Fast Isogeometric Boundary Element Method based on Independent Field Approximation

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology is demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.Comment: 32 pages, 27 figure

A concept for aortic dissection with fluid‐structure‐crack interaction

In aortic dissection, the layers composing the aorta rupture, allowing blood to enter the vessel wall. This process is modeled applying a monolithic fluid-structure interaction framework, formulating the Navier-Stokes equations for incompressible flows as well as the mixed finite strain elastodynamics equations in the Lagrangian frame of reference. Continuous test- and trial function spaces are employed in the whole domain, rendering the coupling straightforward. Within this contribution, a predefined function indicating failure is used to convert solid to fluid elements, thereby mimicing tissue rupture