Finite element methods that use the same basis functions for both the geometry and the dependent variable that is being solved for are called isogeometric methods. Isogeometric methods reduce the approximation errors in the mesh since the geometry is accurately defined.
Cubic-Hermite FEA with Extraordinary NodesCombining isogeometric methods with higher-order finite elements provide distinct advantages over linear ones by enabling faster convergence and lower computational cost. However, in these methods, maintaining continuity of the fields across element boundaries require additional mathematical constraints, especially at nodes that have non-regular number of edges (3, or >5) called extraordinary nodes. We have developed methods that can be used to perform biomechanics simulations with cubic-Hermite unstructured meshes that have extraordinary nodes. These new methods enable us to perform biomechanics simulations on complex heart geometries that include valve annuli. More information can be found in the following CAGD paper.
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