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A 3-D hybrid methodology for the proficient design of optimized microwave absorbers, based on bi-isotropic media, in anechoic facilities is introduced in this paper. Merging an accuracy-adjustable finite-difference time-domain and a pseudospectral time-domain algorithm, the novel technique develops a multimodal projection for sharp field variations and a Fourier-Chebyshev interpolation for the structure's periodic details. For the frequently encountered curvatures and discontinuities, a grid-adaptable process offers the appropriate modeling guidelines and imposes the correct interface conditions. Such benefits are verified via the characterization of different EMC chambers lined with the proposed absorbers, while diverse bi-isotropic setups of very low reflectivity are thoroughly investigated.