tailieunhanh - Numerical_Methods for Nonlinear Variable Problems Episode 6

Tham khảo tài liệu 'numerical_methods for nonlinear variable problems episode 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 6. Applications 187 Exercise . Prove . We refer to Glowinski and Marrocco 5 for a detailed analysis including error estimates of a finite element approximation of see also Ciarlet 2 . From our numerical experiments it appears that solving if s is close to 1 say 1 s or large say s 5 is a very difficult task if one uses standard iterative methods to our knowledge the only very efficient methods are ALG 1 and ALG 2 or closely related algorithms see Glowinski and Marrocco loc. cit. for more details . The augmented Lagrangian r to be used for solving is defined by If Ỵ f f q ụ - I q Is dx f v 7 I Vt q 2 dx p Vi q dx. s Jq 2 Jii Jn Solution of by ALG 1. From - it follows that when applying ALG 1 to we obtain Ằ e Ls O N- then for n 0 rAm f V 2 rV pn in Q __ u r 0 p s 2p rpn rVun 2 2 1 2 p Vm - p . The nonlinear system can be solved by the block-relaxation method of Sec. and we observe that if u and 2 are known or estimated in the computation of p is an easy task since p is solution of the singlevariable nonlinear equation p s-1 r p rVu 2 which can easily be solved by various methods once I pn I is known we obtain pn by solving a trivial linear equation in L G iV . Solution of by ALG 2. We have to replace by p Ả eHxH and by rAw V 2 rV p 1 __ w r 0. 188 VI Decomposition-Coordination Methods by Augmented Lagrangian Applications Remark still applies to and since G is linear we can take 0 p p 2r if we are using ALG 2. For more details and comparisons with other methods see Glowinski and Marrocco 5 7 and Fortin Glowinski and Marrocco 1 . Remark . ALG 1 and ALG 2 have also been successfully applied to the iterative solution of magneto-static problems see Glowinski and Marrocco 6 . They have also been applied by Fortin Glowinski and Marrocco 1 to the solution of the subsonic flow problem described in

TỪ KHÓA LIÊN QUAN
crossorigin="anonymous">
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.