Results 1  10
of
90
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 148 (9 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.
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 133 (22 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.
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 38 (2 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.
Monte Carlo variance of scrambled net quadrature
 SIAM J. Numer. Anal
, 1997
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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 26 (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 19 (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 : : : : : : : : : : : : : : : :
Comparing sensitivity analysis methods to advance lumped watershed model identification and evaluation
 HYDROLOGY AND EARTH SYSTEM SCIENCES
, 2007
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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 15 (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
, 1996
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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 11 (6 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.