9783642867101 - Finite Element Methods in Linear Ideal Magnetohydrodynamics (Scientific Computation) de Gruber, Ralf; Rappaz, Jacques (12 resultados)

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Condición: New. Idioma/Language: Inglés. For more than ten years we have been working with the ideal linear MHD equations used to study the stability of thermonuc1ear plasmas. Even though the equations are simple and the problem is mathematically well formulated, the numerical problems were much harder to solve than anticipated. Already in the one-dimensional cylindrical case, what we called "spectral pollution" appeared. We were able to eliminate it by our "ecological solution". This solution was applied to the two-dimensional axisymmetric toroidal geometry. Even though the spectrum was unpolluted the precision was not good enough. Too many mesh points were necessary to obtain the demanded precision. Our solution was what we called the "finite hybrid elements". These elements are efficient and cheap. They have also proved their power when applied to calculating equilibrium solutions and will certainly penetrate into other domains in physics and engineering. During all these years, many colleagues have contributed to the construc tion, testing and using of our stability code ERATO. We would like to thank them here. Some ofthem gave partial contributions to the book. Among them we mention Dr. Kurt Appert, Marie-Christine Festeau-Barrioz, Roberto Iacono, Marie-Alix Secretan, Sandro Semenzato, Dr. Jan Vac1avik, Laurent Villard and Peter Merkel who kindly agreed to write Chap. 6. Special thanks go to Hans Saurenmann who drew most of the figures, to Dr. *** Nota: Los envíos a España peninsular, Baleares y Canarias se realizan a través de mensajería urgente. No aceptamos pedidos con destino a Ceuta y Melilla.

Condición: New. pp. 196.

Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - For more than ten years we have been working with the ideal linear MHD equations used to study the stability of thermonuc1ear plasmas. Even though the equations are simple and the problem is mathematically well formulated, the numerical problems were much harder to solve than anticipated. Already in the one-dimensional cylindrical case, what we called 'spectral pollution' appeared. We were able to eliminate it by our 'ecological solution'. This solution was applied to the two-dimensional axisymmetric toroidal geometry. Even though the spectrum was unpolluted the precision was not good enough. Too many mesh points were necessary to obtain the demanded precision. Our solution was what we called the 'finite hybrid elements'. These elements are efficient and cheap. They have also proved their power when applied to calculating equilibrium solutions and will certainly penetrate into other domains in physics and engineering. During all these years, many colleagues have contributed to the construc tion, testing and using of our stability code ERATO. We would like to thank them here. Some ofthem gave partial contributions to the book. Among them we mention Dr. Kurt Appert, Marie-Christine Festeau-Barrioz, Roberto Iacono, Marie-Alix Secretan, Sandro Semenzato, Dr. Jan Vac1avik, Laurent Villard and Peter Merkel who kindly agreed to write Chap. 6. Special thanks go to Hans Saurenmann who drew most of the figures, to Dr.

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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -For more than ten years we have been working with the ideal linear MHD equations used to study the stability of thermonuc1ear plasmas. Even though the equations are simple and the problem is mathematically well formulated, the numerical problems were much harder to solve than anticipated. Already in the one-dimensional cylindrical case, what we called 'spectral pollution' appeared. We were able to eliminate it by our 'ecological solution'. This solution was applied to the two-dimensional axisymmetric toroidal geometry. Even though the spectrum was unpolluted the precision was not good enough. Too many mesh points were necessary to obtain the demanded precision. Our solution was what we called the 'finite hybrid elements'. These elements are efficient and cheap. They have also proved their power when applied to calculating equilibrium solutions and will certainly penetrate into other domains in physics and engineering. During all these years, many colleagues have contributed to the construc tion, testing and using of our stability code ERATO. We would like to thank them here. Some ofthem gave partial contributions to the book. Among them we mention Dr. Kurt Appert, Marie-Christine Festeau-Barrioz, Roberto Iacono, Marie-Alix Secretan, Sandro Semenzato, Dr. Jan Vac1avik, Laurent Villard and Peter Merkel who kindly agreed to write Chap. 6. Special thanks go to Hans Saurenmann who drew most of the figures, to Dr. 196 pp. Englisch.

Condición: New. Print on Demand pp. 196 103 Figures, 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam.

Condición: New. PRINT ON DEMAND pp. 196.

Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 1. Finite Element Methods for the Discretization of Differential Eigenvalue Problems.- 1.1 A Classical Model Problem.- 1.1.1 Exact Problem.- 1.1.2 Approximate Problem.- 1.1.3 Questions on Numerical Stability.- 1.2 A Non-Standard Model Problem.- 1.2.1 Exact .

Taschenbuch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -1. Finite Element Methods for the Discretization of Differential Eigenvalue Problems.- 1.1 A Classical Model Problem.- 1.2 A Non-Standard Model Problem.- 1.3 Spectral Stability.- 1.5 Some Comments.- 2. The Ideal MHD Model.- 2.1 Basic Equations.- 2.2 Static Equilibrium.- 2.3 Linearized MHD Equations.- 2.4 Variational Formulation.- 2.5 Stability Considerations.- 2.6 Mechanical Analogon.- 3. Cylindrical Geometry.- 3.1 MHD Equations in Cylindrical Geometry.- 3.2 Six Test Cases.- 3.3 Approximations.- 3.4 Polluting Finite Elements.- 3.6 Non-Conforming Non-Polluting Elements.- 3.7 Applications and Comparison Studies (with M.-A. Secrétan).- 3.8 Discussion and Conclusion.- 4. Two-Dimensional Finite Elements Applied to Cylindrical Geometry.- 4.1 Conforming Finite Elements.- 4.2 Non-Conforming, Finite Hybrid Elements.- 4.3 Discussion.- 5. ERATO: Application to Toroidal Geometry.- 5.1 Static Equilibrium.- 5.2 Mapping of ( , ) into ( , ) Coordinates in p.- 5.3 Variational Formulation of the Potential and Kinetic Energies.- 5.4 Variational Formulation of the Vacuum Energy.- 5.5 Finite Hybrid Elements.- 5.6 Extraction of the Rapid Angular Variation.- 5.7 Calculation of -Limits (with F. Troyon).- 6. HERA: Application to Helical Geometry (Peter Merkel, IPP Garching).- 6.1 Equilibrium.- 6.2 Variational Formulation of the Stability Problem.- 6.3 Applications.- 7. Similar Problems.- 7.1 Similar Problems in Plasma Physics.- 7.2 Similar Problems in Other Domains.- Appendices.- A: Variational Formulation of the Ballooning Mode Criterion.- B.1 The Problem.- B.2 Two Numberings of the Components.- B.3 Resolution for Numbering (D1).- B.4 Resolution for Numbering (D2).- B.5 Higher Order Finite Elements.- C: Organization of ERATO.- D: Listing of ERATO 3 (with R. Iacono).- References.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 196 pp. Englisch.