A Parallel High-Order Fictitious Domain Approach for Biomechanical Applications

The focus of this contribution is on the parallelization of the Finite Cell Method (FCM) applied for biomechanical simulations of human femur bones. The FCM is a high-order fictitious domain method that combines the simplicity of Cartesian grids with the beneficial properties of hierarchical approximation bases of higher order for an increased accuracy and reliablility of the simulation model. A pre-computation scheme for the numerically expensive parts of the finite cell model is presented that shifts a significant part of the analysis update to a setup phase of the simulation, thus increasing the update rate of linear analyses with time-varying geometry properties to a range that even allows user interactive simulations of high quality. Paralellization of both parts, the pre-computation of the model stiffness and the update phase of the simulation is simplified due to a simple and undeformed cell structure of the computation domain. A shared memory parallelized implementation of the method is presented and its performance is tested for a biomedical application of clinical relevance to demonstrate the applicability of the presented method

The tetrahedral finite cell method for fluids: Immersogeometric analysis of turbulent flow around complex geometries

We present a tetrahedral finite cell method for the simulation of incompressible flow around geometrically complex objects. The method immerses such objects into non-boundary-fitted meshes of tetrahedral finite elements and weakly enforces Dirichlet boundary conditions on the objects’ surfaces. Adaptively-refined quadrature rules faithfully capture the flow domain geometry in the discrete problem without modifying the non-boundary-fitted finite element mesh. A variational multiscale formulation provides accuracy and robustness in both laminar and turbulent flow conditions. We assess the accuracy of the method by analyzing the flow around an immersed sphere for a wide range of Reynolds numbers. We show that quantities of interest such as the drag coefficient, Strouhal number and pressure distribution over the sphere are in very good agreement with reference values obtained from standard boundary-fitted approaches. We place particular emphasis on studying the importance of the geometry resolution in intersected elements. Aligning with the immersogeometric concept, our results show that the faithful representation of the geometry in intersected elements is critical for accurate flow analysis. We demonstrate the potential of our proposed method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor

Direct immersogeometric fluid flow analysis using B-rep CAD models

We present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche\u27s method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the density and distribution of the surface quadrature points are crucial for the weak enforcement of Dirichlet boundary conditions and for obtaining accurate flow solutions. Also, with sufficient levels of surface quadrature element refinement, the quadrature error near the trim curves becomes insignificant. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor directly represented using B-rep

The tetrahedral finite cell method for fluids: Immersogeometric analysis of turbulent flow around complex geometries

We present a tetrahedral finite cell method for the simulation of incompressible flow around geometrically complex objects. The method immerses such objects into non-boundary-fitted meshes of tetrahedral finite elements and weakly enforces Dirichlet boundary conditions on the objects’ surfaces. Adaptively-refined quadrature rules faithfully capture the flow domain geometry in the discrete problem without modifying the non-boundary-fitted finite element mesh. A variational multiscale formulation provides accuracy and robustness in both laminar and turbulent flow conditions. We assess the accuracy of the method by analyzing the flow around an immersed sphere for a wide range of Reynolds numbers. We show that quantities of interest such as the drag coefficient, Strouhal number and pressure distribution over the sphere are in very good agreement with reference values obtained from standard boundary-fitted approaches. We place particular emphasis on studying the importance of the geometry resolution in intersected elements. Aligning with the immersogeometric concept, our results show that the faithful representation of the geometry in intersected elements is critical for accurate flow analysis. We demonstrate the potential of our proposed method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor

Real Time Processing of Large Data Sets from Built Infrastructure

In this paper, we present a framework that gives the user a tool at hand to explore large data sets from built infrastructure. In a first step we describe the integration of fully detailed product models of constructions delivering the geometric and auxiliary information we build up our data exploration from. The main part of this paper follows by presenting the application of a hierarchical data structure, an octree, that is capable of holding building information for a whole region or even a country and the development of complexity reduction algorithms that allow the visualisation of those data. To exploit the full performance of modern hardware platforms, the application of parallelisation techniques is inevitable and we present the implementation of these techniques to the data processing steps performed in the framework. After introducing the framework, we show possible applications to various disciplines such as environmental and civil engineering, architecture, or disaster management

The tetrahedral finite cell method: Higher-order immersogeometric analysis on adaptive non-boundary-fitted meshes

The finite cell method (FCM) is an immersed domain finite element method that combines higher-order non-boundary-fitted meshes, weak enforcement of Dirichlet boundary conditions, and adaptive quadrature based on recursive subdivision. Because of its ability to improve the geometric resolution of intersected elements, it can be characterized as an immersogeometric method. In this paper, we extend the FCM, so far only used with Cartesian hexahedral elements, to higher-order non-boundary-fitted tetrahedral meshes, based on a reformulation of the octree-based subdivision algorithm for tetrahedral elements. We show that the resulting TetFCM scheme is fully accurate in an immersogeometric sense, that is, the solution fields achieve optimal and exponential rates of convergence for h-refinement and p-refinement, if the immersed geometry is resolved with sufficient accuracy. TetFCM can leverage the natural ability of tetrahedral elements for local mesh refinement in three dimensions. Its suitability for problems with sharp gradients and highly localized features is illustrated by the immersogeometric phase-field fracture analysis of a human femur bone. Copyright © 2016 John Wiley & Sons, Ltd.This is the peer reviewed version of the following article: Varduhn, Vasco, Ming‐Chen Hsu, Martin Ruess, and Dominik Schillinger. "The tetrahedral finite cell method: Higher‐order immersogeometric analysis on adaptive non‐boundary‐fitted meshes." International Journal for Numerical Methods in Engineering 107, no. 12 (2016): 1054-1079, which has been published in final form at doi: 10.1002/nme.5207. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Posted with permission.</p