Methods to Accelerate Ray Tracing in the Monte Carlo Method for Surface-to-Surface Radiation Transport

2006 ◽  
Vol 128 (9) ◽  
pp. 945-952 ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Ray Tracing ◽  
Radiation Transport ◽  
Three Dimensional ◽  
Intersection Point ◽  
Surface Radiation ◽  
Computational Domain ◽  
Two Dimensional ◽  
Spatial Partitioning ◽  
The Monte Carlo Method

Two different algorithms to accelerate ray tracing in surface-to-surface radiation Monte Carlo calculations are investigated. The first algorithm is the well-known binary spatial partitioning (BSP) algorithm, which recursively bisects the computational domain into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The second algorithm is the volume-by-volume advancement (VVA) algorithm. This algorithm is new and employs the volumetric mesh to advance the ray through the computational domain until a legitimate intersection point is found. The algorithms are tested for two classical problems, namely an open box, and a box in a box, in both two-dimensional (2D) and three-dimensional (3D) geometries with various mesh sizes. Both algorithms are found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. For three-dimensional geometries, the VVA algorithm is found to be clearly superior to BSP, particularly for cases with obstructions within the computational domain. For two-dimensional geometries, the VVA algorithm is found to be superior to the BSP algorithm only when obstructions are present and are densely packed.

The Binary Spatial Partitioning Algorithm for Efficient Tracing of Rays in the Monte Carlo Method for Surface-to-Surface Radiation Transport

2006 ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Binary Tree ◽  
Radiation Transport ◽  
Three Dimensional ◽  
Surface Radiation ◽  
Computational Domain ◽  
Spatial Partitioning ◽  
The Monte Carlo Method ◽  
Discrete Surface

The Binary Spatial Partitioning (BSP) algorithm has found prolific usage within the computer graphics community for efficient tracing of rays. In this paper, the BSP algorithm is described and demonstrated in the context of the Monte Carlo method for surface-to-surface radiation transport. In the BSP algorithm the computational domain is recursively bisected into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The geometric information pertaining to these hierarchically linked boxes is stored in the form of a binary tree or table. The algorithm is tested for two classical problems, namely an open box, and a box in a box, in both two-dimensional (2D) and three-dimensional (3D) geometries with various mesh sizes, and is found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. In theory, the BSP algorithm is expected to scale logarithmically, i.e., the CPU time is expected to increase logarithmically with increase in the number of discrete surface elements (or faces) that the boundaries of the computational domain are broken into. In practice, however, it was found that balancing of the binary tree is critical for logarithmic scaling of the algorithm. Without balancing of the binary tree, only super-linear scaling can be attained.

Concentration Phase Transition in a Two-Dimensional Ferromagnet

2020 ◽  
Vol 312 ◽  
pp. 244-250
Author(s):  
Alexander Konstantinovich Chepak ◽  
Leonid Lazarevich Afremov ◽  
Alexander Yuryevich Mironenko
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermal Effect ◽  
Spin State ◽  
Critical Concentration ◽  
Two Dimensional ◽  
Percolation Transition ◽  
Magnetic Cluster ◽  
The Monte Carlo Method

The concentration phase transition (CPT) in a two-dimensional ferromagnet was simulated by the Monte Carlo method. The description of the CPT was carried out using various order parameters (OP): magnetic, cluster, and percolation. For comparison with the problem of the geometric (percolation) phase transition, the thermal effect on the spin state was excluded, and thus, CPT was reduced to percolation transition. For each OP, the values ​​of the critical concentration and critical indices of the CPT are calculated.

Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

2020 ◽  
Vol 26 (3) ◽  
pp. 484-496
Author(s):  
Yu Yuan ◽  
Hendrix Demers ◽  
Xianglong Wang ◽  
Raynald Gauvin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Analytical Model ◽  
Hybrid Model ◽  
Three Dimensional ◽  
Heterogeneous Materials ◽  
X Ray ◽  
The Monte Carlo Method ◽  
Secondary Fluorescence ◽  
Good Agreement

AbstractIn electron probe microanalysis or scanning electron microscopy, the Monte Carlo method is widely used for modeling electron transport within specimens and calculating X-ray spectra. For an accurate simulation, the calculation of secondary fluorescence (SF) is necessary, especially for samples with complex geometries. In this study, we developed a program, using a hybrid model that combines the Monte Carlo simulation with an analytical model, to perform SF correction for three-dimensional (3D) heterogeneous materials. The Monte Carlo simulation is performed using MC X-ray, a Monte Carlo program, to obtain the 3D primary X-ray distribution, which becomes the input of the analytical model. The voxel-based calculation of MC X-ray enables the model to be applicable to arbitrary samples. We demonstrate the derivation of the analytical model in detail and present the 3D X-ray distributions for both primary and secondary fluorescence to illustrate the capability of our program. Examples for non-diffusion couples and spherical inclusions inside matrices are shown. The results of our program are compared with experimental data from references and with results from other Monte Carlo codes. They are found to be in good agreement.

scholarly journals Safety Evaluation of Underground Caverns Based on Monte Carlo Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Qifeng Guo ◽  
Zhihong Dong ◽  
Meifeng Cai ◽  
Fenhua Ren ◽  
Jiliang Pan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Three Dimensional ◽  
Safety Evaluation ◽  
Cumulative Distribution ◽  
Three Dimensional Model ◽  
Maximum Displacement ◽  
The Monte Carlo Method ◽  
Underground Caverns ◽  
The Stability

In order to study the influence of joint fissures and rock parameters with random characteristics on the safety of underground caverns, several parameters affecting the stability of surrounding rock of underground caverns are selected. According to the Monte Carlo method, random numbers satisfying normal distribution characteristics are established. A three-dimensional model of underground caverns with random characteristics is established by discontinuous analysis software 3DEC and excavation simulations are carried out. The maximum displacement at the numerical monitoring points of arch and floor is the safety evaluation index of the cavern. The probability distribution and cumulative distribution function of the displacement at the top arch and floor are obtained, and the safety of a project is evaluated.

FluorWPS: A Monte Carlo ray-tracing model to compute sun-induced chlorophyll fluorescence of three-dimensional canopy

2016 ◽  
Vol 187 ◽  
pp. 385-399 ◽  
Author(s):  
Feng Zhao ◽  
Xu Dai ◽  
Wout Verhoef ◽  
Yiqing Guo ◽  
Christiaan van der Tol ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Chlorophyll Fluorescence ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Ray Tracing Model
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