Quadrature Methods with Adjusted Grids for Stochastic Models of Coupled Problems
We consider coupled problems with uncertain parameters modelled as random variables. Due to the largely differing behaviour of subsystems in coupled problems, we introduce a strategy of adjusted grids defined in the parameter domain for resolving the stochastic model. This allows us to adapt quadrature grids to each subsystem. The communication between the different grids requires global approximations of coupling variables in the random space. Since implicit time integration methods are typically included, we investigate dynamic iteration schemes to realise this approach. Numerical results for a thermal-electric test circuit outline the feasibility of the method.
KeywordsCoupled problems Stochastic modeling Thermal-electric circuit Uncertain parameters
This work is a part of the project ‘Nanoelectronic Coupled Problems Solutions’ (NANOCOPS) funded by the European Union within FP7-ICT-2013 (grant no. 619166).
- 1.Bartel, A., Pulch, R.: A concept for classification of partial differential algebraic equations in nanoelectronics. In: Bonilla, L.L., Moscoso, M., Platero, G., Vega, J.M. (eds.) Progress in Industrial Mathematics at ECMI 2006. Mathematics in Industry, vol. 12, pp. 506–511. Springer, Berlin (2007)CrossRefGoogle Scholar