Stochastic Reduced Basis Methods
نویسندگان
چکیده
منابع مشابه
Application of new basis functions for solving nonlinear stochastic differential equations
This paper presents an approach for solving a nonlinear stochastic differential equations (NSDEs) using a new basis functions (NBFs). These functions and their operational matrices are used for representing matrix form of the NBFs. With using this method in combination with the collocation method, the NSDEs are reduced a stochastic nonlinear system of equations and unknowns. Then, the error ana...
متن کاملUncertainty Assessment Using Stochastic Reduced Basis Method for Flow in Porous Media
We apply a hybrid formulation combining the stochastic reduced basis methods with polynomial chaos expansions, which has been introduced recently by Nair [1] for solving the linearized stochastic partial differential equation governing single-phase flow in porous media. We use a generalization of stochastic reduced basis projection schemes to nonGaussian uncertainty models. The Karhunen-Loeve e...
متن کاملAn Adaptive Reduced Basis Collocation Method Based on Pcm Anova Decomposition for Anisotropic Stochastic Pdes
The combination of reduced basis and collocation methods enables efficient and accurate evaluation of the solutions to parameterized PDEs. In this paper, we study the stochastic collocation methods that can be combined with reduced basis methods to solve high-dimensional parameterized stochastic PDEs. We also propose an adaptive algorithm using a probabilistic collocation method (PCM) and ANOVA...
متن کاملComparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems
The stochastic collocation method [43, 1, 31, 30] has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method [28, 40, 33], primarily developed for solving parametric systems, has been recently used to deal with stochastic problems [7, 6]. In this work, we aim at comparing the performance of the two methods when applied t...
متن کاملPC expansions to a wide class of stochastic Partial Differential
This paper presents multi-element Stochastic Reduced Basis Methods (ME-SRBMs) for solving linear stochastic partial differential equations. In ME-SRBMs, the domain of definition of the random inputs is decomposed into smaller subdomains or random elements. Stochastic Reduced Basis Methods (SRBMs) are employed in each random element to evaluate the response statistics. These elemental statistics...
متن کامل