When performing an analysis of a mat foundation (utilizing finite element methods software), how should the structural engineer utilize the subgrade modulus value determined from a 1-ft plate load test (i.e. should the structural engineer vary this value across the mat and how would this be determined)?

Assuming a general case, large mat foundation on deep homogeneous stiff clay, no groundwater.

I am particularly interested in learing about the application of the discrete area method or any other
state of the art methods for assigning k-values.

Well, there are some standar formulas (see Bowles or Das) on adjusting the sub-grade modulus up to a larger size or a non-square footing size. But, that is still assuming a uniform spring constant over the whole mat.

Usually the FEM method will use un-coupled springs for analyzing the foundation, so it is really just direct support with not interaction between adjacent springs. If so, then the ACI publication 336.2R-88 "suggested analysis and design procedures for combined footings and mats" gives some recommendations for how to locally adjust these springs in order to create the dishing or cupping effect that would really occur.

Not sure if I am quoting the paper correctly, but I believe this is referred to as using a "Winkler Foundation" approach to account for node couple effects between soil springs.