tailieunhanh - The MEMS Handbook (1st Ed) - M. Gad el Hak Part 6

Tham khảo tài liệu 'the mems handbook (1st ed) - m. gad el hak part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | thus the OTD and DTO approaches are not necessarily equivalent even upon refinement of the space time grid Vogel and Wade 1995 . However by carefully framing the discrete identity defining the DTO adjoint operator as a discrete approximation of the identity given in Eq. these two approaches can be posed in an equivalent fashion for Navier-Stokes systems. It remains the topic of some debate whether or not the DTO approach is better than the OTD approach for marginally resolved PDE systems. The argument for DTO is that it clearly is the most direct way to optimize the discrete problem actually being solved by the computer. The argument against DTO is that one really wants to optimize the continuous problem so gradient information that identifies and exploits deficiencies in the numerical discretization that can lead to performance improvements in the discrete problem might be misleading when interpreting the numerical results in terms of the physical system. Robustification Appealing to Murphy s Law Though optimal control approaches possess an attractive mathematical elegance and are now proven to provide excellent results in terms of drag and turbulent kinetic energy reduction in fully developed turbulent flows they are often impractical. One of the most significant drawbacks of this nonlinear optimization approach is that it tends to over-optimize the system leaving a high degree of designpoint sensitivity. This phenomenon has been encountered frequently in for example the adjoint-based optimization of the shape of aircraft wings. Overly optimized wing shapes might work quite well at exactly the flow conditions for which they were designed but their performance is often abysmal at off-design conditions. In order to abate such system sensitivity the noncooperative framework of robust control provides a natural means to detune the optimized results. This concept can be applied easily to a broad range of related applications. The noncooperative approach to