...array whose number of columns is 6 and number of rows is equal to the number of elements owned by that proccesor. For the situation in figure 5, the first row of Elnode on the first proccesor will be =-=[0,2,18,10,9,1]-=- (the first three are corner points, the last 3 are middle points). It is also neccesary to have a list of boundary nodes on each proccesor which will be used to eliminate Dirichlet boundary condition...

...conditions after doing the assembly. A local variable called boundary will store the indices of boundary nodes on each processor. For example, in figure 5 on the first proccesor we will have boundary==-=[0,1,2,3,4,5,6,7,8,9,18,27,36,17,26,35,44]-=-. The function Veltopres creates a correspondence between the index of a node as a velocity node and its index as a pressure node provided that the node is both a velocity and a pressure node. In the ...

...l tests to illustrate the value of using LES as a reduced order model in shape optimization. 1 General Methodology To compute the fluid velocity and pressure on a domain Ω the Navier Stokes equations =-=[2]-=- which model the motion of an incompressible viscous, Newtonian fluid ut − ν∆u + (u · ∇)u + ∇p = f in (0, T ) × Ω ∇ · u = 0 in (0, T ] × Ω u = g in (0, T ] × ∂Ω u |t=0 ∫ = u0 in Ω pdx = 0 in (0, T ]. ...