A FETI-DP-BASED PARALLEL ALGORITHM FOR SOLVING HIGH DIMENSIONAL STOCHASTIC PDES USING COLLOCATION

Numerical solution of stochastic partial differential equations often faces the challenge of large dimensionality due to discretization of the equation, random field coefficients, and the source term. Recently, domain decomposition (DD) methods have been successful in reducing the computational complexity and achieving parallelization for such problems. This improvement is due to reduction in the number of random variables, and inherent parallelizability of DD methods. However, in order to make this approach more amenable to easier parallel implementation, an efficient non- intrusive method is necessary. With this goal, a stochastic collocation method based formulation is proposed here in the finite element tearing and interconnecting dual primal (FETI-DP) framework. This nonintrusive formulation uses the collocation method at both subdomain and interface levels of FETI-DP. Finally, at the postprocessing stage, realizations of subdomain solutions are computed by sampling from the true distribution. From an implementation viewpoint, this method has two advantages: (1) existing mechanics solvers can be reused with minimal modification, and (2) it is independent of the probability distribution of the input random variables. Numerical studies suggest a significant improvement in speed-up compared to the current literature and scalable parallel performance.

Automated summary

The numerical solution of stochastic partial differential equations often faces the challenge of high dimensionality. Recently, domain decomposition methods have successfully reduced computational complexity and achieved parallelization. To make this approach more amenable to parallel implementation, a non-intrusive formulation based on stochastic collocation method is proposed, which uses collocation method at both subdomain and interface levels. The method shows significant improvement in speed-up and scalable parallel performance.