What is it about?
Simulating laser dynamics using methods like finite-difference time-domain (FDTD) requires storing and accessing large structured grids. The memory access pattern affects performance significantly because modern CPUs rely on spatial locality, accessing data that is stored nearby in memory is much faster than jumping around. Space-filling curves (Hilbert, Z-order) map multi-dimensional grids to one-dimensional memory layouts that preserve spatial locality better than the standard row-major or column-major orderings. This paper explored applying space-filling curve orderings to the grids used in semiclassical lasing simulations, combined with sparse matrix storage formats for the resulting operators. The work was conceptual, laying out the approach and expected benefits rather than presenting full benchmark results. It was presented at the URSI Asia-Pacific Radio Science Conference.
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Why is it important?
Memory access patterns dominate performance for grid-based PDE solvers on modern hardware, where the gap between compute throughput and memory bandwidth continues to widen. Space-filling curve orderings are well-established in other domains (adaptive mesh refinement, databases) but have not been widely applied to laser physics simulations. The paper connected these ideas to a specific application domain and identified where the locality improvements would have the largest impact (the time-stepping inner loop of FDTD-like methods). As a conference paper, it served as a roadmap rather than a complete implementation.
Perspectives
This was an early conference paper from my undergraduate work. The idea was straightforward: space-filling curves improve memory locality for grid traversals, and laser simulations use grids. The connection seemed obvious, but working out the details of how to apply Hilbert curves to the specific grid structures used in semiclassical simulations took more effort than I expected. The paper was more ambitious than I could deliver at the time, a full implementation with benchmarks would have been a much larger project. But the conceptual framework was sound, and the exercise of connecting computer science optimization techniques to a specific physics problem was formative for my later work.
Rohit Goswami
University of Iceland
Read the Original
This page is a summary of: Space Filling Curves: Heuristics For Semi Classical Lasing Computations, March 2019, Institute of Electrical & Electronics Engineers (IEEE),
DOI: 10.23919/ursiap-rasc.2019.8738612.
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