Modeling and Simulation for Everyone

By Svante Littmarck

Scientists like Newton, Maxwell and others have given us the mathematical models, the “laws of science,” that make it possible to accurately predict how physical objects and systems will develop in space and time given certain boundary conditions and initial conditions. Applied mathematicians have invented numerical methods that can generate numbers and graphics to accurately describe how such objects and systems would develop in space and time.

This makes it possible for us to simulate, modify parameters and ultimately make a better—if not the best—design.

The physics, the math, the computational tools and the engineering community are all in place to achieve wonders using simulation. Sending exploration vehicles to the surface of Mars that report back to Earth, creating communication devices like cell phones and GPS are just two examples.

Many breakthrough technological innovations have seen daylight in the last several decades. But many areas that would benefit greatly remain almost untouched by the powerful computational tools available today. Why is this?

The Obstacles

It is a fact that current computational tools are so complicated to use that there are very few engineers trained to do it—at least compared to the number of potential beneficiaries.

The setup of mathematical models needs to be done by a mathematician or a physicist. Model simplifications are necessary in order to save computational time, memory and solution data management. Negligible phenomena should be ignored. The phenomena that should be ignored depend on the application and what is to be achieved. This requires a modeling expert.

Once the model is set up, solving the equations numerically means replacing the continuous differential equations, space and time, with discretized difference equations and points in space and time. The discretization must be done in such a way that the solution to the difference equation converges to the solution of the differential equation. Otherwise, it has no physical meaning. Additionally, in order to obtain an accurate solution, the discretization must be fine enough. There are theories for good default numerical solver settings for many physics areas, but they are not all the same. It sometimes takes a numerical analysis expert to define the solver settings.

As a result, the typical user of a simulation package is someone who holds a Ph.D. or an M.Sc. and has several years of experience in modeling and simulation. The user also underwent thorough training to use the specific package. He or she typically works as a scientist in a big organization’s research & development department. It is up to that person to employ his or her expertise to create and validate the model and the simulation.

This all means that a small group of people is servicing a much larger group of people working in product development, design or production. Simulation models are oftentimes so complicated that the person who implemented the model is the only one who can safely provide the input data needed to get useful output. Hence, we have a bottleneck.

The Solution

In order to make it possible for this small group to service a much larger group, there is an obvious solution: Create a simulation package that makes it possible for the simulation expert to build an intuitive and specific user interface for his or her otherwise general model—a ready-to-use application. The application should include user documentation, checks for “input within bounds,” and predefined reports at the click of a button. A simulation application with these capabilities makes it possible for a user to avoid accidental input errors while keeping the focus on relevant output details. The application can then be shared with a larger group of users.

Making this happen is easy compared to the achievements listed in the beginning of this article. It is happening as you read this.

The spread of such applications will be immediate. No design engineer will want to be left behind. No company can afford to let their competitor get an advantage through earlier adoption. Eventually consumers will be running simulation applications to make better purchase decisions.

Svante Littmarck is co-founder and CEO of the COMSOL Group and the president and CEO of COMSOL, Inc. He can be reached via comsol.com.