MATHICSE Technical Report : Convergence of quasi-optimal stochastic Galerkin methods for a class of PDES with random coefficients
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Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...
The aim of this work is the development of a geometrical multiscale framework for the simulation of the human cardiovascular system under either physiological or pathological conditions. More precisely, we devise numerical algorithms for the partitioned so ...
We propose certified reduced basis methods for the efficient and reliable evaluation of a general output that is implicitly connected to a given parameterized input through the harmonic Maxwell's equations. The truth approximation and the development of th ...
In this project report, we first present the application of the finite elements method to the numerical approximation of elliptic and parabolic PDEs over two-dimensional domains. We then consider the theory and numerical approximation of optimal control pr ...
We investigate the convergence rate of approximations by finite sums of rank-1 tensors of solutions of multiparametric elliptic PDEs. Such PDEs arise, for example, in the parametric, deterministic reformulation of elliptic PDEs with random field inputs, ba ...
Society for Industrial and Applied Mathematics2010
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as w ...
In this paper Monte Carlo finite element approximations for elliptic homogenization problems with random coefficients, which oscillate on n is an element of N a priori known, separated microscopic length scales, are considered. The convergence of multileve ...
Randomized techniques play a fundamental role in theoretical computer science and discrete mathematics, in particular for the design of efficient algorithms and construction of combinatorial objects. The basic goal in derandomization theory is to eliminate ...
Presenting stimuli of two or more stimulus types randomly interleaved, so called roving, disrupts perceptual learning in many paradigms. Recently, it was shown that no disruption occurs when Gabor stimuli were presented interleaved in sequence, instead of ...
Randomness is of fundamental importance in various fields, such as cryptography, numerical simulations, or the gaming industry. Quantum physics, which is fundamentally probabilistic, is the best option for a physical random number generator. In this articl ...