Load Balanced Parallel Node Generation for Meshless Numerical Methods
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914541689896960 |
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| author | Vehovar, Jon Rot, Miha Depolli, Matjaž Kosec, Gregor |
| author_facet | Vehovar, Jon Rot, Miha Depolli, Matjaž Kosec, Gregor |
| contents | Meshless methods are used to solve partial differential equations by approximating differential operators at a node as a weighted sum of values at its neighbours. One of the algorithms for generating nodes suitable for meshless numerical analysis is an n-dimensional Poisson disc sampling based method. It can handle complex geometries and supports variable node density, a crucial feature for adaptive analysis. We modify this method for parallel execution using coupled spatial indexing and work distribution hypertrees. The latter is prebuilt according to the node density function, ensuring that each leaf represents a balanced work unit. Threads advance separate fronts and claim work hypertree leaves as needed while avoiding leaves neighbouring those claimed by other threads. Node placement constraints and the partially prebuilt spatial hypertree are combined to eliminate the need to lock the tree while it is being modified. Thread collision handling is managed by the work hypertree at the leaf level, drastically reducing the number of required mutex acquisitions for point insertion collision checks. We explore the behaviour of the proposed algorithm and compare the performance with existing attempts at parallelisation and consider the requirements for adapting the developed algorithm to distributed systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_16347 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Load Balanced Parallel Node Generation for Meshless Numerical Methods Vehovar, Jon Rot, Miha Depolli, Matjaž Kosec, Gregor Distributed, Parallel, and Cluster Computing Meshless methods are used to solve partial differential equations by approximating differential operators at a node as a weighted sum of values at its neighbours. One of the algorithms for generating nodes suitable for meshless numerical analysis is an n-dimensional Poisson disc sampling based method. It can handle complex geometries and supports variable node density, a crucial feature for adaptive analysis. We modify this method for parallel execution using coupled spatial indexing and work distribution hypertrees. The latter is prebuilt according to the node density function, ensuring that each leaf represents a balanced work unit. Threads advance separate fronts and claim work hypertree leaves as needed while avoiding leaves neighbouring those claimed by other threads. Node placement constraints and the partially prebuilt spatial hypertree are combined to eliminate the need to lock the tree while it is being modified. Thread collision handling is managed by the work hypertree at the leaf level, drastically reducing the number of required mutex acquisitions for point insertion collision checks. We explore the behaviour of the proposed algorithm and compare the performance with existing attempts at parallelisation and consider the requirements for adapting the developed algorithm to distributed systems. |
| title | Load Balanced Parallel Node Generation for Meshless Numerical Methods |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2602.16347 |