Evaluating View Factors Using a Hybrid Monte-Carlo Method (2024)

Cumber, P. S. (2022). Evaluating View Factors Using a Hybrid Monte-Carlo Method. Journal of Heat Transfer, 144(12), Article 122801. https://doi.org/10.1115/1.4055516

Cumber, Peter Stewart. / Evaluating View Factors Using a Hybrid Monte-Carlo Method. In: Journal of Heat Transfer. 2022 ; Vol. 144, No. 12.

@article{57e1bdc6cdf54c26b4527034fa6925e3,

title = "Evaluating View Factors Using a Hybrid Monte-Carlo Method",

abstract = "This paper demonstrates that the well-known method for calculating view factors, the Monte Carlo method, combined with ray tracing is not necessarily the most efficient strategy. The Monte Carlo method and quasi-Monte Carlo method combined with numerical integration, provided the surfaces in a configuration are not too close together, are more accurate for the same run-time than a ray tracing-based Monte Carlo method. The Monte Carlo method based on numerical integration is complementary to the Monte Carlo method based on ray tracing. When many rays are required to calculate an accurate view factor, few function evaluations in a numerical integration approach are necessary to achieve the same accuracy. Where the surfaces in a configuration are touching, the Monte Carlo method with numerical integration converges to the exact view factor very slowly due to a singularity in the view factor multi-integral. For these configurations, a hybrid Monte Carlo method and quasi-Monte Carlo method are demonstrated to be the stochastic methods of choice.",

keywords = "Monte-Carlo method, numerical integration, quasi-Monte-Carlo method, ray tracing",

author = "Cumber, {Peter Stewart}",

note = "Publisher Copyright: Copyright {\textcopyright} 2022 by ASME.",

year = "2022",

month = dec,

doi = "10.1115/1.4055516",

language = "English",

volume = "144",

journal = "Journal of Heat Transfer",

issn = "0022-1481",

publisher = "American Society of Mechanical Engineers",

number = "12",

}

Cumber, PS 2022, 'Evaluating View Factors Using a Hybrid Monte-Carlo Method', Journal of Heat Transfer, vol. 144, no. 12, 122801. https://doi.org/10.1115/1.4055516

Evaluating View Factors Using a Hybrid Monte-Carlo Method. / Cumber, Peter Stewart.
In: Journal of Heat Transfer, Vol. 144, No. 12, 122801, 12.2022.

Research output: Contribution to journal › Article › peer-review

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T1 - Evaluating View Factors Using a Hybrid Monte-Carlo Method

AU - Cumber, Peter Stewart

N1 - Publisher Copyright:Copyright © 2022 by ASME.

PY - 2022/12

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N2 - This paper demonstrates that the well-known method for calculating view factors, the Monte Carlo method, combined with ray tracing is not necessarily the most efficient strategy. The Monte Carlo method and quasi-Monte Carlo method combined with numerical integration, provided the surfaces in a configuration are not too close together, are more accurate for the same run-time than a ray tracing-based Monte Carlo method. The Monte Carlo method based on numerical integration is complementary to the Monte Carlo method based on ray tracing. When many rays are required to calculate an accurate view factor, few function evaluations in a numerical integration approach are necessary to achieve the same accuracy. Where the surfaces in a configuration are touching, the Monte Carlo method with numerical integration converges to the exact view factor very slowly due to a singularity in the view factor multi-integral. For these configurations, a hybrid Monte Carlo method and quasi-Monte Carlo method are demonstrated to be the stochastic methods of choice.

AB - This paper demonstrates that the well-known method for calculating view factors, the Monte Carlo method, combined with ray tracing is not necessarily the most efficient strategy. The Monte Carlo method and quasi-Monte Carlo method combined with numerical integration, provided the surfaces in a configuration are not too close together, are more accurate for the same run-time than a ray tracing-based Monte Carlo method. The Monte Carlo method based on numerical integration is complementary to the Monte Carlo method based on ray tracing. When many rays are required to calculate an accurate view factor, few function evaluations in a numerical integration approach are necessary to achieve the same accuracy. Where the surfaces in a configuration are touching, the Monte Carlo method with numerical integration converges to the exact view factor very slowly due to a singularity in the view factor multi-integral. For these configurations, a hybrid Monte Carlo method and quasi-Monte Carlo method are demonstrated to be the stochastic methods of choice.

KW - Monte-Carlo method

KW - numerical integration

KW - quasi-Monte-Carlo method

KW - ray tracing

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DO - 10.1115/1.4055516

M3 - Article

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SN - 0022-1481

VL - 144

JO - Journal of Heat Transfer

JF - Journal of Heat Transfer

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Cumber PS. Evaluating View Factors Using a Hybrid Monte-Carlo Method. Journal of Heat Transfer. 2022 Dec;144(12):122801. Epub 2022 Sept 21. doi: 10.1115/1.4055516