nonsymmetric linear systems, Num. Lin. Alg. with Appl, vol.07, p.2016 ,
Introduction to plasma physics, 2007. ,
Drive of parallel flows by turbulence and large-scale e×b transverse transport in divertor geometry, Nucl. Fusion, vol.57, issue.3, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01398227
A new look at density limits in tokamaks, Nucl. Fusion, vol.28, issue.12, pp.2199-2207, 1988. ,
Modelling of heat transport in magnetised plasmas using non-aligned coordinates, J. Comp. Phys, vol.209, pp.354-370, 2005. ,
Developments in the gyrofluid approach to tokamak turbulence simulations, Plasma Phys. and Con. Fusion, vol.2, pp.973-985, 1962. ,
A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comp. Phys, vol.160, issue.2, pp.481-499, 2000. ,
Approximation of diffusion operators with discontinuous coefficients on distorted meshes, Comp. Meth. in Appl. Mech. and Eng, vol.192, 1939. ,
Benchmark on discretization schemes for anisotropic diffusion problems on general grids. Finite volumes for complex applications, vol.5, pp.659-692, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00429843
A flux-coordinate independent field-aligned approach to plasma turbulence simulations, Comp. Phys. Comm, vol.184, pp.2419-2429, 2013. ,
Asymptotic preserving (ap) schemes for multiscale kinetic and hyperbolic equations: a review, Riv. Mat. Univ. Parma, vol.3, pp.177-216, 2012. ,
A high-order cell-centered finite volume scheme forsimulating three dimensional anisotropic diffusionequations on unstructured grids, IMA Journal of Numerical Analysis, vol.26, 2013. ,
Generalized finite volume strategies for simuating transport in strongly orthotropic porous media, Australian & New Zealand Industrial and Applied Mathematics Journal, vol.44, issue.1, pp.1-21, 2003. ,
A Second Order Control-Volume Finite-Element Least-Squares Strategy For Simulation Diffusion In Strongly Anisotropic Media, J. Comp. Math, vol.23, issue.1, pp.1-16, 2005. ,
Relationships among some locally conservative discretization methods which handle discontinuous coefficients, Comp. Geo, vol.8, issue.4, p.341, 2005. ,
Some criteria for a power producing thermonuclear reactor, Proc. Phys. Soc, pp.70-71, 1957. ,
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes, J. Comp. Phys, vol.69, pp.283-324, 1987. ,
Mimetic finite difference method, J. Comp. Phys, vol.257, pp.1163-1227, 2014. ,
Weighted essentially non-oscillatory schemes, J. Comp. Phys, vol.115, issue.1, pp.200-212, 1994. ,
Finite volume monotone scheme for highly anisotropic diffusion operators on unstructured triangular meshes, Comptes Rendus. Mathématique. Académie des Sciences, vol.12, p.12, 2005. ,
A cell-centered scheme for heterogeneous anisotropic diffusion problems on general meshes, Int. J. on Finite, vol.8, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-01116990
An efficient method for constructing an ilu preconditioner for solving large sparse nonsymmetric linear systems by the gmres method, Comp. & Math. with Applications, vol.45, issue.10, pp.1757-1772, 2003. ,
A high-order finite volume cell-centered scheme for anisotropic diffusion on two-dimensional unstructured grids, HAL, vol.11, pp.76-91, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00605548
A nominally second-order accurate finite volume cell-centered scheme for anisotropic diffusion on two-dimensional unstructured grids, J. Comp. Phys, vol.231, issue.5, pp.2259-2299, 2012. ,
Asymptotic-preserving scheme for highly anisotropic non-linear diffusion equations, J. Comp. Phys, vol.231, pp.8229-8245, 2012. ,
A local support-operators diffusion discretization scheme for quadrilateral r-z meshes, J. Comp. Phys, vol.144, pp.17-51, 1998. ,
Finite volume methods and the equations of finite scale: A mimetic approach, Int. J. Num. Meth. Fluids, vol.56, pp.991-1002, 2008. ,
A discrete operator calculus for finite difference approximations, Comp. Methods Appl. Mech. Engrg, vol.187, pp.365-383, 2000. ,
Asymptotic preserving scheme for strongly anisotropic parabolic equations for arbitrary anisotropy direction, J. Comp. Phys, vol.185, pp.3189-3203, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01881564
An implicit high-order hybridizable discontinuous galerkin method for linear convection-diffusion equations, J. Comp. Phys, vol.228, issue.9, pp.3232-3254, 2009. ,
An implicit high-order hybridizable discontinuous galerkin method for the incompressible navier-stokes equations, J. Comp. Phys, vol.230, issue.4, pp.1147-1170, 2011. ,
Certain topics in telegraph transmission theory, 1928. ,
, ITER organization. Plasma heating. ITER.org, 2019.
An alternative approach to field-aligned coordinates for plasma turbulence simulations, Phys. Letters, vol.375, pp.1677-1685, 2011. ,
Magnetic field pitch angle and perpendicular velocity measurements from multi-point time-delay estimation of poloidal correlation reflectometry. Plasma Phys. and Con, Fusion, vol.59, issue.2, 2017. ,
Sampling and reconstruction of wave-number-limited functions in n-dimensional euclidean spaces, Information and Control, vol.5, issue.4, pp.279-323, 1962. ,
The compact discontinuous galerkin (cdg) method for elliptic problems, SIAM Journal on Scientific Computing, vol.30, issue.4, pp.1806-1824, 2008. ,
Solution of sparse indefinite systems of linear equations, SIAM J. Num. Analysis, vol.12, issue.4, pp.617-629, 1975. ,
The plasma boundary of magnetic fusion devides, 2000. ,
Etude des flux de matière dans le plasma de bord des tokamaks: Alimentation, 2007. ,
The TOKAM3X code for edge turbulence fluid simulations of tokamak plasmas in versatile magnetic geometries, J. Comp. Phys, vol.321, pp.606-623, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01461797
Tokam-3d: A 3d fluid code for transport and turbulence in the edge plasma of tokamaks, J. of Nuc. Mat, vol.229, pp.361-378, 2009. ,
, , 2001.
On numerical solution of strongly anisotropic diffusion equation on misaligned grids, Num. Heat Transfer, B, vol.47, pp.533-554, 2005. ,
Finite-difference schemes for anisotropic diffusion, J. Comp. Phys, vol.272, pp.526-549, 2014. ,
An introduction to multigrid methods, 1992. ,
, J. Wesson. Tokamaks. Clarendon, 1997.
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
, JID, vol.11, pp.1-24
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
, JID, vol.15, pp.1-24
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
, JID, vol.17, pp.1-24
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
, JID, vol.23, pp.1-24
The TOKAM3X code for edge turbulence fluid simulations of tokamak plasmas in versatile magnetic geometries, J. Comput. Phys, vol.321, pp.606-623, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01461797
, J. Nucl. Mater, pp.347-350, 2009.
On numerical solution of strongly anisotropic diffusion equation on misaligned grids, Numer. Heat Transf, vol.47, pp.533-554, 2005. ,
Finite-difference schemes for anisotropic diffusion, J. Comput. Phys, vol.272, pp.526-549, 2014. ,
A new conservative finite-difference scheme for anisotropic elliptic problems in bounded domain, J. Comput. Phys, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02477007
Preserving monotonicity in anisotropic diffusion, J. Comput. Phys, vol.227, pp.123-142, 2007. ,
On locking and robustness in the finite element method, J. Comput. Phys, vol.29, issue.5, pp.1261-1293, 1992. ,
Modelling of heat transport in magnetised plasmas using non-aligned coordinates, J. Comput. Phys, vol.209, pp.354-370, 2005. ,
Finite volume methods and the equations of finite scale: a mimetic approach, Int. J. Numer. Methods Fluids, vol.56, pp.991-1002, 2008. ,
Support-operator finite-difference algorithms for general elliptic problems, J. Comput. Phys, vol.118, pp.131-151, 1994. ,
Approximation of boundary conditions for mimetic finite-difference methods, Comput. Math. Appl, vol.36, issue.5, pp.79-99, 1998. ,
A local support-operators diffusion discretization scheme for quadrilateral r-z meshes, J. Comput. Phys, vol.144, pp.17-51, 1998. ,
Gravitational resistive instability of an incompressible plasma in a sheared magnetic field, Phys. Fluids, vol.8, issue.2, pp.315-322, 1965. ,
Considerations of ion-temperature-gradient-driven turbulence, Phys. Fluids B, vol.3, issue.10, pp.2767-2782, 1991. ,
Developments in the gyrofluid approach to tokamak turbulence simulations, Plasma Phys. Control. Fusion, vol.35, pp.973-985, 1993. ,
Ballooning mode spectrum in general toroidal systems, Phys. Fluids, vol.26, issue.10, pp.3038-3052, 1983. ,
Shifted metric procedure for flux tube treatments of toroidal geometry: avoiding grid deformation, Phys. Plasmas, vol.8, issue.2, pp.447-458, 2001. ,
Hydromagnetic equilibria and their proper coordinates, Nucl. Fusion, vol.2, pp.23-37, 1962. ,
An alternative approach to field-aligned coordinates for plasma turbulence simulations, Phys. Lett, vol.375, pp.1677-1685, 2011. ,
A flux-coordinate independent field-aligned approach to plasma turbulence simulations, Comput. Phys. Commun, vol.184, pp.2419-2429, 2013. ,
Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow, part i, J. Comput. Phys, vol.135, pp.103-114, 1997. ,
The field line map approach for simulations of magnetically confined plasmas, Comput. Phys. Commun, vol.198, pp.139-153, 2016. ,
Advances in the flux-coordinate independent approach, Comput. Phys. Commun, vol.213, pp.111-121, 2017. ,
Asymptotic-preserving scheme for highly anisotropic non-linear diffusion equations, J. Comput. Phys, vol.231, issue.24, pp.8229-8245, 2012. ,
An asymptotic-preserving semi-lagrangian algorithm for the time-dependent anisotropic heat transport equation, J. Comput. Phys, vol.272, p.719, 2014. ,
Local and nonlocal parallel heat transport in general magnetic fields, Phys. Rev. Lett, vol.106, p.5, 2011. ,
Mimetic finite difference method, J. Comput. Phys, vol.257, pp.1163-1227, 2014. ,
A discrete operator calculus for finite difference approximations, Comput. Methods Appl. Mech. Eng, vol.187, pp.365-383, 2000. ,
Certain topics in telegraph transmission theory, 1928. ,
A mathematical theory of communication, Bell Syst. Tech. J, vol.27, pp.623-656, 1948. ,
Algorithm 832: UMFPACK v4.3-an unsymmetric-pattern multifrontal method, ACM Trans. Math. Softw, vol.30, issue.2, pp.196-199, 2004. ,