An equation-free, multiscale approach to uncertainty quantification

An equation-free, multiscale computational method to uncertainty quantification (UQ) that combines sampling methods with nonsampling methods is proposed. The method uses short bursts of appropriately initialized sampling runs to estimate quantities arising in Stochastic Galerkin (SG) methods. The method is also used to integrate the nonlinear dynamical equations in SG projections and present computations of their fixed points and limit cycles. The fixed-point of the system are computed through short bursts of dynamic simulation, combining it with matrix-free techniques of iterative linear algebra. The method also combines the simplicity of MC simulations with the power and convergence of nonsampling generalized polynomial chaos (gPC) representations.