Why write a blog about numerical simulation?

Numerical simulation has been a mainstay of modern engineering even before computers were accessible. There’s almost no one that works in engineering-related fields that have not heard of the Finite Element Method (FEM) or Computer Fluid Dynamics (CFD) and other simulation-related methods.

As a subject that has been in research for over seven decades¹, one would expect that it is a field that is widely understood by engineers and has sophisticated, modern, solutions. That couldn’t be further from the truth. While we do have a very active and prolific field of study in numerical simulation, I would have to disagree on the “being understood” part of the sentence. Another aspect that plagues the field is the inertia of modern methods to be implemented in commercial software.

These misunderstandings and inertia are my justification to write about numerical simulation. We have great tools at our disposal and knowledge to further our capabilities in engineering, however, there’s a rift between academia and engineering companies when the subject is simulation.

Understanding why such a rift exists is important. The reasons that I believe such a gap in understanding exists are:

• Supply and demand: engineering companies are not particularly interested in developing new commercial software that is cutting-edge, as they feel current solutions are enough for their problems.
• Lack of specialized individuals in prominent positions to push for new tech: it is rare to find people that have profound knowledge in numerical analysis that also have decision-making power over new products. Numerical analysis is a multi-disciplinary field that requires heavy specialization. Most simulation engineers are inside universities and do not make decisions for product development.
• Communication barriers: We are not getting the message to the decision-makers in software development across, either due to the lack of communication skills or due to poor networking. You can also attribute to the communication barrier a gap of knowledge between a specialist in simulation and an engineer who simulates. There’s a big difference between someone who spent the last 6 years researching simulation to a newly graduated engineer who has to learn how to simulate in his new job.
• Development costs: It is possible that new solutions require a shift in paradigm that is too costly to implement, either in cash or in time. Isogeometric Analysis (IGA) is a good example of this, as implementing a fully functional software for IGA requires not only building numerical software from scratch, it also requires a lot of rework of CAD software to transform all geometries into B-Splines and NURBS².

Personally, I do not believe in the supply and demand argument, as I can think of the top of my head at least two industries that require better simulation software: Formula 1 and crash-test analysis. I’ll elaborate.

Formula 1 teams have an artificial demand for more accuracy per degree of freedom thanks to their regulation on computing power by teams. F1 teams are restricted to 30 Teraflops of computational power (adjusted depending on where they ended up in the Constructor’s championship) for their CFD computations. Here, the efficiency of calculations play a huge role in getting their bang for the buck in simulation, so there’s demand.

Vehicle crash simulation, to understand how safe a vehicle is in a crash also suffers from the requirement of higher accuracy in simulations. In order to properly simulate a crash, you have to define the minimum timestep of the simulation, and this is bounded by the highest eigenvalue of the structure. It turns out the FEM is notably bad for eigenvalue analysis past the mid-frequencies and has a tendency to grossly overestimate them. This, then, forces the minimum timestep to be very small and computing 10 to 30 seconds of a phenomenon is very computationally costly. There’s a clear demand for methods that are more accurate in eigenvalue analysis.

While these are examples of arguments for demand, my objective with this blog is to address the communication part that might be lacking. I hope to bring you some cool ideas, solutions, and rants about this small but entrancing world of simulation. While this post is mostly a rant, other content you can expect to see here in the future:

• Current problems in numerical simulation and what are the new approaches to solve them
• Lessons and explanations of technical stuff that you probably did not see in college and that can help you in your engineering job
• Tutorials on free software for everything simulation-wise. One of my objectives is to show that you don’t need fancy expensive software to do analysis by yourself
• Some cool applications outside of textbook examples

With this, I kick-off my blog with a question for the reader: what are the problems that you see in the world of numerical analysis? Feel free to reach out!

¹ Turner’s first work in FEM, Stiffness and deflection analysis of complex structures, dates from 1956, while Galerkin’s (and Bubnov’s) works are from the early 1900s. Numerical Simulation is old.

² Not only that, there are some problems with dealing with solids. As CAD software has absolutely no need to describe volumes, just their boundaries, a proper IGA software needs algorithms that can transform a 2D representation into a 3D one. This is a problem closely related to Poincaré’s Conjecture. While Poincaré’s Conjecture was proven to be true by Grigori Perelman, we still lack generic algorithms that are able to create a 3D parametric basis of a volume given its 2D parametric boundary. There is, however, plenty of research in this field.