Parallelization of adaptive MC Integrators

Monte Carlo (MC) methods for numerical integration seem to be embarassingly parallel on first sight. When adaptive schemes are applied in order to enhance convergence however, the seemingly most natural way of replicating the whole job on each processor can potentially ruin the adaptive behaviour. Using the popular VEGAS-Algorithm as an example an economic method of semi-micro parallelization with variable grain-size is presented and contrasted with another straightforward approach of macro-parallelization. A portable implementation of this semi-micro parallelization is used in the xloops-project and is made publicly available.Comment: 10 pages, LaTeX2e, 1 pstricks-figure included and 2 eps-figures inserted via epsfig. To appear in Comput. Phys. Commu

Adaptation of a long-period composite random number generator for parallel processing

An efficient and statistically reliable random number generator is one of the most important requirements for effective Monte Carlo simulation. The latest trend in supercomputing being towards parallelization, a random number generator was designed that will allow the generation of several uncorrelated streams of random numbers in parallel. This is achieved by the division of one period of a good serial random number generator into intervals of uniform length, one interval per processor. The serial random number generator chosen was the Marsaglia - Zaman random number generator which is a long period composite random number generator combining a linear congruential sequence with a lagged Fibonacci sequence. The mathematical relation between distantly separated seed values in each of the sequences was considered and a method was developed to obtain values from the Marsaglia - Zaman sequence spaced from each other by the length of a specified interval called the jump distance. Program\u27s implementing the algorithm were written in C and Fortran. Seed values obtained from the programs can be used to initialize different processors to use different portions of the Marsaglia - Zaman sequence. The seed values obtained by looping through all the random numbers in a section of the Marsaglia - Zaman sequence were shown to be identical to the seed values obtained from the developed algorithm. The execution time for the developed method was shown to increase only as the order of log2(jump distance)

Parallel hierarchical global illumination

Solving the global illumination problem is equivalent to determining the intensity of every wavelength of light in all directions at every point in a given scene. The complexity of the problem has led researchers to use approximation methods for solving the problem on serial computers. Rather than using an approximation method, such as backward ray tracing or radiosity, we have chosen to solve the Rendering Equation by direct simulation of light transport from the light sources. This paper presents an algorithm that solves the Rendering Equation to any desired accuracy, and can be run in parallel on distributed memory or shared memory computer systems with excellent scaling properties. It appears superior in both speed and physical correctness to recent published methods involving bidirectional ray tracing or hybrid treatments of diffuse and specular surfaces. Like progressive radiosity methods, it dynamically refines the geometry decomposition where required, but does so without the excessive storage requirements for ray histories. The algorithm, called Photon, produces a scene which converges to the global illumination solution. This amounts to a huge task for a 1997-vintage serial computer, but using the power of a parallel supercomputer significantly reduces the time required to generate a solution. Currently, Photon can be run on most parallel environments from a shared memory multiprocessor to a parallel supercomputer, as well as on clusters of heterogeneous workstations