When I was an undergraduate four decades ago, we studied functions of a complex variable (i.e. the square root of -1) not only for the intrinsic interest of the special properties of these functions but also as a lead-in to a class on ‘mathematical methods’. One of our professors would spend the summer holidays solving differential equations as a consultant to Nasa. Highly abstract mathematics was applicable in the real world and in some of the highest technology of the age – only a few years earlier, the Apollo programme had first put a man on the moon.
Now, all those skills so painfully acquired are redundant. Computers can simulate problems in science and engineering to a far greater degree of accuracy than ‘exact methods’ can ever hope to achieve, and most problems today are so complex that they are not amenable to anything other than numerical solution.
In fact, this is to understate the situation. As Bill Clark of CD-adapco puts it in his contribution to this special edition marking Scientific Computing World’s 20th anniversary: ‘An uncomfortable truth about modern engineering is that there really are no easy problems left to solve’. Complex industrial problems require solutions that span a multitude of physical phenomena, which often can only be solved using simulation techniques that cross several engineering disciplines from fluid dynamics to stress analysis. The demand moreover is for the simulation of whole systems rather than just individual components, so as to get an idea of those factors that affect the product’s performance (and longevity).
It is no surprise therefore to find many of the contributors focusing on optimisation as well as simulation. Clark describes the process as ‘automated design exploration’, in which the simulation results automatically drive improvements in a design, with minimal input from the engineer. In this way, engineers can compile databases of simulation results that explore the complete range of usage scenarios, or use optimisation software to determine the best solution to a given problem automatically.
Ironically for me, I was learning those now-redundant mathematical methods as an undergraduate just about the time that, according to MSC Software’s Dominic Gallello, the major simulation codes that are running in industry today were coming on to the market. Forty years on, it is time, in his view, for some significant changes. Simulation has been the domain of specialised analysts but he believes that, just as my skills have been superseded, it is now time for engineers who are not specialist analysts to start using the software tools to predict performance of products. The key will be ease of learning and ease of use of the next generation of software packages.
The MathWorks’ Jack Little also sees change approaching, driven not only by the demands of industrial customers but by developments in technology. He points out that when mainframe computers were dominant, millions of users could sit at terminals around the world performing thousands of applications. While the advent of the PC increased that reach by a factor of ten or even a hundred, the cloud now provides a computing service that can be accessed by billions of people performing millions of applications on multiple devices. Today, he writes: ‘We do not go somewhere or carry something in order to compute; we expect to be able to compute anywhere.’ Today’s software needs to support computing resources from smartphones to the cloud.
But in the face of this, mathematics has not gone away. Jim Cooper of Maplesoft highlights how it still underpins all technical disciplines, no matter the size or complexity. Nor is the range of organisations that depend on mathematics confined to traditional sectors such as engineering, scientific research, space and defence work, but electronics manufacturers and financial institutions also use mathematics to solve problems critical to their business. Engineers, scientists, and mathematicians need solutions and tools that help them find better, more efficient ways to work. But Cooper also highlights the importance of educating future scientists and equipping them with the intellectual tools that they need to confront this changing environment.
And the importance of people is key to Blakelee Midyett from Golden Software. She points out that according to official statistics in the USA, there were more than a million innovative and talented people working in software development. Developers have always had an incentive to optimise source code, to allow customers to utilise their hardware fully and work quickly and efficiently. In a world of ‘Big Data’, she continues, processing huge amounts of information takes a lot of power so that hardware and software must continue to improve. Applications must be able to handle these large sets of data and, with educated and talented people driving development, she is confident that they will.
