Abstract High-dimensional transport equations frequently occur in science and engineering. Computing their numerical solution, however, is challenging due to its high dimensionality. In this work we develop an algorithm efficiently solve the equation moderately complex geometrical domains using a Galerkin method stabilized by streamline diffusion. The ansatz spaces are tensor product of sparse ...

A novel tensor interpolation method is introduced that allows Diffusion Tensor Imaging (DTI) streamlining to overcome low-anisotropy regions and permits branching of trajectories using information gathered from the neighbourhood of low-anisotropy voxels met during the tracking. The interpolation method is performed in Log-Euclidean space and collects directional information in a spherical neigh...

This paper présents a stabilization technique for approximating transport équations. The key idea consists in introducing an artificial diffusion based on a two-level décomposition of the approximation space. The technique is proved to have stability and convergence properties that are similar to that of the streamline diffusion method. AMS Subject Classification. 35L50, 65N30. Received: Februa...

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...