We present a multilevel stochastic collocation method that, as do multilevel Monte Carlo methods, uses a hierarchy of spatial approximations to reduce the overall computational complexity when solving partial differential equations with random inputs. For approximation in parameter space, a hierarchy of multi-dimensional interpolants of increasing fidelity are used. Rigorous convergence and computational cost estimates for the new multilevel stochastic collocation method are derived and used to demonstrate its advantages compared to standard single-level stochastic collocation approximations as well as multilevel Monte Carlo methods.
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Research Article| March 10 2015
A multilevel stochastic collocation method for SPDEs
AIP Conf. Proc. 1648, 020005 (2015)
Max Gunzburger, Peter Jantsch, Aretha Teckentrup, Clayton Webster; A multilevel stochastic collocation method for SPDEs. AIP Conf. Proc. 10 March 2015; 1648 (1): 020005. https://doi.org/10.1063/1.4912309
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