Search Results - Stochastic Collocation Methods

An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use by Galetzka, Armin, Loukrezis, Dimitrios, Georg, Niklas, De Gersem, Herbert, Römer, Ulrich

“…This article introduces an hp $$ hp $$ ‐adaptive multi‐element stochastic collocation method, which additionally allows to re…”
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Stochastic Collocation Method for Stochastic Optimal Boundary Control of the Navier–Stokes Equations by Zhao, Wenju, Gunzburger, Max

“… of functions having first order weak derivative along the boundary. To simulate the system, numerical solutions are approximated using the stochastic collocation/finite…”
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An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling by Zhang, Guannan, Lu, Dan, Ye, Ming, Gunzburger, Max, Webster, Clayton

“…‐order stochastic collocation (aSG‐hSC) method. Unlike previous works using first‐order hierarchical basis, this paper utilizes a compactly supported higher…”
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Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients by Nobile, F., Tempone, Raul

“… The stochastic coefficients of the PDE are approximated by truncated Karhunen–Loève expansions driven by a finite number of uncorrelated random variables…”
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Deterministic–stochastic modeling of transcranial magnetic stimulation featuring the use of method of moments and stochastic collocation by Cvetković, Mario, Šušnjara, Anna, Poljak, Dragan

“…). A combination of deterministic modeling and the stochastic collocation method (SCM) is used for the assessment of the input parameter uncertainties…”
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Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design by Beck, Joakim, Mansour Dia, Ben, Espath, Luis, Tempone, Raúl

“…), multilevel methods have been proven to reduce the computational complexity of their single…”
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Multi-fidelity stochastic collocation method for computation of statistical moments by Zhu, Xueyu, Linebarger, Erin M., Xiu, Dongbin

“…We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities…”
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A direct meshless local collocation method for solving stochastic Cahn–Hilliard–Cook and stochastic Swift–Hohenberg equations by Abbaszadeh, Mostafa, Khodadadian, Amirreza, Parvizi, Maryam, Dehghan, Mehdi, Heitzinger, Clemens

“…In this study, the direct meshless local Petrov–Galerkin (DMLPG) method has been employed to solve the stochastic Cahn–Hilliard–Cook and Swift–Hohenberg equations…”
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Simplex-stochastic collocation method with improved scalability by Edeling, W.N., Dwight, R.P., Cinnella, P.

“…The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code…”
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Stochastic collocation method for computing eigenspaces of parameter-dependent operators by Grubišić, Luka, Saarikangas, Mikael, Hakula, Harri

“… A stochastic collocation method on an anisoptropic sparse grid in the parameter domain is proposed for computing a basis for the eigenspace of interest. The convergence of this method is verified in a series of numerical examples based on the eigenvalue problem of a stochastic diffusion operator…”
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A SPARSE GRID STOCHASTIC COLLOCATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA by NOBILE, F., TEMPONE, R., WEBSTER, C. G.

“…This work proposes and analyzes a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations…”
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A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data by Babuška, Ivo, Nobile, Fabio, Tempone, Raúl

“…This work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms…”
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Investigations on the restrictions of stochastic collocation methods for high dimensional and nonlinear engineering applications by Dannert, Mona M., Bensel, Fynn, Fau, Amelie, Fleury, Rodolfo M.N., Nackenhorst, Udo

“… It is known in the scientific community that global stochastic collocation methods using isotropic sparse grids are very efficient for simple problems but can become computationally expensive…”
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Topology optimization considering material and geometric uncertainties using stochastic collocation methods by Lazarov, Boyan S., Schevenels, Mattias, Sigmund, Ole

“…The aim of this paper is to introduce the stochastic collocation methods in topology optimization for mechanical systems with material and geometric uncertainties…”
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A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data by Babuška, Ivo, Nobile, Fabio, Tempone, Raúl

“…In this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms…”
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A sparse grid stochastic collocation method for structural reliability analysis by He, Jun, Gao, Shengbin, Gong, Jinghai

“… This paper develops a sparse grid stochastic collocation method for the reliability analysis of structures with uncertain parameters and loads…”
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Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations by Pulch, Roland

“… Alternatively, stochastic collocation methods or the stochastic Galerkin approach yield larger coupled systems of differential algebraic equations…”
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AN ANISOTROPIC SPARSE GRID STOCHASTIC COLLOCATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA by NOBILE, F., TEMPONE, R., WEBSTER, C. G.

“…This work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving partial differential equations with random coefficients and forcing terms…”
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Stochastic Optimal Power Flow for Power Systems Considering Wind Farms Based on the Stochastic Collocation Method by Xia, Bingqing, Chen, Yuwei, Yang, Wenbin, Chen, Qing, Wang, Xiaohe, Min, Kuan

“… To solve the problem, this paper proposes an approach based on the stochastic collocation method (SCM…”
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Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties by Giulia Bertaglia, Liu Liu, Lorenzo Pareschi, Xueyu Zhu

“… The need for efficient methods capable of quantifying uncertainty in the mathematical model is essential in order to produce realistic scenarios of the spread of infection…”
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