4 papers
Stochastic Modelling of Elasticity Tensor Fields
Sharana Kumar Shivanand, Bojana Rosić, Hermann G. Matthies
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 defin…
Covariance estimation using h-statistics in Monte Carlo and multilevel Monte Carlo methods
Sharana Kumar Shivanand
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 proce…
Stochastic Modelling of Symmetric Positive Definite Material Tensors
Sharana Kumar Shivanand, Bojana Rosić, Hermann G. Matthies
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 h…
Scale-invariant Monte Carlo and multilevel Monte Carlo estimation of mean and variance: An application to simulation of linear elastic bone tissue
Sharana Kumar Shivanand, Bojana Rosić
We propose novel scale-invariant error estimators for the Monte Carlo and multilevel Monte Carlo estimation of mean and variance. For any linear transformation of the distribution…