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42
Interactive Global Illumination using Fast Ray Tracing
, 2002
"... Rasterization hardware provides interactive frame rates for rendering dynamic scenes, but lacks the ability of ray tracing required for efficient global illumination simulation. Existing ray tracing based methods yield high quality renderings but are far too slow for interactive use. We present a ..."
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Cited by 110 (19 self)
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Rasterization hardware provides interactive frame rates for rendering dynamic scenes, but lacks the ability of ray tracing required for efficient global illumination simulation. Existing ray tracing based methods yield high quality renderings but are far too slow for interactive use. We present a new parallel global illumination algorithm that perfectly scales, has minimal preprocessing and communication overhead, applies highly efficient sampling techniques based on randomized quasiMonte Carlo integration, and benefits from a fast parallel ray tracing implementation by shooting coherent groups of rays. Thus a performance is achieved that allows for applying arbitrary changes to the scene, while simulating global illumination including shadows from area light sources, indirect illumination, specular effects, and caustics at interactive frame rates. Ceasing interaction rapidly provides high quality renderings.
GALERKIN FINITE ELEMENT APPROXIMATIONS OF STOCHASTIC ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
, 2004
"... We describe and analyze two numerical methods for a linear elliptic problem with stochastic coefficients and homogeneous Dirichlet boundary conditions. Here the aim of the computations is to approximate statistical moments of the solution, and, in particular, we give a priori error estimates for the ..."
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Cited by 77 (5 self)
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We describe and analyze two numerical methods for a linear elliptic problem with stochastic coefficients and homogeneous Dirichlet boundary conditions. Here the aim of the computations is to approximate statistical moments of the solution, and, in particular, we give a priori error estimates for the computation of the expected value of the solution. The first method generates independent identically distributed approximations of the solution by sampling the coefficients of the equation and using a standard Galerkin finite element variational formulation. The Monte Carlo method then uses these approximations to compute corresponding sample averages. The second method is based on a finite dimensional approximation of the stochastic coefficients, turning the original stochastic problem into a deterministic parametric elliptic problem. A Galerkin finite element method, of either the h or pversion, then approximates the corresponding deterministic solution, yielding approximations of the desired statistics. We present a priori error estimates and include a comparison of the computational work required by each numerical approximation to achieve a given accuracy. This comparison suggests intuitive conditions for an optimal selection of the numerical approximation.
Monte Carlo Variance of Scrambled Net Quadrature
 SIAM J. Numer. Anal
, 1997
"... . Hybrids of equidistribution and Monte Carlo methods of integration can achieve the superior accuracy of the former while allowing the simple error estimation methods of the latter. This paper studies the variance of one such hybrid, scrambled nets, by applying a multidimensional multiresolution (w ..."
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Cited by 28 (1 self)
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. Hybrids of equidistribution and Monte Carlo methods of integration can achieve the superior accuracy of the former while allowing the simple error estimation methods of the latter. This paper studies the variance of one such hybrid, scrambled nets, by applying a multidimensional multiresolution (wavelet) analysis to the integrand. The integrand is assumed to be measurable and square integrable but not necessarily of bounded variation. In simple Monte Carlo, every nonconstant term of the multiresolution contributes to the variance of the estimated integral. For scrambled nets, certain lowdimensional and coarse terms do not contribute to the variance. For any integrand in L 2 , the sampling variance tends to zero faster under scrambled net quadrature than under Monte Carlo sampling, as the number of function evaluations n tends to infinity. Some finite n results bound the variance under scrambled net quadrature by a small constant multiple of the Monte Carlo variance, uniformly ove...
Efficient Multidimensional Sampling
, 2002
"... Image synthesis often requires the Monte Carlo estimation of integrals. Based on a generalized concept of stratification we present an efficient sampling scheme that consistently outperforms previous techniques. This is achieved by assembling sampling patterns that are stratified in the sense of jit ..."
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Cited by 25 (1 self)
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Image synthesis often requires the Monte Carlo estimation of integrals. Based on a generalized concept of stratification we present an efficient sampling scheme that consistently outperforms previous techniques. This is achieved by assembling sampling patterns that are stratified in the sense of jittered sampling and Nrooks sampling at the same time. The faster convergence and improved antialiasing are demonstrated by numerical experiments.
The Dimension Distribution, and Quadrature Test Functions
"... This paper introduces the dimension distribution for a square integrable function f on [0; 1]^s. The dimension distribution is used to relate several definitions of the effective dimension of a function. Functions of low effective dimension can be easy to integrate numerically. ..."
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Cited by 24 (4 self)
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This paper introduces the dimension distribution for a square integrable function f on [0; 1]^s. The dimension distribution is used to relate several definitions of the effective dimension of a function. Functions of low effective dimension can be easy to integrate numerically.
Random Walks On Boundary For Solving Pdes
, 1994
"... Contents 1. Introduction 1 2. Random walk algorithms for solving integral equations 7 2.1. Conventional Monte Carlo scheme : : : : : : : : : : : : : : : : : : : : : : : 7 2.2. Biased estimators : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13 2.3. Linearfractional transformations ..."
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Cited by 16 (5 self)
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Contents 1. Introduction 1 2. Random walk algorithms for solving integral equations 7 2.1. Conventional Monte Carlo scheme : : : : : : : : : : : : : : : : : : : : : : : 7 2.2. Biased estimators : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13 2.3. Linearfractional transformations and relations to iterative processes : : : : 15 2.4. Asymptotically unbiased estimators based on singular approximation of the kernel : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 21 2.5. Integral equation of the first kind : : : : : : : : : : : : : : : : : : : : : : : 28 3. Random Walk on Boundary algorithms for solving the Laplace equation 33 3.1. Newton potentials and boundary integral equations of the electrostatics : : 33 3.2. The interior Dirichlet problem and isotropic Random Walk on Boundary process : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 35 3.3. Solution of the Neumann problem : : : : : : : : : : : : : : : :
Interactive Global Illumination in . . .
 EUROGRAPHICS SYMPOSIUM ON RENDERING
, 2003
"... Global illumination algorithms have traditionally been very time consuming and were only suitable for offline computations. Recent research in realtime ray tracing has improved global illumination performance to allow for illumination updates at interactive rates. However, both the traditional of ..."
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Cited by 14 (2 self)
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Global illumination algorithms have traditionally been very time consuming and were only suitable for offline computations. Recent research in realtime ray tracing has improved global illumination performance to allow for illumination updates at interactive rates. However, both the traditional offline and the new interactive systems show significant limitations when dealing with realistically complex scenes containing millions of surfaces, thousands of light sources, and a high degree of occlusion. In this paper,
Quasirandom Number Generators for Parallel Monte Carlo Algorithms
 Journal of Parallel and Distributed Computing
, 1995
"... A method for generating sequences of quasirandom numbers allows conventional serial Monte Carlo algorithms to be parallelized with no loss of computation efficiency. Specifically, a Sobol' sequence can be broken up into interleaved subsets; with each processing node calculating a unique subset of ..."
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Cited by 13 (0 self)
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A method for generating sequences of quasirandom numbers allows conventional serial Monte Carlo algorithms to be parallelized with no loss of computation efficiency. Specifically, a Sobol' sequence can be broken up into interleaved subsets; with each processing node calculating a unique subset of the full sequence, all of the computational advantages of quasirandom Monte Carlo methods over purerandom algorithms or gridbased techniques are retained. Tests with several parallel supercomputers demonstrate that greater than 10 5 integration points (1D6D regions) can be generated per second per node, independent of the number of nodes. Subject headings: Monte Carlo methods  parallel computation. 1 Introduction The purpose of this work is to introduce a method for efficiently generating quasirandom number sequences on parallel computers. These sequences can be used in Monte Carlo algorithms which have a wide range of scientific and engineering applications. Here we conside...
30.1 SRAM Parametric Failure Analysis
"... With aggressive technology scaling, SRAM design has been seriously challenged by the difficulties in analyzing rare failure events. In this paper we propose to create statistical performance models with accuracy sufficient to facilitate probability extraction for SRAM parametric failures. A piecewis ..."
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Cited by 8 (5 self)
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With aggressive technology scaling, SRAM design has been seriously challenged by the difficulties in analyzing rare failure events. In this paper we propose to create statistical performance models with accuracy sufficient to facilitate probability extraction for SRAM parametric failures. A piecewise modeling technique is first proposed to capture the performance metrics over the large variation space. A controlled sampling scheme and a nested Monte Carlo analysis method are then applied for the failure probability extraction at celllevel and arraylevel respectively. Our 65nm SRAM example demonstrates that by combining the piecewise model and the fast probability extraction methods, we have significantly accelerated the SRAM failure analysis.
Architecture and Design of a Diagnostic Information Fusion Tool
 AI in Equipment Service
, 2001
"... This paper introduces an architecture for aggregation of output from different diagnostic tools. The diagnostic fusion tool deals with conflict resolution where diagnostic tools disagree, temporal information discord where the estimate of different tools is separated in time, differences in informat ..."
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Cited by 6 (4 self)
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This paper introduces an architecture for aggregation of output from different diagnostic tools. The diagnostic fusion tool deals with conflict resolution where diagnostic tools disagree, temporal information discord where the estimate of different tools is separated in time, differences in information updates where the classifiers are updated at different rates, fault coverage discrepancies, and integration of a priori performance specifications. To this end a hierarchical weight manipulation approach is introduced which creates and successively refines a fused output. The performance of the fusion tool is evaluated throughout its design. This allows impact assessment of adding heuristics and enables early tuning of parameters. Results obtained from diagnosing onboard faults from aircraft engines are shown which demonstrate the fusion toolâ€™s operation.