The role of analysis in an age of computers: view from the numerical side (electromagnetic research)

The role of analysis in electromagnetics (EM) research is examined from the viewpoints of code validation, code improvement, and unexpected synergies arising between the large-scale partial differential equations (PDE), Maxwell´s solvers and pure analytical approaches. It is noted that physical phenomena associated with full-vector three-dimensional EM wave interactions can be so complicated that neither analysis nor computational simulation can exist within a vacuum. In an age of supercomputers and PDE solvers that, in principle, can deal with hundreds of millions of vector field unknowns, the role of analysis is not abolished. The role of analysis may be changed, however, to better reflect the needs of the large-scale solvers for validation and code improvement. It is concluded that both analysis and numerics will be enlivened and enriched as a result of emerging synergies arising between these two approaches.<>