Yesterday I watched a demonstration of Maple being applied to the modeling and simulation of the internal deformations of human bones. The researcher was a mathematician working primarily in the biomedical modeling fields. The actual technique was to utilize the symbolic mathematical power of Maple to formulate the necessary equation pieces for a finite element model (FEM) of the internals of the bone. The equations are then fed into the legendary FEM solver ABAQUS.
Due to the notoriously non-linear qualities of human flesh and bone, traditional formulation methods developed for modeling beams and metals simply do not work. So as in the case of so many impressive engineering applications, the power of Maple is being deployed in the formulation or the pre-solution phase of modeling and in doing so, previously infeasible models now become feasible.
In many ways, the MapleSim concept embodies strong parallels. By applying more ambitious mathematics at the front end, greater complexity and performance can be achieved. The similarities, however, end there.
Thomas Kuhn (arguably the greatest modern thinker on philosophy of science) observed the growing communication gap among the various modern factions of the physical sciences, social sciences, and the humanities. Short of cocktail party chit chat, it is virtually impossible for two practitioners from different disciplines to collaborate in any meaningful way without a major investment of effort to learn their colleague’s “language”.
Within engineering, one of the most troubling (IMHO) divides is that between the lumped parameter modeling world, and the continuum modeling world. The lumped parameter people (which currently includes those of us cheering for MapleSim) work with a reduced view of the system details to get a sense of overall behavior -- so a component’s mass would be lumped into one number and a stick figure and forces only apply at singular points. The continuum people (like our bone-modeling friend) are interested in the intimate details – internal stresses, flow patterns of fluids around objects, etc. Mathematically, lumped people use ordinary differential equations (ODEs), continuum people use partial differential equations (PDEs).
Computationally, both solitudes have their own favorite tools and over time, well-known companies became large and wealthy by supporting the respective worldview with more and more specialized features and techniques. We now have weapons of mass computation ready to deal with any problem that comes its way … as long as it’s posed in the precise way that these tools (and their inventors) understand.
As we continue to look forward at our own plans for Maplesoft modeling tools, this is one of the fundamental challenges that we want to address. How can we provide a richer modeling environment that properly integrates the respective advantages of the lumped and continuum worlds. Success in this would take the whole notion of virtual modeling or model-based design to a new level of efficiency and effectively. This is a daunting challenge and so far the few examples that exist are really “plumbing” examples – i.e. how do you get data flowing from one side to another but the necessary scientific formalisms for integrating the two perspectives still needs substantial refinement.
If the world’s problems were solved by optimism alone, I’d say we’re in pretty good shape. The good news is, we are not part of the traditional pool of players in either lumped parameter modeling or continuum modeling. So we’ve had the opportunity, indeed luxury, of fresher thinking on the needs of next generation modeling. More good news, our user base has all sorts of people so we tend to draw guidance from a very diverse and creative bunch. And still more good news – if it’s absolutely necessary for you to delve into some mathematical concepts from other fields, having a vast array of symbolic math tools is a godsend when you try to sort through unfamiliar techniques. So the optimism is not formed in a vacuum – I think we have some pretty solid raw material to work with.
Kuhn also got us talking about “Paradigms” and “Paradigm Shifts”. Everyone was so impressed by these words that we’re now numb from overuse. We’ll use the terms in light conversation for the silliest things. My cat has moved from canned food to dry food … what a paradigm shift that was! If we succeed in producing effective modeling tools that properly integrate lumped and continuum view points, I think it may be a candidate for the title of paradigm shift. It’s relatively easy for us to further categorize and further divide complex contexts but bringing seemingly disparate contexts together into a better whole is far more difficult. But I was always taught that bringing people and ideas together was a good thing to do and I’m proud that Maplesoft is making a real attempt at doing this.