The simulation of many real-world phenomena (such as elastoplastic deformations, sound propagation, and heat diffusion) relies on an explicit discretization of the space, which allows storage of physical quantities and performance of computations upon them. However, the Computer Aided Design (CAD) tools used to design shapes rely on a different discretization, usually a collection of disconnected high-order polynomial patches, which cannot be used in simulations. It is thus necessary to convert CAD models into simulation meshes, a procedure that can introduce geometric errors due to the use of linear elements and requires manual interaction, which limits its use to high-end applications. This research will develop a novel, automatic approach to tackle this conversion "exactly" by using high order elements, thereby avoiding unnecessary geometric approximations. The project will study high-order mesh generation and simulation as a single problem, building upon recent advances in robust linear meshing and developing new finite element method techniques that will allow non-expert users to benefit from simulation at a fraction of the time and cost currently needed to accomplish that task, which in turn will open the doors to new applications in medicine and digital fabrication. The project will involve extensive testing of the developed algorithms on a large collection of real-world CAD models. Both the data collected during this project and the reference implementation of the algorithms will be released in the public domain to foster adoption of the new technique as well as future research in this direction.
The goal of this project is to develop a robust meshing pipeline that generates curvilinear elements that can reproduce both CAD models and subdivision surfaces with high fidelity, uses a direct measure of approximation errors, leading to coarse meshes that are designed to match the simulation accuracy required by applications, and can robustly and automatically process large collections of real-world CAD models. For interactive applications, the combination of the generated curved elements and the new error estimate will lead to extremely coarse models ideal for fast simulation. In CAD settings, it will for the first time enable precise modeling of complex scenarios such as the driving of a screw or the simulations of the stress concentration on fillets. The approach will close the gap between design tools, providing an automatic conversion of curved geometry to analysis-suitable curved meshes.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
