An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo Simulations
In this work, we introduce a novel variance reduction approach utilising the integral formulation of the radiative transfer equation to calculate the radiance in a planar symmetric slab geometry. Due to its integral nature, our method offers a fundamental advantage over well-established variance red...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Photonics |
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| Online Access: | https://www.mdpi.com/2304-6732/11/1/5 |
| _version_ | 1797342736576151552 |
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| author | David Hevisov Dominik Reitzle André Liemert Alwin Kienle |
| author_facet | David Hevisov Dominik Reitzle André Liemert Alwin Kienle |
| author_sort | David Hevisov |
| collection | DOAJ |
| description | In this work, we introduce a novel variance reduction approach utilising the integral formulation of the radiative transfer equation to calculate the radiance in a planar symmetric slab geometry. Due to its integral nature, our method offers a fundamental advantage over well-established variance reduction methods such as the local estimate technique. As opposed to the local estimate procedure, photons add to the overall radiance not only at specific points of interaction but also throughout each consecutive path element; hence, our variance reduction approach can be thought of as an integral local estimate method. This facilitates a substantial enhancement in statistical efficiency, especially in scenarios where only a small number of scattering events or a high attenuation along the detection paths is to be anticipated. To evaluate the overall performance of the integral approach, we incorporated it into a self-developed GPU-accelerated Monte Carlo software, together with a conventional local estimate implementation adapted to slab geometry for a comprehensive comparison. |
| first_indexed | 2024-03-08T10:37:37Z |
| format | Article |
| id | doaj.art-8d4f7ebed8644903b6abf446216e3cd4 |
| institution | Directory Open Access Journal |
| issn | 2304-6732 |
| language | English |
| last_indexed | 2024-03-08T10:37:37Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Photonics |
| spelling | doaj.art-8d4f7ebed8644903b6abf446216e3cd42024-01-26T18:09:09ZengMDPI AGPhotonics2304-67322023-12-01111510.3390/photonics11010005An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo SimulationsDavid Hevisov0Dominik Reitzle1André Liemert2Alwin Kienle3Institut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm, Helmholtzstr. 12, D-89081 Ulm, GermanyInstitut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm, Helmholtzstr. 12, D-89081 Ulm, GermanyInstitut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm, Helmholtzstr. 12, D-89081 Ulm, GermanyInstitut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm, Helmholtzstr. 12, D-89081 Ulm, GermanyIn this work, we introduce a novel variance reduction approach utilising the integral formulation of the radiative transfer equation to calculate the radiance in a planar symmetric slab geometry. Due to its integral nature, our method offers a fundamental advantage over well-established variance reduction methods such as the local estimate technique. As opposed to the local estimate procedure, photons add to the overall radiance not only at specific points of interaction but also throughout each consecutive path element; hence, our variance reduction approach can be thought of as an integral local estimate method. This facilitates a substantial enhancement in statistical efficiency, especially in scenarios where only a small number of scattering events or a high attenuation along the detection paths is to be anticipated. To evaluate the overall performance of the integral approach, we incorporated it into a self-developed GPU-accelerated Monte Carlo software, together with a conventional local estimate implementation adapted to slab geometry for a comprehensive comparison.https://www.mdpi.com/2304-6732/11/1/5Monte Carlo simulationvariance reduction methodlocal estimate methodangular reflectance and transmittanceplanar radianceradiative transfer equation |
| spellingShingle | David Hevisov Dominik Reitzle André Liemert Alwin Kienle An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo Simulations Photonics Monte Carlo simulation variance reduction method local estimate method angular reflectance and transmittance planar radiance radiative transfer equation |
| title | An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo Simulations |
| title_full | An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo Simulations |
| title_fullStr | An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo Simulations |
| title_full_unstemmed | An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo Simulations |
| title_short | An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo Simulations |
| title_sort | integral equation based variance reduction method for accelerated monte carlo simulations |
| topic | Monte Carlo simulation variance reduction method local estimate method angular reflectance and transmittance planar radiance radiative transfer equation |
| url | https://www.mdpi.com/2304-6732/11/1/5 |
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