  Time-periodic form or expression is a ubiquitous natural and man-made
phenomenon observable in all the scientific and engineering disciplines. In
this article, we propose a theory of periodic sequence (TPS), which can be
formulated as a foundational theory for computational sciences and engineering,
to transform arbitrary time-periodic electromagnetic (EM) problems into a
computational space with mapped discrete events, which is characterized in
neither frequency domain nor time domain. Within the TPS framework,
periodic-sequential Maxwell's curl equations are decomposed and decoupled to
independent and paralleled instances via designated mappings. The fundamental
solutions and mapped responses of EM periodic sequences are elucidated, and
corroborated by RF/microwave measurements. The nature of outstanding
computational parallelism and the unique frequency-independent property make
TPS a promising methodology for computational electromagnetics such as analysis
of high-speed signal integrity and broadband RF transmission.
