Composite Finite Elements for Trabecular Bone Microstructures

Numerical simulations in medical or technical applications ofteninvolve objects or material interfaces of geometrically complicatedshape. Composite Finite Elements are an efficient simulation tool forsuch problems, particularly for objects given by 3D image data. Usingthe uniform hexahedral voxel grid, global meshing is avoided and thegeometry is represented by appropriate basis functions adapted toeither the object boundary or the discontinuity of the coefficient.
In his dissertation, Lars Ole Schwen describes the construction ofComposite Finite Elements. After treating isotropic and anisotropicheat diffusion as scalar model problems, the main focus lies on linearelasticity of trabecular structures. The author also presents anefficient multigrid solver tailored to the Composite Finite Elementapproach and addresses the implementation of the methods. As anapplication framework, he finally discusses numerical homogenizationfor periodic and statistically periodic objects. The book is aimed atresearchers interested in efficient numerical simulation tools.