Results 1 to 10 of about 691 (194)
Analytic regularity and stochastic collocation of high-dimensional Newton iterates. [PDF]
Adv Comput Math, 2020 In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the solution with respect to the random variables. This justifies the application of sparse grids for the computation
Castrillón-Candás JE, Kon M.
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Stochastic Collocation Applications in Computational Electromagnetics [PDF]
Mathematical Problems in Engineering, 2018 The paper reviews the application of deterministic-stochastic models in some areas of computational electromagnetics. Namely, in certain problems there is an uncertainty in the input data set as some properties of a system are partly or entirely unknown.
Dragan Poljak +6 more
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A numerical approach to solve the stochastic Allen-Cahn equation of fractional order [PDF]
Mathematics and Computational Sciences, 2021 In this paper, we employ a collocation method based on Legendre polynomials (LPs) to solve the time-fractional stochastic Allen-Cahn equation. This method is applied to convert the solution of this stochastic equation to the solution of a nonlinear ...
Afshin Babaei, Seddigheh Banihashemi
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Solving Stochastic Nonlinear Poisson-Boltzmann Equations Using a Collocation Method Based on RBFs
Mathematics, 2023 In this paper, we present a numerical scheme based on a collocation method to solve stochastic non-linear Poisson–Boltzmann equations (PBE). This equation is a generalized version of the non-linear Poisson–Boltzmann equations arising from a form of ...
Samaneh Mokhtari +4 more
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Stochastic Collocation on Unstructured Multivariate Meshes [PDF]
Communications in Computational Physics, 2015 AbstractCollocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction are becoming standard tools used in a variety of applications.
Narayan, Akil, Zhou, Tao
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Multi-quadric collocation model of horizontal crustal movement [PDF]
Solid Earth, 2016 To establish the horizontal crustal movement velocity field of the Chinese mainland, a Hardy multi-quadric fitting model and collocation are usually used.
G. Chen, A. Zeng, F. Ming, Y. Jing
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Fully Legendre spectral collocation technique for stochastic heat equations
Open Physics, 2021 For the stochastic heat equation (SHE), a very accurate spectral method is considered. To solve the SHE, we suggest using a shifted Legendre Gauss–Lobatto collocation approach in combination with a shifted Legendre Gauss–Radau collocation technique.
Abdelkawy Mohamed A. +3 more
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Multi-Index Stochastic Collocation for random PDEs [PDF]
Computer Methods in Applied Mechanics and Engineering, 2016 In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data.
AL HajiAli +3 more
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Risks, 2022 We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined
Shuaiqiang Liu +2 more
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Positive Stochastic Collocation for the Collocated Local Volatility Model
, 2021 This paper presents how to apply the stochastic collocation technique to assets that can not move below a boundary. It shows that the polynomial collocation towards a lognormal distribution does not work well. Then, the potentials issues of the related collocated local volatility model (CLV) are explored. Finally, a simple analytical expression for the
Floc'h, Fabien Le +1 more
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