WengCho Chew (Illinois. USA)

The physics of electromagnetic field and its computational algorithms

Abstract

The physical nature of electromagnetic field from static to high frequency will be discussed. This physical nature affects how fast algorithms are designed for the solution of Maxwell's equations from static to microwave and optical frequencies. At very low frequencies, electromagnetic field behaves like Laplacian field which is very smooth and non-oscillatory. At higher frequencies, electromagnetic field behaves like Helmholtz field which is oscillatory. It can be shown that Laplacian field cannot convey information long distance, whereas Helmholtz field can carry information through galaxies. The information content of the field affects the nature of the fast algorithm designed to solve Maxwell's equations. At extremely high frequencies, electromagnetic wave behaves like particles or rays, and yet, a different strategy is needed to design fast algorithms at the high frequency end.