New techniques are needed because makers of microelectromechanical systems (MEMS) need efficient and robust simulation tools to investigate design alternatives. Since most MEMS devices are geometrically complicated and electromechanically coupled, the development of such simulation tools is no small task.

"Typical computer-aided design systems require the generation of an elaborate mesh to perform computational analysis," said Narayana Aluru, a UI professor of general engineering and a researcher in the university's Beckman Institute for Advanced Science and Technology. "The mesh consists of many thousands of small, interconnected elements, upon which the specific equations are solved."

But generating such a mesh for a complicated, three-dimensional microdevice with mixed energy domains -- including mechanical, electrical, optical, magnetic and thermal -- can be too time consuming and computationally expensive for practical use, Aluru said. "To develop fast and reliable CAD systems for MEMS, advances are needed that minimize the time spent on mesh generation."

Aluru and graduate student Gang Li have developed meshless numerical methods that provide simple and fast alternatives to traditional mesh-based techniques. Instead of generating a complicated, interconnected mesh, the researchers perform computational analysis on points randomly sprinkled across the domain of the microdevice. Connectivity information among the scattered points is not required.

"Because the points don't need to talk to one another, the cost and complexity of mesh generation is eliminated," Aluru said. "This greatly simplifies the making of efficient CAD tools for MEMS use."

Meshless methods also avoid the difficulties of mesh distortion in problems involving large surface deformations, and make it much easier to interface two or more energy domains.

"For example, to analyze a MEMS device that has coupled elastic- and electrostatic-energy domains, we need to generate both a volume mesh for the elastic analysis and a surface mesh for the electrostatic analysis," Aluru said. "With traditional techniques, these two meshes must be compatible or we can't interpolate solutions from one to the other."

When a microfluidic energy domain is also encountered -- such as in the design of MEMS-based accelerometers -- three different meshes are required, with corresponding complications, Aluru said. "Meshless methods can easily interpolate not only between random points in a domain, but between different domains as well, significantly reducing both time and expense."

Aluru and Li will present their latest meshless simulation techniques at the International Congress of Theoretical and Applied Mechanics, to be held Aug. 27-Sept. 2 in Chicago.

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