By E. M. Abdalass, J. F. Maitre, F. Musy (auth.), Wolfgang Hackbusch, Ulrich Trottenberg (eds.)
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Extra info for Multigrid Methods II: Proceedings of the 2nd European Conference on Multigrid Methods held at Cologne, October 1–4, 1985
12) as a function of the current residual F. To answer this question one must consider the principal terms of the change 6F under the displacements (12), viz. those terms in which ~ is twice differentiated: 5F ~ (B- V)(B- V)~ + (B 2 + 3p)V(V • ~) (14) - B(B. V)(V. - (B. V)V(B • (The operator V acts on ~ only). A desirable relaxation scheme should have 5F ~- - F , at least for the short wavelength components. Fourier analysis transforms 5F into 5F and ~ into ~, related by 5F -~ A. ~, where A = -B (kp+ (1 + Z)kk - k,j(bk + kb)) where k is the wavevector, fl = "Tp/B 2, b = B / B , and ktl = k - b .
Mastin, Boundary-Fitted Coordinate Systems for Numerical Solution of Partial Differential Equations--A Review, J. Cornput. Phys. 47 (1982), 1-108. 18. R. Chodura and A. Schlfiter, A 3D Code for MHD Equilibrium and Stability, J. Comput. Phys. 41 (1981), 68-88. 19. F. Troyon, R. Gruber, H. Saurenmarm, S. Semenzato and S. Succi, MHD-Limits to Plasma Confinement, 11th European Conference on Controlled Fusion and Plasma Physics, Aachen, 1983, Plasma Phys. Contr. Fusion 26 (1984), 209-215. R. G e r m a n y M u l t i g r i d a l g o r i t h m s and c o n j u g a t e g r a d i e n t m e t h o d s with a p p r o p r i a t e p r e c o n d i t i o n i n g are both e f f i c i e n t tools for the solution of e q u a t i o n s which arise from the d i s c r e t i z a t i o n of partial d i f f e r e n t i a l equations.
H -I" This follows from LIB u+l 2 ~ lIBTull2 ~ ch -I o The inequalities, were derived functions. Neumann which  are from The g r o w t h boundary dition in c o n t r a s t estimates as h -I a r i s e s condition operators in a p c g - a ! , is one. 1 for d i s c r e t e fact the d i f f e r e n c e of u n k n o w n s . 6) approximated as if N d e n o t e s liB uH 2 o that in the the n u m b e r is p r o p o r t i o n a l , original by a b o u n d a r y between  harmonic the of to con- order of iteration
Multigrid Methods II: Proceedings of the 2nd European Conference on Multigrid Methods held at Cologne, October 1–4, 1985 by E. M. Abdalass, J. F. Maitre, F. Musy (auth.), Wolfgang Hackbusch, Ulrich Trottenberg (eds.)