A Dimension-Adaptive Multi-Index Monte Carlo Method Applied to a Model of a Heat Exchanger
For researchers simulating PDEs with random fields, this adaptive method reduces computational cost, though the improvement is incremental.
The paper presents an adaptive Multi-Index Monte Carlo method for PDEs with random coefficients, automatically selecting Karhunen-Loève expansion terms and spatial discretizations. Applied to a heat exchanger model, it shows consistent computational savings.
We present an adaptive version of the Multi-Index Monte Carlo method, introduced by Haji-Ali, Nobile and Tempone (2016), for simulating PDEs with coefficients that are random fields. A classical technique for sampling from these random fields is the Karhunen-Loève expansion. Our adaptive algorithm is based on the adaptive algorithm used in sparse grid cubature as introduced by Gerstner and Griebel (2003), and automatically chooses the number of terms needed in this expansion, as well as the required spatial discretizations of the PDE model. We apply the method to a simplified model of a heat exchanger with random insulator material, where the stochastic characteristics are modeled as a lognormal random field, and we show consistent computational savings.