The discrete convection-diffusion equations obtained from streamline diffusion finite element discretization are solved on both uniform meshes and adaptive meshes. The performance of geometric multigrid method (GMG) and algebraic multigrid method (AMG), both as a solver and as a preconditioner of the generalized minimal residual method (GMRES), are evaluated. Our numerical results show that GMR...

One-dimensional convection-diffusion problem with interior layers caused by the discontinuity of data is considered. Though standard Galerkin finite element method (FEM) generates oscillations in the numerical solutions, we prove its convergence in the ε-weighted norm of the first order on a class of layer-adapted meshes. We use streamline-diffusion finite element method (SDFEM) in order to sta...

— We prove error estimâtes for the streamline diffusion and the discontinuous Galerkin finite element methods for discretization of the Vlasov-Poisson équation. Résumé. — Nous démontrons des estimations d'erreur pour la méthode de Galerkin discontinue pour la discrétisation de l'équation de Vlasov-Poisson.

For the visualization of diffusion tensor imaging data, different approaches have been presented such as scalar metrics, glyphs or streamlines. Thereby, streamline techniques commonly referred to as fiber tracking provide a comprehensive and intuitive representation. For this reason, they are preferably applied for preoperative planning. The visualization of streamlines is solved by rendering l...

The dependence of the computation of advective-diffusive transport phenomena on the orientation of the mesh with respect to the flow direction is analyzed. Poor performance of the classical Galerkin finite element method in the convectiondominated regime is alleviated by stabilization. We propose definitions of the stability parameter that rationally incorporate the flow direction. Numerical te...

Diffusion-weighted magnetic resonance imaging has the ability to map neuronal architecture by estimating the 3D diffusion displacement within fibrous brain structures. This approach has non-invasively been demonstrated in the human brain with diffusion tensor tractography. Despite its valuable application in neuroscience and clinical studies however, it faces an inherent limit in mapping fiber ...

This paper proposes a methodology to segment near-tubular fiber bundles from diffusion weighted magnetic resonance images (DW-MRI). Segmentation is simplified by locally reorienting diffusion information based on large-scale fiber bundle geometry. Segmentation is achieved through simple global statistical modeling of diffusion orientation. Utilizing a modification of a recent segmentation appro...

Diffusion tensor magnetic resonance imaging (DT-MRI) is the first noninvasive in vivo imaging modality with the potential to generate fiber tract trajectories in soft fibrous tissues, such as the brain white matter. Several newly developed fiber reconstruction and tractography techniques based on DT-MRI are reviewed in this article, including streamline fiber tracking techniques, diffusion tens...