In a world full of automated design tools, do we need to worry about the mathematical details in our models? As engineers, the notion of "doing the math" often conjures anxious memories of pulling "all-nighters" at university, solving differential equations, and inverting matrices. So, it is with some relief that we find that there are tools that handle many of those tasks for us.
Today's engineer does much more than enter models and run simulations. In fact, analysis performed at Maplesoft indicates that engineers spend 15% to 25% of their time working directly with automated design systems. Furthermore, studies have shown that up to 85% of all product development costs are determined by decisions made at the design stage. So if the design stage determines 85% of all costs but automated design software supports only 15% to 25% of design time, what kind of tools are being used in the vast majority of the design time?
Some important elements in real-world design include crisply scoping the design and analysis ("How complex a model?" "What assumptions?" "Which constraints?" "Initial values of parameters?" etc.) and doing and interpreting sanity checks on simulation results to ensure that the input information is sound and the results are being used appropriately. No amount of design automation has ever defeated the axiom of "Garbage in, garbage out."
These are very important factors in good design that historically have not been well-supported by conventional automated design systems. Typical tools for these steps are calculators, spreadsheets, reference books, programming languages, and colleagues, all of which have severe limitations that cannot capture the complexities of modern engineering.
The one common framework that connects all of these complementary tasks in automated design is math. Models, formulas, data, graphs, assumptions, constraints—all are forms of math. This perspective is the foundation of the newest generation of general-purpose interactive math systems. These powerful systems offer a range of math solvers and exploratory and knowledge tools to express, manipulate, and manage the core mathematical information accurately and naturally.
While these systems have been around for over 20 years, engineers have only recently discovered them. Early adopters were academic researchers and educators who found the ability to manage complex math naturally to be critical in the derivation of models and the solution of complex problems. As engineering becomes more complex and the timelines to innovations continue to shorten, more engineers (many of whom were educated on these systems) are discovering the benefits of comprehensive math systems. Elimination of sign and unit errors, the ability to perform "pre-simulations" on idealized models to determine feasible parameter spaces, and checking results can mean significant time savings and increased quality of design information.
As the popularity of math systems grows, the math software industry is responding with significant improvements to its technology, specifically with the engineer in mind. Systems are becoming very easy to use with quick entry of math, instant interactive visualization, and fast access to powerful solvers. More tasks are being integrated into a common environment.
The near future promises to be just as exciting, as math in design is expected to become even more critical. In chip design, as we approach the limits of the physics inherent in a lot of design software, organizations are increasingly turning to more mathematically sophisticated methods: field models as opposed to lumped system models, for instance. Mechatronics, multiphysics, and other interdisciplinary or mixed-signal modeling challenges are more situations where a mathematical approach is often the fastest way to effective models.
Design is changing, and one of the drivers of this change is analytical agility. Math is re-emerging as a fundamental tool in engineering. Fortunately, software technology is keeping pace with a new generation of productivity tools to help harness the power of math. Math becomes a pump, not a filter.
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