Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A comparison of adaptive refinement techniques for elliptic problems
ACM Transactions on Mathematical Software (TOMS)
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
The immersed interface method using a finite element formulation
Applied Numerical Mathematics
The black box multigrid numerical homogenization algorithm
Journal of Computational Physics
A review of algebraic multigrid
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Multigrid
The Immersed Interface/Multigrid Methods for Interface Problems
SIAM Journal on Scientific Computing
Weighted Extended B-Spline Approximation of Dirichlet Problems
SIAM Journal on Numerical Analysis
An Introduction to Algebraic Multigrid
Computing in Science and Engineering
Topology optimization of heat conduction problem involving design-dependent heat load effect
Finite Elements in Analysis and Design
Composite finite elements for 3D image based computing
Computing and Visualization in Science
Brain shift computation using a fully nonlinear biomechanical model
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Hi-index | 0.00 |
For scalar and vector-valued elliptic boundary value problems with discontinuous coefficients across geometrically complicated interfaces, a composite finite element approach is developed. Composite basis functions are constructed, mimicking the expected jump condition for the solution at the interface in an approximate sense. The construction is based on a suitable local interpolation on the space of admissible functions. We study the order of approximation and the convergence properties of the method numerically. As applications, heat diffusion in an aluminum foam matrix filled with polymer and linear elasticity of microstructured materials, in particular, specimens of trabecular bone, are investigated. Furthermore, a numerical homogenization approach is developed for periodic structures and real material specimens which are not strictly periodic but are considered as statistical prototypes. Thereby, effective macroscopic material properties can be computed.