Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Energy Group Treatments for Monte Carlo Neutron Transport Simulations Nick Horelik 22.107 Project May 17, 2012 Nick Horelik Energy Monte Carlo
Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Introduction 1 Monte Carlo Domain Decomposition 2 Space Energy Analysis of Approach High-Order/Low-Order Iteration 3 CMFD Precedent Extension to Energy Analysis of Approach Summary 4 Nick Horelik Energy Monte Carlo
Introduction Domain Decomposition Monte Carlo High-Order/Low-Order Iteration Summary Introduction Linear Time-independent Transport Equation Nick Horelik Energy Monte Carlo
Introduction Domain Decomposition Monte Carlo High-Order/Low-Order Iteration Summary Tally fluxes and reaction rates w j 1 φ = � WV Σ T ( E j ) j Embarrasingly parallel Memory intense for large problems Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary Domain Decomposition Over 100 billion histories required for 1% statistics in each depletion region Many 10s of GBytes required per processor for the large number of tallies needed We need to split the problem up to have any hope Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary Space Distribute the spatial domain among different compute nodes Follow particles from birth to death, communicating information space (weight, energy, direction, etc) to the appropriate node when it hits a boundary All compute nodes need access to energy entire energy spectrum of cross-section data for all isotopes Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary Energy Current Approach Split up the domain in energy instead of space Track particles through the entire geometry until they hit an energy space boundary Conserving total weight, run different numbers of particles in each energy group energy Focus computing power where it is harder to converge Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary Analysis of Approach Method Batches of Particles Energy Batch 1 start Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary Analysis of Approach Method Batches of Particles Energy Batch 2 start Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary Analysis of Approach Method Batches of Particles Energy Batch 3 start Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary Analysis of Approach Method Batches of Particles Energy Batch 4 start Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary Analysis of Approach Method Batches of Particles Energy Batch 1 done Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary Analysis of Approach Method Need to run more batches of particles than active tally batches Problem dependent (how scattering) Must conserve weight of all scatter sites for consistency In each group g − → g ′ For each unfinished batch Tallies need to be tracked until the active batch finishes Significantly increases memory requirements This is a book-keeping nightmare! Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary At least it gives the expected results... Nick Horelik Energy Monte Carlo
Introduction Space Domain Decomposition Energy High-Order/Low-Order Iteration Analysis of Approach Summary Cost/Benefit Fission site sampling requires more communications now, to start particles in the proper groups Inhibits scaling – before fission sites could stay on the same compute node for the next batch At worst all particles scatter out of the group to all other groups For space, at worst they all scatter out to only the adjacent compute nodes Cutting up the energy domain reduces cross section memory requirements for each node However, more groups compounds the communications burden, and keeps batches alive longer (more tally memory needed) As implemented, this hurts more than it helps Nick Horelik Energy Monte Carlo
Introduction CMFD Precedent Domain Decomposition Extension to Energy High-Order/Low-Order Iteration Analysis of Approach Summary High-Order/Low-Order Iteration Perhaps we can find a way to separate batches from one another and not have to communicate as many sites between compute nodes Use Monte Carlo (high-order) as a fixed source solver in each group Use Diffusion (low-order) to set weights and ensure consistency of global tallies Nick Horelik Energy Monte Carlo
Introduction CMFD Precedent Domain Decomposition Extension to Energy High-Order/Low-Order Iteration Analysis of Approach Summary CMFD Precedent Tally 1-group cross-sections and solve the spatial coarse mesh finite difference equations Update the weights of the next batch’s fission particles based on results Speeds up Monte Carlo convergence for large problems that don’t interact much across large spatial distances Hopefully we can acheive similar convergence acceleration However this method is still fundamentally different, beacause we bank scatter sites Nick Horelik Energy Monte Carlo
Introduction CMFD Precedent Domain Decomposition Extension to Energy High-Order/Low-Order Iteration Analysis of Approach Summary Extension to Energy Initially fully cover the energy spectrum Bank fission and scatter Run full MC sites, noting g − → g ′ Tally group XSs & particle sites Tally group and Solve multigroup diffusion group-to-group cross sections for diffusion Run fixed source MC Use the diffusion solution to start the series of fixed source MC runs Nick Horelik Energy Monte Carlo
Introduction CMFD Precedent Domain Decomposition Extension to Energy High-Order/Low-Order Iteration Analysis of Approach Summary Only scatter site sampling, no diffusion weighting Nick Horelik Energy Monte Carlo
Introduction CMFD Precedent Domain Decomposition Extension to Energy High-Order/Low-Order Iteration Analysis of Approach Summary Only diffusion weighting Nick Horelik Energy Monte Carlo
Introduction CMFD Precedent Domain Decomposition Extension to Energy High-Order/Low-Order Iteration Analysis of Approach Summary Diffusion weighting & collision scaling Nick Horelik Energy Monte Carlo
Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Summary Brute-force energy domain decomposition doesn’t appear feasible, at least as implented here Deterministic acceleration in energy looks promising Still much work to be done, different avenues to explore Re-do the detailed Monte Carlo run periodically? Keep running update of tallied group cross sections? Nick Horelik Energy Monte Carlo
Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Thank You Questions? Nick Horelik Energy Monte Carlo
Recommend
More recommend
