#### Optimisation of products is the main concern of any industry today, and it has become very important for every design to consider principles of various disciplines to achieve an optimal solution.

#### Founded in July 1986, the COMSOL Group sells software licenses and provide software solutions for multiphysics modeling. The company with its modules claims to cover everything which is in science and can be expressed as PDEs. Svante Littmarck, the co-founder, CEO and president, and Bjorn Sjodin, VP of Product Management at COMSOL talk to Dilin Anand and Anagha P about multiphysics modeling.

**Q. What is the most important aspect that multiphysics modelling offers design engineers today?**

** A.** It is a very competitive market out there, so it is very important for the industries to optimize their designs and have a competitive edge. With multiphysics modeling, engineers can incorporate more than one physics phenomena and make more realistic simulations. While designing, you don’t only have structural phenomena but it is coupled with physics and other phenomena. If you don’t incorporate all those phenomena into one simulation, you will lose accuracy and it will not match reality to the same extent, than if you produce a multiphysics model.

**Q. What is the importance of multidisciplinary skills for industrial product development?**

** A.** Multidisciplinary skills are very important for optimisation of any design. Whoever is able to master more disciplines will be able to optimise its design to the greater extent and have a competitive edge. Currently, every industrial product development includes a collaboration of specialists from different disciplines. With multiphysics, the designer can enable effective cross disciplinary product development where you can use one tool for variety of different types of analysis and simulations. Specialists can contribute their expertise to the same prototype including physics from different disciplines.

**Q. The terms, modeling and simulation are often used as synonyms, so how exactly do they differ from each other and how much are they inter-related?**

** A.** Modeling is the mathematical way of describing any physics phenomena. Most people have heard about the laws of science and they are all expressed in mathematical terms. Modeling is expression of the things we experience in mathematical terms, for example, if you drop a pen, you can experience the force and bounce but you can express these in mathematical terms and that is partial differential equations or we can say, modeling.

Simulation, on the other hand, is the numerical solution or approximation of the solution to the modeling or the differential equations. Generally, the laws of science which are expressed with boundary conditions or initial conditions cannot be solved mathematically. They may have a unique solution, no solution or multiple solutions which can not be solved in a closed form by mathematical expressions. You can approximate the differential equations with a difference equation and then you can solve that on a computer, numerically. It simulates the solution to the differential equation. You can get the solution to the difference equation, and if its done correctly you can approximate the solution to the differential equation with certain accuracy.

**Q. What are the key points to be considered while making approximations for simulation?**

** A.** While shifting from a mathematical differential equation to a mathematical difference equation, you have to discretize space. For example, you cannot calculate the temperature in all the possible points as it is an infinite number, so you have to decide a certain number of points to discretize space, the same way you discretize a differential equation to a difference equation. The ideal way of simulating a phenomena is to do it with a certain step size and then decrease that step size. The more you decrease the discrete step size in space or time, the closer you get to the differential equation and if you take infinitely small step size then you will converge to differential equation.

**Q. What is the main challenge while simulating any phenomena?**

** A.** The main challenge while simulating is to make sure that you get a converging solution. If you get for instance, -1 first time, +2 second time and then -3, then you probably don’t have any accuracy, but if it goes from 3.1 to 3.14 to 3.145 and so forth, then you can start trusting your solution. Remember that you have two discrepancies, one between the physics at hand and the mathematical differential equations and the other one between differential equations and the difference equations, i.e. the simulation. If everything is done right, the simulation will reflect the physics at hand. So there always be some noise to the mathematical model and the reality and accuracy will always remain one challenge.

**Q. How is mathematical modeling done in multiphysics tools?**

** A.** Mathematical modeling is more based on the disciplines or you can say on the laws of science. Laws of science for a specific discipline are grouped and packaged. We have different packages depending upon the different disciplines within them. Those add-on packages constitute the differential equations from the specific discipline and have a user interface that hides the mathematical complexity behind the scenes.

**Q. What is the importance of multiphysics tools for academic and R&D institutions?**

** A.** Multiphysics tools are important for research as well as training students. Most of the engineers are not focused on the maths, they are more focused on the physics at hand. They are not concerned about the differential equations, boundary conditions or any such formula. But people with mathematical focus like those in academic side and R&Ds, can have their own specific PDEs added to the ones we provide in the package and customize and adapt the tool for their requirements. Also, servicing the academic research market gives us a benefit of having a close and quicker access to the information about what they are developing, if there is a new algorithm or method developed for solving a problem.