Dimension reduction for PDE using local Karhunen Loeve expansions [report]

Yi Chen, Dongbin Xiu, John Davis Jakeman, Claude Gittelson
2015 unpublished
 Develop efficient methods for sampling linear partial differential equations subject to uncertain random fields  Use domain decomposition and local Karhunen Loeve expansions (KLE) to represent a random field with small correlation length with local KLE defined over subdomains with relatively larger correlation lengths.  Show the use of local KLE reduces the high dimensional global field to a set of lower dimensional KLE  Method is composed of highly independent sub-problems and could
more » ... ially be very suitable to large HPC systems  Facilitates rigorous uncertainty quantification and predictive simulation improvements for high-fidelity linear PDE Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.  Method results in significant dimension reduction when solving local problems  Demonstrated that dimension reduction can be leveraged to reduce the computational expense of solving linear PDE subject to high-dimensional random fields.  Provides at least one order of magnitude reduction in the total computational cost of generating sets of simulations for varying parameter values.
doi:10.2172/1221524 fatcat:u4vmx5vwofaxnmrvqpoxupmz64