Skip to main content
Image of gear mesh with a tangled element
May 1, 2024

A game-changing solution to a knotty problem in computational engineering

Written By: Adam Malecek


University of Wisconsin-Madison engineers have developed a remarkably easy-to-implement solution for handling tangled computational meshes—a major computational engineering challenge that can garble an object’s shape.

To predict how various structures or components—a turbine, for example—will behave in real-world conditions, engineers use a simulation process called finite element analysis. A critical step in this process is “meshing,” which involves breaking down the geometry of the structure into smaller, simpler pieces, called elements.

Krishnan Suresh
Krishnan Suresh

However, the process of generating or optimizing the mesh of a complex structure can sometimes result in smaller pieces with distorted shapes, known as “tangled” elements.

“If there is just one tangled element, it ruins the entire mesh, so we can’t analyze that component and get trustworthy results,” says Krishnan Suresh, a professor of mechanical engineering at the University of Wisconsin-Madison. “Engineers usually need to throw out that tangled mesh and start from scratch to try to create a better mesh. An easy solution for dealing with tangled meshes is like a holy grail for the field.”

Bhagyashree Prabhune
Bhagyashree Prabhune

Now, Suresh and recent PhD graduate Bhagyashree Prabhune have developed a novel approach, called the Tangled Finite Element Method (TFEM), that can tackle tangled meshes and produce accurate results. The new method hinges on identifying and correcting two fundamental flaws in current finite element method framework. First, when a mesh gets tangled, any physical field, such as a temperature field, that a person is attempting to capture using the mesh is rendered ambiguous over the tangled region. The new method addresses this by carefully defining the field so that the ambiguity is eliminated. Second, the underlying field also becomes discontinuous over the tangled region; this essentially violates a fundamental principle of the finite element method. However, in TFEM, continuity is guaranteed through an explicit constraint imposed over the tangled region.

Implementing the researchers’ method involves making two simple changes to the software code, which ensures that the resulting solution is unambiguous, continuous and accurate.

“The beauty of this method is that it’s so easy to implement,” Suresh says. “The work involved is extremely minimal, making this a very practical solution for companies. With this method, it doesn’t matter if your mesh has a bunch of tangled elements. You can use that tangled mesh in your normal finite element analysis software and you will get accurate results.”

In contrast, other approaches to solving this challenge require significant time and labor to implement and can involve rewriting the entire software code.

Prabhune says this advance can enable companies to greatly speed up their simulation work. “Our new method is a game-changer,” says Prabhune, who is now a postdoctoral research associate at Oak Ridge National Lab. “Generating a high-quality mesh without tangled elements requires lots of work by engineers and is extremely time-consuming, causing a big bottleneck for industry. But our method provides an easy way around this bottleneck.”

The researchers published their advance in the journal Engineering with Computers and have patented their invention through the Wisconsin Alumni Research Foundation.

Krishnan Suresh is the Mead Witter Foundation Professor in mechanical engineering.

This research was supported by the National Science Foundation through grant CMMI 1715970, and the U.S. Office of Naval Research under PANTHER award number N00014-21-1-2916.

Featured image caption: An image of a computational mesh of a gear with a tangled element (circled). Credit: Bhagyashree Prabhune.