On a mathematical model arising in MHD perturbed equilibrium for Stellarator devices. A numerical approach
| dc.book.title | The International Conference on High Performance Computing & Simulation (HPCS 2012) | |
| dc.contributor.author | Padial Molina, Juan Francisco | |
| dc.contributor.author | Galan del Sastre, Pedro | |
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.date.accessioned | 2023-06-20T05:46:44Z | |
| dc.date.available | 2023-06-20T05:46:44Z | |
| dc.date.issued | 2012 | |
| dc.description | The 2012 International Conference on High Performance Computing & Simulation(HPCS 2012)July 2 – 6, 2012 Madrid, Spain | |
| dc.description.abstract | We consider a mathematical model related to the stationary regime of a plasma of fusion nuclear, magnetically confined in a Stellarator device. Using the geometric properties of the fusion device, a suitable system of coordinates and averaging methods, the mathematical problem may be reduced to a two dimensional free boundary problem of nonlocal type, where the corresponding differential equation is of the Grad?Shafranov type. The current balance within each flux magnetic gives us the possibility to define the third covariant magnetic field component with respect to the averaged poloidal flux function. We present here some numerical experiences and we give some numerical approach for the averaged poloidal flux and for the third covariant magnetic field component. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Unión Europea. FP7 | |
| dc.description.sponsorship | UCM | |
| dc.description.sponsorship | DGISPI, Spain | |
| dc.description.sponsorship | MEC, Spain | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/29554 | |
| dc.identifier.doi | 10.1109/HPCSim.2012.6266984 | |
| dc.identifier.isbn | 978-1-4673-2359-8 | |
| dc.identifier.relatedurl | http://ieeexplore.ieee.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/45555 | |
| dc.language.iso | eng | |
| dc.page.final | 634 | |
| dc.page.initial | 628 | |
| dc.publisher | IEEE | |
| dc.relation.projectID | FIRST (238702) | |
| dc.relation.projectID | Research Group MOMAT (Ref. 910480), | |
| dc.relation.projectID | MTM2011-26119 | |
| dc.relation.projectID | CGL2007-66440-C04-01 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 519.8 | |
| dc.subject.keyword | Mathematical model | |
| dc.subject.keyword | Grad–Safranov equaiton | |
| dc.subject.keyword | equilibrium | |
| dc.subject.keyword | rearrangement | |
| dc.subject.keyword | fix point | |
| dc.subject.keyword | Stellarator | |
| dc.subject.ucm | Investigación operativa (Matemáticas) | |
| dc.subject.unesco | 1207 Investigación Operativa | |
| dc.title | On a mathematical model arising in MHD perturbed equilibrium for Stellarator devices. A numerical approach | |
| dc.type | book part | |
| dcterms.references | J.I. Díaz, Modelos bidimensionales de equilibrio magnetohidrodinamico ´para Stellarators, Informe #2. CIEMAT Repports. Madrid, July 1992. J.I. Díaz, Un problema de frontera libre en el estudio del equilibrio magnetohidrodinamico de un plasma en una configuración Stellarator ´, in Modelos matematicos en Física de Plasmas (J.I. Díaz y A.Galindo eds.), Memorias de la RAC, Tomo XXX, 73-132, 1995. S. Semenzato, R. Gruber and H.P. Zehrfeld, “Computation of symmetric ideal MHD flow equlibria”, Computer Physics Reports, Vol. 1, 7&8, 389-425, 1984. A.H. Boozer, “Establishment of magnetic coordinates for given magnetic field”, Phys. Fluids, 25, 3, pp. 520–521, March 1982. J.M. Greene and J.L. Johnson, “Determination of Hydromagnetic Equilibria”, Phys. Fluids 27, pp. 2101–2120, 1984. T.C. Hender and B.A. Carreras, “Equilibrium calculation for helical axis Stellarators”, Phys. Fluids, 27, pp. 2101–2120, 1984. R. Temam, “A nonlinear eigenvalue problem: equilibrium shape of a confined plasma”, Arch. Rational Mec. Anal., 60, pp. 51–73, 1975. J.I. Díaz and J.M. Rakotoson; “On a non local stationary free–boundary problem arising in the confinement of a plasma in a Stellarator geometry”, Archive for Rational Mechanics and Analysis 134, pp. 53–95,1996. J. Blum; Numerical simulation and optimal control in plasma physics,John Wiley & Sons, New York, 1989. R. Temam, “Remarks on a Free Boundary Value Problem Arising in Plasma Physics”, Comm. in Partial Differential Equations, 2 (6), pp. 563–585, 1977. H. Berstycki and H. Brezis, “On a free boundary problem arising in plasma physics”, Nonlinear Anal., 4, pp. 415–436, 1980. A. Friedman, Variational principles and free–boundary problems, John Wiley and Sons, New York, 1982. J. Mossino and R. Temam, “Directional derivative of the increasing rearrangement mapping and application to a queer differential equation in Plasma physics”, Duke Math. J., 48, pp. 475–495, 1981. J. Mossino and J.M. Rakotoson, “Isoperimetric inequalities in parabolic equations”, Annalli della Scuola Normale Superiore de Pisa, Serie IV, 13, pp. 51–73, 1986. E. Beretta and M. Vogelius, “An inverse problem originating from Magnetohydrodynamics II: the case of the Grad–Shafranov Equation”, Indiana University Mathematics Journal, 41 (4), pp. 1081–1117, 1992. W. A. Cooper; Global External Ideal Magnetohydrodynamic Instabilities in Three-dimensional Plasmas, Theory of Fusion Plasmas, Proc. of the Joint Varenna–Laussane Workshop, Edit. Compositori, Bologna 1990. J.I. Díaz, J.F. Padial and J.M. Rakotoson,“Mathematical treatment of the magnetic confinement in a current carrying Stellarator”, Nonlinear Analysis Theory Methods and Applications 34, pp. 857–887, 1998. A. Bermudez and M.L. Seoane; “Numerical solution of a non local problem arising in plasma physics”, Mathematical and Computer Modelling, 27 (5), pp. 45–59, 1998. J.M. Rakotoson and M. L. Seoane, “Numerical approximations of the relative rearrangement. Applications to some non local problems”,M2AN, 34 (2), pp. 477–499, 2000. J. Mossino, Inegalit ´ es isoperimétriques ´ . Collection “Travaux en cours”,Herman Paris 1984 J.M. Rakotoson, “Some properties of the relative rearrangement”, J.Math. Anal. Appl., 135, pp. 488–500, 1988. J.M. Rakotoson, “Strong continuity of the relative rearrangement maps and application to a Galerkin approach for non local problems”, Applied Math. Letters, 8 (6), pp. 61–63, 1995. J.M. Rakotoson, “Galerkin approximation, strong continuity of the relative rearrangement and application to plasma physics equations”,Diff. and Integral Equations, 12 (1), pp. 67–81, 1999. J.M. Rakotoson, Rearrangement Relatif: Un instrument d’estimations ´dans les problemes aux limites ` Mathematiques et Applications, SMAI, ´Springer, Paris 2008. P.G. Ciarlet, Intorduction a l’analyse num ` erique matriciaelle et ´ a`l’optimisation, Masson, Paris 1990. J.I. Díaz, M.B. Lerena and J.F. Padial, On a nonlocal quasilinear parabolic model related to a current-carrying Stellarator, Nonlinear Analysis: Real World Application, 3 (2002), 503–514. J.I. Díaz, M.B. Lerena, J.F. Padial and J.M. Rakotoson, An elliptic-parabolic equation with nonlocal term for transient regime of a plasma in Stellarator, J. Differential Equations, 198 (2004), 321–355. J. Mossino, “A Priori Estimates for a Model of Grad Mercier Type in Plasma Confinement”, Applicable Analysis, 13, pp. 185–207, 1982. A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations. Clarendon Press Oxford 1999 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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