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pro vyhledávání: '"Shivanand, Sharana Kumar"'
We present a novel framework for the probabilistic modelling of random fourth order material tensor fields, with a focus on tensors that are physically symmetric and positive definite (SPD), of which the elasticity tensor is a prime example. Given th
Externí odkaz:
http://arxiv.org/abs/2409.16714
Autor:
Shivanand, Sharana Kumar
We present novel Monte Carlo (MC) and multilevel Monte Carlo (MLMC) methods to determine the unbiased covariance of random variables using h-statistics. The advantage of this procedure lies in the unbiased construction of the estimator's mean square
Externí odkaz:
http://arxiv.org/abs/2311.01336
Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive definite tensors
Externí odkaz:
http://arxiv.org/abs/2109.07962
Publikováno v:
In Journal of Computational Physics 15 May 2024 505
We propose a novel scale-invariant version of the mean and variance multi-level Monte Carlo estimate. The computation cost across grid levels is optimised using a normalized error based on t-statistics. By doing so, the algorithm achieves convergence
Externí odkaz:
http://arxiv.org/abs/2106.13723
Autor:
Shivanand, Sharana Kumar
In this thesis, the simulation of macroscopic bone tissue is studied in a probabilistic framework, where special emphasis is given to how to model and generate random material tensors that are symmetric and positive definite (SPD). The goal of this t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d72a757d677bbe8b0a3983c853459c7f
In this paper, the scale-invariant version of the mean and variance multi-level Monte Carlo estimate is proposed. The optimization of the computation cost over the grid levels is done with the help of a novel normalized error based on t-statistic. In
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::80647a63de5d07284698f67e9d6cf05e