An adaptive Monte Carlo integration algorithm with general division approach

2008 ◽  
Vol 79 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Mahmoud H. Alrefaei ◽  
Houssam M. Abdul-Rahman
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Integration ◽  
Integration Algorithm ◽  
Adaptive Monte Carlo

Distributed Monte Carlo Integration Using Corba and Java

1998 ◽  
Vol 09 (07) ◽  
pp. 903-915 ◽  
Author(s):  
Fritz Solms ◽  
Willi-Hans Steeb
Keyword(s):  
Monte Carlo ◽  
Distributed Computing ◽  
Scientific Computing ◽  
Object Oriented ◽  
Monte Carlo Integration ◽  
The Internet ◽  
Integration Algorithm

The object-oriented middleware standard, CORBA, is a very useful platform for distributed computing, and in particular for sharing a workload among a collection of possibly polymorphic computers. CORBA has, however, received relatively little attention from the scientific computing community. In this article we demonstrate how CORBA and Java can be used to implement a distributed multi-dimensional Monte Carlo integration algorithm which runs on the internet.

scholarly journals Primary-space Adaptive Control Variates Using Piecewise-polynomial Approximations

2021 ◽  
Vol 40 (3) ◽  
pp. 1-15
Author(s):  
Miguel Crespo ◽  
Adrian Jarabo ◽  
Adolfo Muñoz
Keyword(s):  
Monte Carlo ◽  
Importance Sampling ◽  
High Frequency ◽  
Low Frequency ◽  
Monte Carlo Integration ◽  
Piecewise Polynomial ◽  
Integration Algorithm ◽  
Participating Media ◽  
Control Variate ◽  
Primary Space

We present an unbiased numerical integration algorithm that handles both low-frequency regions and high-frequency details of multidimensional integrals. It combines quadrature and Monte Carlo integration by using a quadrature-based approximation as a control variate of the signal. We adaptively build the control variate constructed as a piecewise polynomial, which can be analytically integrated, and accurately reconstructs the low-frequency regions of the integrand. We then recover the high-frequency details missed by the control variate by using Monte Carlo integration of the residual. Our work leverages importance sampling techniques by working in primary space, allowing the combination of multiple mappings; this enables multiple importance sampling in quadrature-based integration. Our algorithm is generic and can be applied to any complex multidimensional integral. We demonstrate its effectiveness with four applications with low dimensionality: transmittance estimation in heterogeneous participating media, low-order scattering in homogeneous media, direct illumination computation, and rendering of distribution effects. Finally, we show how our technique is extensible to integrands of higher dimensionality by computing the control variate on Monte Carlo estimates of the high-dimensional signal, and accounting for such additional dimensionality on the residual as well. In all cases, we show accurate results and faster convergence compared to previous approaches.

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