Does Coreform's IGA solver eliminate the need of costly pre-processing?

When you’ve been writing about simulation for as long as I have, you hear a lot about model pre-processing, computational loads and how both hold back the technology. Due to limited computational resources, companies that use simulation must restrict how much they can assess and/or are forced to spend days, maybe weeks, simplifying models to get faster stable solutions. The time spent on these simplifications is estimated to take over 70 percent of the whole simulation process.

It’s estimated that over 70 percent of the simulation process is dedicated to geometry and mesh preparation. IGA solvers can reduce that time significantly. (Image courtesy of Coreform and DART system analysis.)

Meanwhile, companies that have yet to take up simulation see computational resources and model preparations as another step up the ivory tower. A lot of the big players, and even a few smaller ones, have looked towards the cloud as an answer. The idea being that the more you push off computations to the cloud, the more you can reduce the pre-processing, the more accessible simulation becomes. Though this tactic has worked for some and will likely be a part of the solution to this industry problem (see simulation apps), the uptake of simulation is still lacking.

Coreform, on the other hand, has a different democratization strategy. It is looking to commercialize a tool that has been known in academic circles since 2005: isogeometric analysis (IGA) solvers. By combining that technology with their new spline surface definition, called U-splines, they eliminate most of the costly pre-processing process while keeping simulations accurate and lightning fast.

How much faster is this method and how accurate is it? According to simulations on flex cables performed by Kansas City National Security Campus, comparing Coreform’s technology to traditional FEA, Coreform was able to get more accurate results using 1000x fewer elements, 20,000x fewer timesteps, a 1000x faster runtime and better geometry.

In this example of the simulation of electronic flex cables, Coreform demonstrates how Kansas City National Security Campus was able to get more accurate results using 1000x fewer elements, 20,000x fewer timesteps, a 1000x faster runtime and better geometry. (Image courtesy of Coreform and Kansas City National Security Campus.)

Matt Sederberg, CEO of Coreform, said, “There’s been a lot of effort over the past few years to make simulation more accessible to designers, but it’s often at the cost of the quality of the [results]. So, you’ve seen various meshless methods or voxel-based methods. While they are very fast, the level of accuracy is just not there. We’re in a completely different error area with IGA, having higher accuracy, per degree of freedom, than traditional FEA.”

Coreform explains its IGA is faster and has higher accuracy than the competition. (Image courtesy of Coreform.)

What is a U-Spline?

First let’s go back to basics and ask, “What is a spline?”

Gregory Vernon, Director of Product Management at Coreform, says that “the fundamental definition of splines are piecewise functions in some space. Whether it’s 1D, 2D or 3D, you partition space into little regions and you define a function over that region. Like a linear basis function, which is what traditional FEA does. Colloquially though, splines typically infer that those functions are smooth, not just continuous.”

Image of a U-spline. (Image courtesy of Coreform.)

Sederberg added, “In simulation, we have linear elements that are faceted meshes. But when you bring the CAD data in, it’s smooth. Those smooth arbitrary shapes, those are splines, or NURBS (non-uniform rational B-splines).”

The benefits of using U-splines to represent simulation models. (Image courtesy of Coreform and Kansas City National Security Campus.)

Many simulation and CAD users will be familiar with NURBS and the linear elements that represent geometry. A more recent incarnation are T-splines. They eliminated a lot of the restrictions of NURBS and made it easier to produce organic shapes.

Coreform argues that U-splines are related, or perhaps are the next iteration of T-splines. They can capture the curvature of critical geometry using fewer elements. The idea is that because the simulation will have fewer elements, it will run faster. Additionally, since the smoothness of U-splines can capture the geometry and physics better, per degree of freedom, this added speed shouldn’t reduce accuracy.

Sederberg explained, “To capture a circle with line segments, you’re always going to have an approximation. You’d have a very high number of edges to do that. But if you have smoothness, then you can capture it in a couple of curves. It’s a similar thing with U-splines, especially with models that have high curvature. You can get away with far fewer elements.”

“When we build U-splines,” said Vernon, “we are still solving these physics over those same discretizations to help us produce a solution. Colloquially speaking, a U-spline serves the same purpose as a traditional mesh. It just approximates to a higher level of accuracy what that geometry is. So, we have a highly accurate description of the domain, and we have this high accuracy basis that can describe the physics.”

What is an IGA Solver?

IGA solvers are nothing new. Since 2005 they have had thousands of papers written about them and a conference dedicated to them. However, the technology stayed in the academic domain. What Coreform aims to do is commercialize a version of the technology.

“The thought was,” Sederberg said, “if we could run simulation right on the smooth blind data on the CAD models, instead of on the faceted mesh models, then it would save a ton of time and potentially improve accuracy.”

He continued to explain that the major difference between IGA and traditional solvers is that FEA is based on LaGrange elements. IGA solvers, on the other hand, are based on U-spline elements.

“We’re treating this new solver that accepts splines as the basis functions instead of traditional fastened LaGrange elements,” said Sederberg. “We’re working with a number of automotive, defense and nuclear energy companies where they just need to accelerate their overall time to solution.”

Coreform IGA can handle various mesh types. (Image courtesy of Coreform.)

Vernon expanded, “From a mathematical standpoint, when we do FEA, or any kind of simulation, we’re typically building systems of linear equations, or nonlinear equations (we then approximated with linear equations). The systems that arise from U-splines are typically much smaller than a traditional FEA system of equations might be. And so, because it’s smaller and requires less compute effort per equation, you have higher accuracy.”

Additionally, the simpler the system of equations, the more robust it becomes. Vernon notes that when he used to work with FEA, he would be spending hours tweaking settings (or as he put it, turning knobs) to solve the equations. “You might get a simulation to solve through the first quarter of its [computation], but then those settings aren’t sufficient for the next quarter.”

The capabilities of Coreform IGA. (Image courtesy of Coreform.)

“Just by making the overall problem much simpler, it becomes more robust,” he added. “It becomes less sensitive to changes in the model as you’re going through simulation. So, it becomes easier for the analyst to get results. There’s no value-added [by] twisting knobs. I just want the answer and I want to have confidence in the answer. And I don’t want to get a PhD in algebra, just to figure out what knobs to turn and win.”

How Coreform is Bringing IGA to the Industry?

The first step to adapting U-spline and IGA technology for the industry is through the meshing tool Cubit. Coreform recently acquired the technology, which is already used within nuclear, energy, geomechanics, defense and automotive workflows. Coreform believes that by inserting this functionality into something already accepted by the industry, it will hasten the uptake of IGA and U-spline technology.

A sample pre-processing process using U-splines and Cubit. (Image courtesy of Coreform.)

Vernon confirmed, “It’s one of the strategic decisions behind Cubit, it’s been used since the 80’s in industry to build workflows for simulation. We’ve acquired Cubit and taken those decades of meshing algorithms and model preprocessing and traditional workflows. We’ve now augmented our U-spline technology on top. So, we’re plugging into the industry workflows. In my opinion, that’s been one of the things that has kept IGA on the other side of the fence.”

Effectively, Vernon notes Coreform is extending Cubit from a meshing tool into a full pre-processing software. Sederberg added, “When you go from a smooth CAD to the mesh, you can tell it is a less accurate representation of the geometry. This is where you would end if you had a traditional mesher. But what we’ve been adding to Cubit is the chance to take this kind of mesh and convert it into a smooth U-spline.”

The data shared by Coreform points to improvements in accuracy when utilizing this method. In the example, the simulation converged faster and produced similar results with a thousandth of the elements needed for FEA.

In this example comparing IGA and FEA simulation, IGA had faster convergence, and similar results with much less elements. (Image courtesy of Coreform.)

“This is the differentiating technology,” said Sederberg. “Rather than running your simulation on a course discretization of geometry, you’re running it on the smooth model definition. Which is a much more accurate representation of the reality of the physics.”

What do you think? Will IGA solvers be the future of simulation? Comment below.