Obtaining accurate solutions for convection–diffusion equations is challenging due to the presence of layers when convection dominates the diffusion. To solve this problem, we design an adaptive meshing algorithm which optimizes the alignment of anisotropic meshes with the numerical solution. Three main ingredients are used. First, the streamline upwind Petrov–Galerkin method is used to produce...

Numerical solutions of convection–diffusion equations obtained using the Streamline–Upwind Petrov–Galerkin (SUPG) stabilisation typically possess spurious oscillations at layers. Spurious Oscillations at Layers Diminishing (SOLD) methods aim to suppress or at least diminish these oscillations without smearing the layers extensively. In the recent review by John and Knobloch (2007), numerical st...

This paper proposes a methodology to segment 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 approach b...

Many computer aided diagnosis (CAD) schemes have been developed for colon cancer detection using Virtual Colonoscopy (VC). In earlier work, we developed an automatic polyp detection method integrating flow visualization techniques, that forms part of the CAD functionality of an existing Virtual Colonoscopy pipeline. Curvature streamlines were used to characterize polyp surface shape. Features d...

Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical tests are performed. The method is based on an unfitted discontinuous Galerkin approach where the surface is not explicitly tracked by the mesh which means the method is extremely flexible with respec...

NI-13. RESOLVING THE CHALLENGES OF PERITUMORAL EDEMA IN TRACING ARCUATE FASCICULUS FOR SURGICAL PLANNING USING TWO-TENSOR UNSCENTED KALMAN FILTER TRACTOGRAPHY Zhenrui Chen1,4, Yanmei Tie1, Lauren O’Donnell1,2, Laura Rigolo1, Alireza Mehrtash1,2, Olutayo Olubiyi1, Isaiah Norton1, Ofer Pasternak3, Yogesh Rathi3, and Alexandra Golby1,2; Department of Neurosurgery, Brigham and Women’s Hospital, Har...

In this study, we consider the simulation of subsurface flow and solute transport processes in the stationary limit. In the convection-dominant case, the numerical solution of the transport problem may exhibit non-physical diffusion and underand overshoots. For an interior penalty discontinuous Galerkin (DG) discretization, we present a h-adaptive refinement strategy and, alternatively, a new e...