Jin updates his electromagnetics classic

For every vocation there’s a go-to reference book. It could be the dog-eared style guide on the desks at a publishing house, or the splattered and tattered cookbook on the counters of eminent chefs. For electrical engineers, one of those books is The Finite Element Method in Electromagnetics (Wiley), written by ECE Professor Jianming Jin, which has recently been released in its third edition.

“It’s the first comprehensive textbook on the finite element method in electromagnetics in the entire field,” Jin said of the book, which was published, first edition, in 1993. “In the last decade, people made a lot of progress, and three years ago,

I realized that I needed to incorporate the progress into the book.”

The result is the new edition. It contains 30 percent more material than the second edition, published in 2002, which, in turn, has almost 40 percent more material than the first. The rapid growth mirrors the pace of innovation. 

The finite element method is a technique that can simulate the movement of electromagnetic waves: the signal pulsing within an integrated circuit or the radar scattering from a travelling aircraft. Understanding these movements requires increasingly complicated algorithms, and one of the most reliable and accurate approaches is the finite element method. “On a piece of paper, you can only solve extremely simple problems,” Jin said. “Any practical problem requires computer simulation.”

One major addition to the third edition is a chapter that explicates the parsing of these massive algorithms, breaking them into subunits for simultaneous processing on parallel computers. This is known as domain decomposition. Twelve years ago, when the second edition was published, solving equations with one million unknown variables was impressive and difficult. Now, with parallel computers and domain decomposition, researchers can deal with billions of unknown variables.

In fact, Jin and his graduate students have solved a problem with 3.5 billion unknowns using this technique. “With four processors, I think it took about 10 hours,” Jin said, “but to give you an idea, without domain decomposition, I think 10 years would not be [enough time] to give you a solution.”

Other novel textbook material addresses new applications of the finite element theory—for antennas, phased arrays, electrical machines, and so forth. Two chapters were also added, in addition to the one on domain decomposition.

The first focuses on accounting for time in electromagnetic equations, instead of modeling only at a single frequency. “We usually do the analysis in frequency domain because mathematically it is a three-dimensional problem ... X, Y, Z,” Jin said.

“This adds the time-dimension, so it’s a four-dimensional problem. It’s much more difficult, but it’s a more interesting problem, because then you can see how electromagnetic waves propagate.”

For students and practicing engineers alike, this fourth-dimension is easier to conceptualize. The simulations can be rendered in video form, such that the signal within an integrated circuit, for example, can be visualized. “Students often struggle with electromagnetics because it’s too abstract, you cannot see electromagnetic waves,” Jin said. “[But] they can understand the physics much better when they can see the movie.”

The other new chapter deals with the analysis of wave propagation, scattering, and radiation in periodic structures, including artificially engineered materials like the photonic crystals used in biosensors and other optoelectronic devices. “The ability to analyze periodic structures has many, many applications,” Jin said. “That’s another [major] progress we made during the past 10 years.”

These innovations stem both from Jin’s research team and from the research of others. “When I started research on the finite element method, the method was at a fairly primitive stage. It could only solve extremely simple problems,” Jin said. “I’m fortunate to see that during the past 30 years, this method has been developed from a method to solve simple problems to a method that can deal with very, very complicated, large-scale problems.”

Whether Jin’s new edition is toted around in backpacks by graduate engineering students or kept for easy reference on the desks of industry engineers, there’s no doubt that it will become another definitive resource. “Many, many companies use finite element method on a daily basis, with hundreds of engineers ... to design electronic devices, to design integrated circuits, to design the computer chips,” Jin said. “This is one of the most important methods and the most, I would say, dominant method.”