Jacobs School Engineer Designs Adaptive Simulation Technique

ADAPTIVE FINITE ELEMENT REFINEMENT can be an important tool for engineering and scientific simulations, for instance for analyzing the performance of structures and materials when subjected to stress.

Programming adaptive finite element mesh refinement usually proves to be a formidable task. Structural Engineering Professor Petr Krysl, in collaboration with researchers at the California Institute of Technology, offers an alternative, novel algorithm that proves to be significantly simpler and more powerful than current, "classical" approaches. "Its beauty is in its simplicity and flexibility," explains Krysl.

"This new approach allows one to solve a wider range of problems," says Krysl. "It is applicable to old, traditional areas of mesh refinement, as well as a new area – adaptive approximations on subdivision surfaces. With subdivision, we can construct numerical schemes with excellent approximation properties. Furthermore, our approach complements recent advances in so-called partition- of-unity methods. The result will be an extremely powerful, yet simple to implement adaptive simulation software applicable in many areas of mathematical modeling."

Krysl has spoken with a commercial CAD software developer about creating a library of modeling tools centered around his groundbreaking algorithm. "It's based on just a simple refinement equation that has been used before, but for different things, and its use for this purpose had been missed so many times. Its usefulness reminds me of C++. It is possible to program everything you need to do in assembly language – but it's going to be very tedious, and costly. Our algorithm is the C++ of mesh refinement," laughs Krysl.