A fundamental bottleneck in computational mechanics is the labor-intensive conversion of engineering geometries into analysis-ready meshes. Our research addresses this by developing geometrically flexible simulation methods that work directly on complex CAD models, point clouds, and AI-generated shapes — eliminating or greatly reducing the meshing step. This work spans isogeometric and immersogeometric methods, and extends to neural implicit representations for next-generation analysis pipelines.
Immersogeometric analysis is a geometrically flexible technique for solving computational fluid-structure interaction (FSI) problems involving large, complex structural deformations. A surface representation of a solid object is immersed into a non-boundary-fitted discretization of the background fluid domain, which is then used to solve for the flow physics using finite-element-based CFD. This alleviates the difficulties of mesh generation around complex geometries while maintaining high simulation accuracy. This project is developed in collaboration with Ming-Chen Hsu at Iowa State University.
We have developed methods to perform fluid-flow simulations over complex boundary-representation (B-Rep) based CAD models consisting of NURBS surfaces. Please refer to the following CAGD paper for more details.
We have extended our immersogeometric methods to perform fluid-flow simulations over complex CAD models consisting of analytic surfaces, and developed methods to generate adaptively-refined fluid domain meshes that accurately capture the flow near immersed surfaces. Please refer to the following CAGD paper for more details.
Finite element methods that use the same basis functions for both the geometry and the dependent variable are called isogeometric methods. By using the exact geometry representation throughout the analysis, isogeometric methods reduce approximation errors and improve convergence rates compared to standard FEA.
Combining isogeometric methods with higher-order finite elements enables faster convergence and lower computational cost. However, maintaining field continuity across element boundaries at extraordinary nodes (those with a non-regular number of edges — 3 or more than 5) requires additional mathematical constraints. We have developed methods to perform biomechanics simulations with cubic-Hermite unstructured meshes containing extraordinary nodes, enabling simulations on complex heart geometries that include valve annuli. More information can be found in the following CAGD paper.