  We have recently proposed an efficient subdomain POD-TPWL (Xiao et al, 2018)
for history matching without the need of model intrusion. From a computational
point of view, a local parameterization where the parameters are separately
defined in each subdomain is very attractive. In this study we present one such
local parameterization through integrating principle component analysis with
domain decomposition to independently represent the spatial parameter field
within low-order parameter subspaces in each subdomain. This local
parameterization allows us to perturb parameters in each subdomain
simultaneously and the effects of all these perturbations can be computed with
only a few full-order model simulations. To avoid non-smoothness at the
boundaries of neighboring subdomains, the optimal local parameters are
projected onto a global parameterization. The performance of subdomain POD-TPWL
with local parameterization has been assessed through two cases tested on a
modified version of SAIGUP model. This local parameterization has high
scalability, since the number of training models depends primarily on the
number of the local parameters in each subdomain and not on the dimension of
the underlying full-order model. Activating more subdomains results in less
local parameter patterns and enables us to run less model simulations. For a
large-scale case-study in this work, to optimize 282 global parameters, LP-SD
POD-TPWL only needs 90 fidelity simulations. In comparison to the
finite-difference based history matching, and subdomain POD-TPWL with global
parameterization where the parameters are defined over the entire domain, the
CPU cost is reduced by a factor of several orders of the magnitude while
reasonable accuracy remains.
