Integral formulation of null-collision Monte Carlo algorithms

Galtier, Mathieu; Blanco, Stéphane; Caliot, Cyril; Coustet, Christophe; Dauchet, Jérémi; Hafi, Mouna El; Eymet, Vincent; Fournier, Richard; Gautrais, Jacques; Khuong, Anaïs; Piaud, Benjamin; Terrée, Guillaume

doi:10.1016/j.jqsrt.2013.04.001

Cited by 80 publications

(120 citation statements)

References 16 publications

Supporting

Mentioning

116

Contrasting

Order By: Relevance

“…Delta tracking first computes an upper bound (can be any upper bound) of the extinction coefficient, called the majorant extinction coefficient σ M . It then fills the entire region with particles that incur null collisions (for convenience we call them 'null particles') of an amount of σ M − σ(x) [9,10], so the extinction coefficient is now σ M everywhere. Those null particles are transparent: a light hitting a null particle will continue its journey along the same direction.…”

Section: Efficient and Unbiased Free Path Samplingmentioning

confidence: 99%

Bringing Computer and Physics Closer

Yue

2018

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Abstract. Physically based simulations are important for predicting the future states of the objects in consideration, and have been one of the major research topics in computer graphics. Applications include optical simulations for realistic image synthesis given a 3D scene, and rigid/fluid dynamics for computer animations. The need for the ultimate realism may sometimes ask for more efficient and accurate methods than those available in other fields. In addition, physically based optimizations are useful for designing and fabricating man-made objects given some desirable functionalities governed by physical laws. The ability to incorporate predictive simulations also allows us to build smarter robots that can optimize for their next movement based on the predictions. We introduce some of our work performed from this perspective. IntroductionOur world is governed by physical laws: the way how light travels from the light source to our eye can be described by the radiative transport equation; the way how the water in a cup behaves as we interact with the cup is described by the Navier-Stokes equations. The ability of predicting such physical behaviors would allow us to estimate how objects would deform and how they would look like, and is hence useful for computer animations.Physical laws also come into play when we want to design and fabricate man-made objects. For example, understanding how the light refracts is essential for designing lenses, and understanding how the contact and frictional forces act against the gravity is important for designing a stable sculpture that is assembled from a number of small bricks. Optimizations with physically based constraints in consideration are thus fundamental for designing and fabricating functional man-made objects.With the ability to incorporate predictive simulations in planning, we can also build smarter robots that use vision techniques to acquire the external information, perform predictive simulations to estimate the future states of the objects, and determine the appropriate control based on the predicted states. In this paper, we will review and introduce a series of our past work done from the above perspective.

show abstract

Section: Efficient and Unbiased Free Path Samplingmentioning

confidence: 99%

Bringing Computer and Physics Closer

Yue

2018

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

“…As shown in [1], introducing null-collisions consists in reformulating the radiative transfer equation…”

Section: The Null-collision Conceptmentioning

confidence: 99%

“…The first immediate benefit of this reformulation is that the new extinction term −k ν I ν no longer depends on the absorption coefficient, but only onk ν . In the configurations studied in [1], the true extinction along a given path was difficult to handle because of large heterogeneities of the temperature and concentration fields, leading to highly varying values of the absorption coefficient. It was much simpler to use a higher but uniformk ν field instead .…”

Section: The Null-collision Conceptmentioning

confidence: 99%

“…Recent advances in Monte Carlo methods [1,2] indicate that null-collision algorithms can be used to simulate radiative transfer in semi-transparent media in such a way that grids are no longer required. Even for highly nonhomogeneous configurations the volume does not need to be discretized and this is achieved while still preserving all the statistical properties of standard Monte Carlo algorithms: convergence toward the exact solution is rigorous (no bias) and for a finite number M of samples, the estimate is associated with a faithful statistical uncertainty (…”

Section: Introductionmentioning

confidence: 99%

“…Using the null-collision algorithm of [1] (assuming that k a,ν is precomputed) would lead to the following w-sampling algorithm:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Radiative transfer and spectroscopic databases: A line-sampling Monte Carlo approach

Galtier

Blanco

Dauchet

et al. 2016

Journal of Quantitative Spectroscopy and Radiative Transfer

View full text Add to dashboard Cite

Dealing with molecular-state transitions for radiative transfer purposes involves two successive steps that both reach the complexity level at which physicists start thinking about statistical approaches: 1/ constructing line-shaped absorption spectra as the result of very numerous state-transitions, 2/ integrating over optical-path domains. For the first time, we show here how these steps can be addressed simultaneously using the null-collision concept. This opens the door to the design of Monte Carlo codes directly estimating radiative transfer observables from spectroscopic databases. The intermediate step of producing accurate high-resolution absorption spectra is no longer required. A Monte Carlo algorithm is proposed and applied to six one-dimensional test cases. It allows the computation of spectrally integrated intensities (over 25cm −1 bands or the full IR range) in a few seconds, regardless of the retained database and line model. But free parameters need to be selected and they impact the convergence. A first possible selection is provided in full detail. We observe that this selection is highly satisfactory for quite distinct atmospheric and combustion configurations, but a more systematic exploration is still in progress.Keywords: Radiative transfer, Monte Carlo method, Null-collision, Line sampling, Statistical approach, Spectroscopic databases NomenclatureWe retain here the following standard statistical formalism: random variables are written in upper-case (e.g. X), free and bound variables in lower-case (e.g. x) and samples of random variables are subscripted (e.g. x m ).

show abstract

Technical note: A GPU‐based shared Monte Carlo method for fast photon transport in multi‐energy x‐ray exposures

Zhou,

Deng,

Kang

et al. 2024

Medical Physics

View full text Add to dashboard Cite

BackgroundThe Monte Carlo (MC) method is an accurate technique for particle transport calculation due to the precise modeling of physical interactions. Nevertheless, the MC method still suffers from the problem of expensive computational cost, even with graphics processing unit (GPU) acceleration. Our previous works have investigated the acceleration strategies of photon transport simulation for single‐energy CT. But for multi‐energy CT, conventional individual simulation leads to unnecessary redundant calculation, consuming more time.PurposeThis work proposes a novel GPU‐based shared MC scheme (gSMC) to reduce unnecessary repeated simulations of similar photons between different spectra, thereby enhancing the efficiency of scatter estimation in multi‐energy x‐ray exposures.MethodsThe shared MC method selects shared photons between different spectra using two strategies. Specifically, we introduce spectral region classification strategy to select photons with the same initial energy from different spectra, thus generating energy‐shared photon groups. Subsequently, the multi‐directional sampling strategy is utilized to select energy‐and‐direction‐shared photons, which have the same initial direction, from energy‐shared photon groups. Energy‐and‐direction‐shared photons perform shared simulations, while others are simulated individually. Finally, all results are integrated to obtain scatter distribution estimations for different spectral cases.ResultsThe efficiency and accuracy of the proposed gSMC are evaluated on the digital phantom and clinical case. The experimental results demonstrate that gSMC can speed up the simulation in the digital case by ∼37.8% and the one in the clinical case by ∼20.6%, while keeping the differences in total scatter results within 0.09%, compared to the conventional MC package, which performs an individual simulation.ConclusionsThe proposed GPU‐based shared MC simulation method can achieve fast photon transport calculation for multi‐energy x‐ray exposures.

show abstract

Integral formulation of null-collision Monte Carlo algorithms

Cited by 80 publications

References 16 publications

Bringing Computer and Physics Closer

Bringing Computer and Physics Closer

Radiative transfer and spectroscopic databases: A line-sampling Monte Carlo approach

Technical note: A GPU‐based shared Monte Carlo method for fast photon transport in multi‐energy x‐ray exposures

Contact Info

Product

Resources

About