Partial Differential Equations in Mechanics 1:Fun- damentals, Laplace's Equation, Diffusion Equation, 2013. ,
Partial Differential Equations in Mechanics 2: the Biharmonic Equation, Poisson's Equation, 2013. ,
DOI : 10.1007/978-3-662-09205-7
Mathematics for physics: a guided tour for graduate students, 2009. ,
DOI : 10.1017/CBO9780511627040
Elements of Green's functions and propagation: potentials, diffusion, and waves, 1989. ,
Lectures on elliptic boundary value problems, 2010. ,
DOI : 10.1090/chel/369
Sensibilit?? de l'??quation de la chaleur aux sauts de conductivit??, Comptes Rendus Mathematique, vol.341, issue.5, pp.333-337, 2005. ,
DOI : 10.1016/j.crma.2005.07.005
Méthodes d'´ eléments finis pour leprobì eme de changement de phase en milieux composites, 2016. ,
Elliptic problems in nonsmooth domains, SIAM, 2011. ,
DOI : 10.1137/1.9781611972030
The immersed boundary method, Acta numerica, vol.11, pp.479-517, 2002. ,
A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies, Journal of Computational Physics, vol.207, issue.2, pp.457-492, 2005. ,
DOI : 10.1016/j.jcp.2005.01.020
A node-centered local refinement algorithm for Poisson's equation in complex geometries, Journal of Computational Physics, vol.201, issue.1, pp.34-60, 2004. ,
DOI : 10.1016/j.jcp.2004.04.022
A Fast Poisson Solver for Complex Geometries, Journal of Computational Physics, vol.118, issue.2, pp.348-355, 1995. ,
DOI : 10.1006/jcph.1995.1104
A Second-Order-Accurate Symmetric Discretization of the Poisson Equation on Irregular Domains, Journal of Computational Physics, vol.176, issue.1, pp.205-227, 2002. ,
DOI : 10.1006/jcph.2001.6977
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
URL : http://www.ann.jussieu.fr/~frey/papers/levelsets/Osher S., Fronts propagating with curvature dependent speed.pdf
Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, 1999. ,
A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids, Journal of Computational Physics, vol.218, issue.1, pp.123-140, 2006. ,
DOI : 10.1016/j.jcp.2006.01.046
High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries, Journal of Scientific Computing, vol.179, issue.2, pp.369-413, 2013. ,
DOI : 10.1006/jcph.2002.7066
Exact subgrid interface correction schemes for elliptic interface problems, Proceedings of the National Academy of Sciences, vol.1, issue.29, pp.9874-9879, 2008. ,
DOI : 10.2140/camcos.2006.1.207
URL : http://www.pnas.org/content/105/29/9874.full.pdf
A locally refined rectangular grid finite element method: Application to computational fluid dynamics and computational physics, Journal of Computational Physics, vol.92, issue.1, pp.1-66, 1991. ,
DOI : 10.1016/0021-9991(91)90291-R
A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains, Journal of Computational Physics, vol.147, issue.1, pp.60-85, 1998. ,
DOI : 10.1006/jcph.1998.5965
High order solution of Poisson problems with piecewise constant coefficients and interface jumps, Journal of Computational Physics, vol.335, pp.497-515, 2017. ,
DOI : 10.1016/j.jcp.2017.01.029
Solving pdes in complex geometries, Communications in Mathematical Sciences, vol.7, issue.1, p.81, 2009. ,
DOI : 10.4310/CMS.2009.v7.n1.a4
Solving elliptic problems with discontinuities on irregular domains ??? the Voronoi Interface Method, Journal of Computational Physics, vol.298, pp.747-765, 2015. ,
DOI : 10.1016/j.jcp.2015.06.026
A stable projection method for the incompressible Navier???Stokes equations on arbitrary geometries and adaptive Quad/Octrees, Journal of Computational Physics, vol.292, pp.215-238, 2015. ,
DOI : 10.1016/j.jcp.2015.03.024
A Numerical Method for Solving Incompressible Viscous Flow Problems, Journal of Computational Physics, vol.135, issue.2, pp.118-125, 1997. ,
DOI : 10.1006/jcph.1997.5716
Simulating water and smoke with an octree data structure, ACM Transactions on Graphics, vol.23, issue.3, pp.457-462, 2004. ,
DOI : 10.1145/1015706.1015745
URL : http://graphics.stanford.edu/~fedkiw/papers/stanford2004-02.pdf
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries, Journal of Computational Physics, vol.190, issue.2, pp.572-600, 2003. ,
DOI : 10.1016/S0021-9991(03)00298-5
URL : https://hal.archives-ouvertes.fr/hal-01445436
A Fast Finite Differenc Method For Solving Navier-Stokes Equations on Irregular Domains, Communications in Mathematical Sciences, vol.1, issue.1, pp.180-196, 2003. ,
DOI : 10.4310/CMS.2003.v1.n1.a11
Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations, Journal of Computational Physics, vol.161, issue.1, pp.35-60, 2000. ,
DOI : 10.1006/jcph.2000.6484
An octree-based solver for the incompressible Navier???Stokes equations with enhanced stability and low dissipation, Computers & Fluids, vol.84, pp.231-246, 2013. ,
DOI : 10.1016/j.compfluid.2013.04.027
A parallel multigrid poisson solver for fluids simulation on large grids, Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp.65-74, 2010. ,
Quad trees a data structure for retrieval on composite keys, Acta Informatica, vol.4, issue.1, pp.1-9, 1974. ,
DOI : 10.1007/BF00288933
Simple and Efficient Traversal Methods for Quadtrees and Octrees, Journal of Graphics Tools, vol.14, issue.3, pp.1-11, 2002. ,
DOI : 10.1111/j.1467-8659.1995.cgf143_0383.x
URL : http://www.merl.com/papers/docs/TR2002-41.pdf
A brief introduction to quadtrees and their applications ,
Hierarchical spatial data structures Design and Implementation of Large Spatial Databases, pp.191-212, 1990. ,
An Overview of Quadtrees, Octrees, and Related Hierarchical Data Structures, Theoretical Foundations of Computer Graphics and CAD, pp.51-68, 1988. ,
DOI : 10.1007/978-3-642-83539-1_2
Table-driven quadtree traversal algorithms, 1989. ,
The Quadtree and Related Hierarchical Data Structures, ACM Computing Surveys, vol.16, issue.2, pp.187-260, 1984. ,
DOI : 10.1145/356924.356930
URL : http://www.cs.umd.edu/~hjs/pubs/SameCSUR84-ocr.pdf
Adaptive mesh refinement strategies for immersed boundary methods, " in 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, p.162, 2009. ,
Dynamic octree load balancing using space-filling curves, 2003. ,
Space-filling curves and their use in the design of geometric data structures, Theoretical Computer Science, vol.181, issue.1, pp.3-15, 1997. ,
DOI : 10.1016/S0304-3975(96)00259-9
A computer oriented geodetic data base and a new technique in file sequencing, International Business Machines Company, 1966. ,
: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees, SIAM Journal on Scientific Computing, vol.33, issue.3, pp.1103-1133, 2011. ,
DOI : 10.1137/100791634
Introductory finite difference methods for PDEs, Bookboon, 2010. ,
Lecture notes on numerical analysis of partial differential equations, 2012. ,
Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. SIAM, 2007. ,
DOI : 10.1137/1.9780898717839
Computational Mathematics: Models, Methods, and Analysis with MATLAB R and MPI, 2015. ,
DOI : 10.1201/9780203494479
Local adaptive mesh refinement for shock hydrodynamics, Journal of Computational Physics, vol.82, issue.1, pp.64-84, 1989. ,
DOI : 10.1016/0021-9991(89)90035-1
Adaptive mesh refinement for hyperbolic partial differential equations, Journal of Computational Physics, vol.53, issue.3, pp.484-512, 1984. ,
DOI : 10.1016/0021-9991(84)90073-1
High Order Finite Difference Schemes on Non-uniform Meshes with Good Conservation Properties, Journal of Computational Physics, vol.157, issue.2, pp.746-761, 2000. ,
DOI : 10.1006/jcph.1999.6398
URL : http://ctr-sgi1.stanford.edu/CTR/ResBriefs98/vasilyev.pdf
A Fully Conservative Second-Order Finite Difference Scheme for Incompressible Flow on Nonuniform Grids, Journal of Computational Physics, vol.177, issue.1, pp.117-133, 2002. ,
DOI : 10.1006/jcph.2002.7006
Numerical solution of partial differential equations: an introduction, 2005. ,
DOI : 10.1017/CBO9780511812248
Stability, consistency, and convergence of numerical discretizations, Encyclopedia of Applied and Computational Mathematics, pp.1358-1364, 2015. ,
Survey of the stability of linear finite difference equations, Communications on Pure and Applied Mathematics, vol.5, issue.2, pp.267-293, 1956. ,
DOI : 10.1002/sapm1950291223
Analysis of the nine-point finite difference approximation for the heat conduction equation in a nuclear fuel element, 1983. ,
An optimal 25-point finite difference scheme for the Helmholtz equation with PML, Journal of Computational and Applied Mathematics, vol.236, issue.6, pp.389-410, 2013. ,
DOI : 10.1016/j.cam.2011.08.007
An optimal 9???point, finite???difference, frequency???space, 2-D scalar wave extrapolator, GEOPHYSICS, vol.61, issue.2, pp.529-537, 1996. ,
DOI : 10.1190/1.1443979
A cell-centred finite volume method for the Poisson problem on non-graded quadtrees with second order accurate gradients, Journal of Computational Physics, vol.331, pp.49-72, 2017. ,
DOI : 10.1016/j.jcp.2016.11.035
Electrostrictive materials: modelling and simulation, 7 th European Congress on Computational Methods in Applied Sciences and Engineering, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01411132
A penalization method to take into account obstacles in incompressible viscous flows, Numerische Mathematik, vol.81, issue.4, pp.497-520, 1999. ,
DOI : 10.1007/s002110050401
Boundary layer for a penalization method for viscous incompressible flow, Advances in Differential Equations, pp.1453-1480, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00295077
Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design, Journal of Computational Physics, vol.228, issue.17, pp.6291-6315, 2009. ,
DOI : 10.1016/j.jcp.2009.05.017
URL : https://hal.archives-ouvertes.fr/hal-00385460
Petsc users manual revision 3, tech. rep., Argonne National Laboratory (ANL), p.2014 ,
DOI : 10.2172/1178102
Iterative solution of linear systems, Acta Numerica, vol.13, pp.57-100, 1992. ,
DOI : 10.1137/0720023
URL : ftp://elib.stanford.edu/pub/reports/na/m/91/05/NA-M-91-05.ps
FGMRES for linear discrete ill-posed problems, Applied Numerical Mathematics, vol.75, pp.175-187, 2014. ,
DOI : 10.1016/j.apnum.2013.08.004
URL : http://www.math.kent.edu/~reichel/publications/fgmres.pdf
A Flexible Inner-Outer Preconditioned GMRES Algorithm, SIAM Journal on Scientific Computing, vol.14, issue.2, pp.461-469, 1993. ,
DOI : 10.1137/0914028
URL : ftp://ftp.cs.umn.edu/dept/users/saad/reports/PDF/umsi-91-279.pdf
An overview of numerical methods for solving phase change problems Advances in numerical heat transfer, pp.341-380, 1997. ,
A substructuring method for phase change modelling in hybrid media, Computers & Fluids, vol.88, issue.Complete, pp.81-92, 2013. ,
DOI : 10.1016/j.compfluid.2013.09.003
Comparison of two numerical heat transfer models for phase change material board, Applied Thermal Engineering, vol.128, 2017. ,
DOI : 10.1016/j.applthermaleng.2017.09.015
FAST IMPLICIT FINITE-DIFFERENCE METHOD FOR THE ANALYSIS OF PHASE CHANGE PROBLEMS, Numerical Heat Transfer, Part B: Fundamentals, vol.4, issue.2, pp.155-169, 1990. ,
DOI : 10.1080/10407799008961731
ERAL SOURCE-BASED METHOD FOR SOLIDIFICATION PHASE CHANGE, Numerical Heat Transfer, Part B: Fundamentals, vol.19, issue.2, pp.175-189, 1991. ,
DOI : 10.1080/10407798908944899
Heat transfer analysis of a latent heat thermal energy storage system using graphite foam for concentrated solar power, Solar Energy, vol.103, pp.438-447, 2014. ,
DOI : 10.1016/j.solener.2014.02.038
A Comparison of Enthalpy and Temperature Methods for Melting Problems on Composite Domains, Numerical Mathematics and Advanced Applications, pp.585-592, 2006. ,
DOI : 10.1007/978-3-540-34288-5_55
Effect of an increased thermal contact resistance in a salt PCM-graphite foam composite TES system, Renewable Energy, vol.106, pp.321-334, 2017. ,
DOI : 10.1016/j.renene.2017.01.032
KNO3/NaNO3 ??? Graphite materials for thermal energy storage at high temperature: Part I. ??? Elaboration methods and thermal properties, Applied Thermal Engineering, vol.30, issue.13, pp.1580-1585, 2010. ,
DOI : 10.1016/j.applthermaleng.2010.03.013