Basics of MATLAB and Beyond

25.1 Example: AirfoilSuppose we are doing some finite element modelling of the airflow overan aeroplane wing. In finite element modelling you set up a calculationgrid whose points are more densely spaced where the solution has highgradients. A suitable set of points is contained in the file airfoil:load airfoilclfplot(x,y,’.’)There are 4253 points distributed around the main wing and the twoflaps. In carrying out the calculation, we need to define the network ofinterrelationships among the points; that is, which group of points willbe influenced by each point on the grid. We restrict the influence ofa given point to the points nearby. This information is stored in thevectors i and j, included in the loaded data. Suppose all the points arenumbered 1, 2,... ,4253. The i and j vectors describe the links betweenpoint i and point j. For example, if we look at the first five elements:>> [i(1:5) j(1:5)]’ans =1 2 3 5 42 310 10 11The interpretation is that point 1 is connected to point 2, point 2 isconnected to point 3, points 3 and 5 are connected to point 10, and soon. We create a sparse adjacency matrix, A, by using i and j as inputsto the sparse function:A = sparse(i,j,1);spy(A)The spy function plots a sparse matrix with a dot at the positions ofall the non-zero entries, which number 12,289 here (the length of the iand j vectors). The concentration of non-zero elements near the diagonalreflects the local nature of the interaction (given a reasonable numberingscheme). To plot the geometry of the interactions we can use the gplotfunction:c○ 2000 by CRC Press LLC