User:Eml5526.s11.team01.roark/Mtg01

[[media: Fe1.s11.mtg1.djvu| Mtg 1]]: Wed, 5 Jan 11 [[media: Fe1.s11.mtg1.djvu| Page 1-1]]

Analysis

Engineering Analysis (Computation of Stress Field, Displacement, Velocity….)

Mathematical Analysis (theorems, proofs)

Hamming 1962(Bell Labs): Goal of Computation is insight.

3 important classes of numerical methods of 20th century:


 * 1) Finite difference Methods (FDM): 1950s
 * 2) Finite Element (FEM): 1960s
 * 3) Spectral Methods: 1970s

1) FDE: Direct approximation of partial derivative, awkward in real world engineering Computation with complex geometry (engineering analysis, & design of engine block…) F&B (Fish and Belytschko 2007) p.1: no commercial code using FDM for engineering application with complex geometryin CFD, FVM(Finite Volume Method, close

[[media: Fe1.s11.mtg1.djvu| Page 1-2]] cousin of FEM). (CFM=Computational Fluid Dynamics). For flux or force b.c.’s (boundary Conditions), i.e. b.c.’s involving gradient of the unknown function (temperature, displacement,…)(also called natural b.c.’s), need to approximate gradient by FD at bound.

2) FEM: “Weak” form absorbs natural b.c.’s -> No need for approximation Amenable for problems w/complex geometry.

Note:

At beginning of lecture, course organization: Wiki, Syllabus, Important docs to read, important videos to watch.

End Note