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Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters

Béreš, Michal — 2023

Programs and Algorithms of Numerical Mathematics

In this contribution, we present a solution to the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with uncertain material coefficients in the separable form. The SG system of equations is kept in the compressed tensor form and its solution is a very challenging task. Here, we present the reduced basis (RB) method as a solver which looks for a low-rank representation of the solution. The construction of the RB consists of iterative expanding of the basis using Monte...

A comparison of approaches for the construction of reduced basis for stochastic Galerkin matrix equations

Michal Béreš — 2020

Applications of Mathematics

We examine different approaches to an efficient solution of the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with different, uncertain coefficients in apriori known subdomains. The solution of the SG system of equations is usually a very challenging task. A relatively new approach to the solution of the SG matrix equations is the reduced basis (RB) solver, which looks for a low-rank representation of the solution. The construction of the RB is usually done iteratively...

A comparison of deterministic and Bayesian inverse with application in micromechanics

Radim BlahetaMichal BérešSimona DomesováPengzhi Pan — 2018

Applications of Mathematics

The paper deals with formulation and numerical solution of problems of identification of material parameters for continuum mechanics problems in domains with heterogeneous microstructure. Due to a restricted number of measurements of quantities related to physical processes, we assume additional information about the microstructure geometry provided by CT scan or similar analysis. The inverse problems use output least squares cost functionals with values obtained from averages of state problem quantities...

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