A rarefied gas flow through a channel with arbitrary cross section is studied based on the BGK model. The discrete velocity and streamline diffusion finite element methods are combined to yield a numerical scheme. For this method we derive stability and optimal error estimates in the L2 norm. The optimality is due to the maximal available regularity of the exact solution for the corresponding h...

Adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed. The underlying discretization scheme is the Shock-capturing Streamline Diffusion method. The adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed. A priori error estimates ar...

Diffusion MRI streamlines tractography allows for the investigation of the brain white matter pathways non-invasively. However a fundamental limitation of this technology is its non-quantitative nature, i.e. the density of reconstructed connections is not reflective of the density of underlying white matter fibres. As a solution to this problem, we have previously published the "spherical-decon...

In this paper, we apply streamline-diffusion and Galerkin-least-squares finite element methods for 2D steady-state two-phase model in the cathode of polymer electrolyte fuel cell (PEFC) that contains a gas channel and a gas diffusion layer (GDL). This two-phase PEFC model is typically modeled by a modified Navier-Stokes equation for the mass and momentum, with Darcy’s drag as an additional sour...

The transport and deposition properties of nanoparticles with a range of aerodynamic diameters ( 1 nm ≤ d ≤ 150 nm) were studied for the human airways. A finite element code was developed that solved both the Navier-Stokes and advection-diffusion equations monolithically. When modeling nanoparticle transport in the airways, the finite element method becomes unstable, and, in order resolve this ...

The choice of geometrical shape of the blades has a considerable effect on aerodynamic performance and flow characteristics in axial compressors. In this paper, the effects of the blades shape on the aerodynamic design characteristics are investigated based on Streamline Curvature Method (SCM). Initially, the Streamline Curvature Method (SCM) is used for designing a two-stage axial compressor. ...

BACKGROUND Diffusion imaging tractography is increasingly used to trace critical fiber tracts in brain tumor patients to reduce the risk of post-operative neurological deficit. However, the effects of peritumoral edema pose a challenge to conventional tractography using the standard diffusion tensor model. The aim of this study was to present a novel technique using a two-tensor unscented Kalma...

This report aims to present my research updates on distance function wavelets (DFW) based on the fundamental solutions and general solutions of the Helmholtz, modified Helmholtz, and convection-diffusion equations, which include the isotropic HelmholtzFourier (HF) transform and series, the Helmholtz-Laplace (HL) transform, and the anisotropic convection-diffusion wavelets and ridgelets. The lat...

Diffusion tensor imaging provides information about structure and location of white matter tracts within the human brain which is of particular interest for neurosurgery. The reconstruction of neuronal structures from diffusion tensor data is commonly solved by tracking algorithms based on streamline propagation. These approaches generate streamline bundles that approximate the course of neuron...

We consider an elementwise data-parallel finite element procedure, recently proposed by Layton and Rabier [Appl. Math. Lett., 5 (1992), pp. 67–70], [J. Numer. Linear Algebra Appl., 2 (1995), pp. 363–394], applied to singularly perturbed convection-diffusion equations with possibly highly anisotropic diffusion. It is shown that the number of iterations required for the solution of the linear alg...