عنوان

Finite Element Methods in Linear Ideal Magnetohydrodynamics

شابک

3642867081

شابک

9783642867088

شماره

b574785

عنوان اصلي

Finite Element Methods in Linear Ideal Magnetohydrodynamics

نام عام مواد

[Book]

نام نخستين پديدآور

by Ralf Gruber, Jacques Rappaz.

محل نشرو پخش و غیره

Berlin, Heidelberg

نام ناشر، پخش کننده و غيره

Springer Berlin Heidelberg

تاریخ نشرو بخش و غیره

1985

نام خاص و کميت اثر

(volumes).

عنوان فروست

Springer series in computational physics.

متن يادداشت

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.

متن يادداشت

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.

موضوع مستند نشده

Mathematical physics.

موضوع مستند نشده

Physics.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by Ralf Gruber, Jacques Rappaz.

مستند نام اشخاص تاييد نشده

Jacques Rappaz

مستند نام اشخاص تاييد نشده

Ralf Gruber

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y