Building on a former project of mine on implementing a Multigrid PDE solver in HPF (NPAC Report SCCS 772), I'd like to find out at which grid levels it pays off not to distribute the grids, but to duplicate the processing on all nodes. For small grids (like 3x3x3 or 5x5x5) it certainly would be faster. I'd also like to find out more about the (dis)advantage of (*,*,BLOCK) vs. (*,BLOCK,BLOCK) and (BLOCK,BLOCK,BLOCK) distributions. The code will run under VPL (it's just HPF, after all) but I'll do the actual timings at the Cornell SP-2.
I will implement a solution to Laplaces'equation using Fourier Transformation. The implementation would done in HPF.
I propose to write an HPF program to compute object representations, resulting from graphical transformations (translation, rotation scaling), in parallel. Homogenous-coordinate representations of points in 3D-space will be used to facilitate the representation of transformations as 4x4 matrices. I will conduct timings on large objects and examine speed improvements.
I am interested in working on mathematics for our project. So I chose a simple topic on solving linear equations using directive method and back substitution. This is a basic issue in linear algebra and typical in parallel computing. I'd like to write it in HPF.
Okay, here's my idea for the mini project. Try some flow visualization of inviscid airflow through a duct as shown below. I would like to use HPF for this project. The value of Psi over the grid can be found using Laplace's equation and will be programmed using Jacobi or Guass-Seidel SOR methods. Here these values correspond to stream function values, so we can use a graphics package to make a contour plot of constant PSi and thus show how air would flow through the duct.
This type of grid requires a tricky distribution in HPF. We cannot simply use block, as a severe load imbalance will occur. Rather, I will be forced to experiment with the CYCLIC directive. Hopefully some insight will be gained into the proper distribution for symmetrical grids of this type.
Parallel Ray Tracing using HPF
Ray Tracing: In the real world, a point on a surface can be seen by an observer as a result of the interaction of the surface at that point with rays. There are many surface reflection model to simulate the illumination- reflection model in computer graphics. The Ray Tracing model is currently the most complete one. The difference of Ray Tracing from other model is the 'depth' to which interaction between light rays and objects in the scene is examined. There are also many disadvantages in Ray Tracing model. One of them is the processing overheads. Ray-traced images may take many minutes, hours or even days to cumpute. The significant advantage is that it combines several solutions for the global illumination problem.