EECS 419: Some Comments on Test 3 Final =============================================================================== In the Poisson equation use the following V(x,y,t+1) = (V(x-1,y,t) + V(x,y-1,t) + V(x+1,y,t) + V(x,y+1,t))/4 No C(i,j) function was given. ----------------------------------------------------------------------------- About the mesh simulation problems, it is best to keep the boundary conditions and work through the mesh. ----------------------------------------------------------------------------------------- In the Poisson simulation problem, you may want to consider the following initialization regarding the mesh boundary, so that there will be a propagation effect 0 0 0 0 ... 0 10 ? X X ... 10 10 X X X ... 10 .................. 10 X X X 10 20 20 20 20 20 Then, just change the scanning order from left->right and top->bottom to their reverses -------------------------------------------------------------------------------------------------- About the C model for the domain decomposion The C program is for the architectures given in the figures, the mesh of meshes and the mesh domain. Boundaries for the whole grid as described in the problem statement ---------------------------------------------------------------------------------------------------- More on domain decomposition ***** Let q be a domain index, k be iteration index then q = 0, 1, ... (Q^2)-1 k = 0, 1 ... J (convergence) for example, Domain(i,j) is indexed by q=i+j*Q Now, when you do domain iteration D(i,j)(k+1) you will need the values from four neighbor domains, i.e. D(i,j-1)(k) D(i-1,j)(k) D(i+1,j)(k) D(i,j+1)(k) But you should already have these values stored in corresponding cell memories. ** Interdomain communication is done through memory stored values. D(i,j+1)(k) --------------------------------------------------------------------------------------- About mapping the 8x8 mesh to a hypercube. Of course the outcome will not be a perfect mesh because the near neighbors are not really near physically. But you can still apply the mesh computation using the communication routine given in the broacasting problem. ---------------------------------------------------------------------------------------------- About unrolling the shuffle network. Unrolling the shuffle is just shown in the same figure. Just mark up the paths and settings (of the boxes) to show how a cyclic shift of an input vector, say [0 1 2 3 4 5 6 7] by 3 positions is implemented. ----------------------------------------------------------------------------------------------------- About the PE Array processor There are many ways to allocate. Try to allocate rows of A and columns of B into processors. The processors have sufficient registers to be able to perform a vector cross multiply c11 = (a11b11 + a12b21 + 13b31). You also need some local registers. Depends how you do the allocation of data, you need some shifts to bring matching coeff together. ---------------------------------------------------------------------------------------
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