Efficient Host-Element Determination in Convex Polyhedral Meshes Using an Adaptive Patch-Search Algorithm

Daeyeun Kim

doi:10.1016/j.jcp.2026.115393

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Efficient Host-Element Determination in Convex Polyhedral Meshes Using an Adaptive Patch-Search Algorithm

2026-09-17

Daeyeun Kim

Nathan Ravoisin *

Geoffrey T. Parks

DOI：10.1016/j.jcp.2026.115393

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Abstract

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Locating particles in dense, unstructured polyhedral meshes remains a critical performance bottleneck in high-fidelity physics simulations, including computational fluid dynamics and Monte Carlo neutron transport. To address this, we extend the Patch-Search method—originally limited to tetrahedral topologies—to enable efficient host-element determination in arbitrary convex polyhedral mesh geometries. We introduce an adaptive, multi-layered grid structure to drastically reduce the prohibitive memory requirements of the original algorithm, thereby eliminating the need for a uniform grid resolution constrained by the domain’s smallest geometric features. Performance comparisons against an optimised linear octree baseline are conducted by locating one billion points on unit-cell geometries typical of nuclear engineering applications with varying mesh element types and densities. Results demonstrate that the proposed method consistently accelerates host-element determination by 32–55%. Compared to the original Patch-Search implementation, our adaptive multi-layered approach achieves initialisation time and memory savings of 82% to 99% across all mesh cases tested, making it a robust and efficient alternative to tree-based acceleration structures for particle-tracking applications.

Keywords:

Host-element determination

Particle tracking

Unstructured volume mesh

Patch-Search algorithm

Monte Carlo neutron transport

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