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A novel higher order entire-domain finite element technique is presented for accurate and efficient full-wave three-dimensional (3D) analysis of electromagnetic structures with continuously inhomogeneous material regions, using large generalized curved hierarchical curl-conforming hexahedral vector finite elements that allow continuous change of medium parameters throughout their volumes. This is the first general 3D implementation and numerical demonstration of the inherent theoretical ability of the finite element method (FEM) to directly treat arbitrarily (continuously) inhomogeneous materials. The results demonstrate considerable reductions in both number of unknowns and computation time of the entire-domain FEM modeling of continuously inhomogeneous materials over piecewise homogeneous models. They indicate that, in addition to theoretical relevance and interest, large curved higher order continuous-FEM elements also have great potential for practical applications that include structures with pronounced material inhomogeneities and complexities.