1,445 research outputs found
A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering
An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance
Go with the winners strategy in path tracing
This paper proposes a new random walk strategy that minimizes the variance of the estimate
using statistical estimations of local and global features of the scene. Based on the local and
global properties, the algorithm decides at each point whether a Russian-roulette like random
termination is worth performing, or on the contrary, we should split the path into several child
paths. In this sense the algorithm is similar to the go-with-the-winners strategy invented in general
Monte Carlo context. However, instead of establishing thresholds to make decisions, we compute
the number of child paths on a continuous level and show that Russian roulette can be interpreted
as a kind of splitting using fractional number of children. The new method is built into a path
tracing algorithm, and a minimum cost heuristic is proposed for choosing the number of rejected
rays. Comparing it with the classical path tracing approach we concluded that the new method
reduced the variance significantly
A geometrical model for the Monte Carlo simulation of the TrueBeam linac
Monte Carlo (MC) simulation of linacs depends on the accurate geometrical
description of the head. The geometry of the Varian TrueBeam (TB) linac is not
available to researchers. Instead, the company distributes phase-space files
(PSFs) of the flattening-filter-free (FFF) beams tallied upstream the jaws.
Yet, MC simulations based on third party tallied PSFs are subject to
limitations. We present an experimentally-based geometry developed for the
simulation of the FFF beams of the TB linac. The upper part of the TB linac was
modeled modifying the Clinac 2100 geometry. The most important modification is
the replacement of the standard flattening filters by ad hoc thin filters which
were modeled by comparing dose measurements and simulations. The experimental
dose profiles for the 6MV and 10MV FFF beams were obtained from the Varian
Golden Data Set and from in-house measurements for radiation fields ranging
from 3X3 to 40X40 cm2. Indicators of agreement between the experimental data
and the simulation results obtained with the proposed geometrical model were
the dose differences, the root-mean-square error and the gamma index. The same
comparisons were done for dose profiles obtained from MC simulations using the
second generation of PSFs distributed by Varian for the TB linac. Results of
comparisons show a good agreement of the dose for the ansatz geometry similar
to that obtained for the simulations with the TB PSFs for all fields
considered, except for the 40X40 cm2 field where the ansatz geometry was able
to reproduce the measured dose more accurately. Our approach makes possible to:
(i) adapt the initial beam parameters to match measured dose profiles; (ii)
reduce the statistical uncertainty to arbitrarily low values; and (iii) assess
systematic uncertainties by employing different MC codes
Monte-Carlo analysis of rarefied-gas diffusion including variance reduction using the theory of Markov random walks
Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks
Tenfold your photons -- a physically-sound approach to filtering-based variance reduction of Monte-Carlo-simulated dose distributions
X-ray dose constantly gains interest in the interventional suite. With dose
being generally difficult to monitor reliably, fast computational methods are
desirable. A major drawback of the gold standard based on Monte Carlo (MC)
methods is its computational complexity. Besides common variance reduction
techniques, filter approaches are often applied to achieve conclusive results
within a fraction of time. Inspired by these methods, we propose a novel
approach. We down-sample the target volume based on the fraction of mass,
simulate the imaging situation, and then revert the down-sampling. To this end,
the dose is weighted by the mass energy absorption, up-sampled, and distributed
using a guided filter. Eventually, the weighting is inverted resulting in
accurate high resolution dose distributions. The approach has the potential to
considerably speed-up MC simulations since less photons and boundary checks are
necessary. First experiments substantiate these assumptions. We achieve a
median accuracy of 96.7 % to 97.4 % of the dose estimation with the proposed
method and a down-sampling factor of 8 and 4, respectively. While maintaining a
high accuracy, the proposed method provides for a tenfold speed-up. The overall
findings suggest the conclusion that the proposed method has the potential to
allow for further efficiency.Comment: 6 pages, 3 figures, Bildverarbeitung f\"ur die Medizin 202
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