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Some computational infrastructure is needed before proceeding with other Milestones.
No due date•0/2 issues closedA large scale problem using the SPn implementation in Denovo will be used to challenge the MCSA work for asymmetric systems.
No due date•0/6 issues closedAside from resiliency motivations, the primary driver behind the FANM method is reduced memory pressure due to the lack of additional storage beyond that of the linear system in the MCSA method. The nonlinear benchmark problems we have chosen will let us measure this memory usage and compare it to conventional Newton-Krylov methods. Furthermore, by varying the strength of the nonlinearities in those problems (effectively by increasing the amount of convective transport in the system), the benchmarks will become more difficult to solve and require even more iterations to converge. This will give us a means by which to vary the complexity of the system which we can then compare to memory usage. Additionally, with the finite element assembly framework we can choose functional discretizations of varying accuracy, allowing us to vary the degrees of freedom in the system and therefore also vary the memory required for each problem.
No due date•0/5 issues closedA parallel MCSA implementation and our numerical test framework will allow us to compare its performance to Krylov methods and allow us to experiment with the way we combine it with the Neumann-Ulam solver. We hypothesized that if we can identify the amount of overlap in our Neumann- Ulam experiments required to eliminate most transitions between adjacent domains owned by different processors, then perhaps transport to adjacent domains can be ignored. This will result in a biased estimator for the MCSA correction that cannot be reproduced, however, these studies will aim to determine if that bias and lack of reproducibility affects the numerical results and reproducibility of the MCSA method, yielding a critical outcome for this work. Furthermore, we will use the experimental framework to measure the convergence rates for non-symmetric systems and memory usage of the MCSA algorithm and compare them to conventional Krylov methods using the same framework.
No due date•0/2 issues closedEmploying domain replication with the Neumann-Ulam method will be an exercise in batch statistics. By using replication, we also expect to incur an additional memory overhead. As noted in previous work, domain replication was coupled with domain overlap in order to improve load balancing and scalability in the implementations. As replication will likely be required to solve future resiliency issues and may even by required by this work in order to achieve scalability, its parallel performance must also be measured. We will therefore measure the memory and performance overhead incurred by varying the amount of domain replication leveraged by the Neumann-Ulam solver with respect to a fixed linear system.
No due date•0/1 issues closedCharacterizing and understanding the domain overlap behavior of a parallel Neumann-Ulam method will be critical to efficient implementations of other solvers that will be built on top of these methods. In the reactor physics work that we reviewed, the amount domain overlap used could be directly correlated to physical parameters of the system, namely the dimension of repeated geometric structures and the mean free path of neutrons in the system. We therefore seek analogous measurements for the general linear system. These measurements will characterize how far from its starting state a random walk sequence moves as a function of properties of the linear system. Our experimental framework will allow us to fix various properties of the system while varying others including the size of the linear system, its spectral radius, its sparsity, its asymmetry, and other parameters related to the Eigenvalues, conditioning, and structure of the linear operator. By varying the domain overlap and measuring parallel performance with respect to these properties, we can develop guidelines for setting the overlap with respect to measurable properties of the linear operator. In addition, varying the amount of overlap will allow us to measure the additional memory costs incurred.
No due date•0/1 issues closedThis milestone will organize my work towards a final thesis defense.
Overdue by 12 year(s)•Due by August 9, 2013