Energy-corrected FEM and explicit time-stepping for parabolic problems

The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution effect". Standard remedies based on mesh refinement around the singular corner result in very restrictive stability requirements on the time-step size when explicit time integration is applied. In this article, we introduce and analyse the energy-corrected finite element method for parabolic problems, which works on quasi-uniform meshes, and, based on it, create fast explicit time discretisation. We illustrate these results with extensive numerical investigations not only confirming the theoretical results but also showing the flexibility of the method, which can be applied in the presence of multiple singular corners and a three-dimensional setting. We also propose a fast explicit time-stepping scheme based on a piecewise cubic energy-corrected discretisation in space completed with mass-lumping techniques and numerically verify its efficiency

Energy-corrected FEM and explicit time-stepping for parabolic problems

The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called “pollution effect”. Standard remedies based on mesh refinement around the singular corner result in very restrictive stability requirements on the time-step size when explicit time integration is applied. In this article, we introduce and analyse the energy-corrected finite element method for parabolic problems, which works on quasi-uniform meshes, and, based on it, create fast explicit time discretisation. We illustrate these results with extensive numerical investigations not only confirming the theoretical results but also showing the flexibility of the method, which can be applied in the presence of multiple singular corners and a three-dimensional setting. We also propose a fast explicit time-stepping scheme based on a piecewise cubic energy-corrected discretisation in space completed with mass-lumping techniques and numerically verify its efficiency

A level-set approach to joint image segmentation and registration with application to CT lung imaging

Automated analysis of structural imaging such as lung Computed Tomography (CT) plays an increasingly important role in medical imaging applications. Despite significant progress in the development of image registration and segmentation methods, lung registration and segmentation remain a challenging task. In this paper, we present a novel image registration and segmentation approach, for which we develop a new mathematical formulation to jointly segment and register three-dimensional lung CT volumes. The new algorithm is based on a level-set formulation, which merges a classic Chan–Vese segmentation with the active dense displacement field estimation. Combining registration with segmentation has two key advantages: it allows to eliminate the problem of initializing surface based segmentation methods, and to incorporate prior knowledge into the registration in a mathematically justified manner, while remaining computationally attractive. We evaluate our framework on a publicly available lung CT data set to demonstrate the properties of the new formulation. The presented results show the improved accuracy for our joint segmentation and registration algorithm when compared to registration and segmentation performed separately

Increasing the Reliability of Simulation Tests in Navigation and Maneuvering Simulators Using the k-Epsilon Model Based on the RANS Method

The influence of wind on the maneuverability of sea-going vessels is a known factor limiting their maneuverability, especially in the case of very large vessels. Adverse weather conditions often limit the maneuverability of vessels or even make it impossible to enter the port. This results in longer delivery times for transported goods as well as measurable material losses for both carriers and their owners. This situation is often caused by a lack of information on differences in the prevailing weather conditions at the entrance to the port and at the seaport itself. There are simulation tools, such as the methods of computational fluid dynamics (CFD), which, after their appropriate adaptation and use in a virtual environment, have become important decision-making tools supporting the port administration when deciding about the movement of vessels. In this article, the authors present the results of research aimed at adapting one of the CFD methods for the needs of maritime navigation. The effects of the work were verified in a virtual environment and were successfully implemented in the port waters of Gdansk, Poland

The Relationship Between Specific Fatty Acids of Serum Lipids and Serum High Sensitivity C- Reactive Protein Levels in Morbidly Obese Women

Background/Aims: The fatty acid profile in plasma lipids contributes to the increase of plasma high sensitivity C-reactive protein (hsCRP), a marker of inflammation and predictor of cardiovascular risk. The aim of this study was to examine the relationship between specific fatty acids (FA) of serum lipids and serum hsCRP in morbidly obese woman. Methods: The study included 16 morbidly obese (mean BMI= 43 ± 2.2 kg/m2) non-diabetic woman awaiting bariatric surgery. FA extracted from serum lipids were methylated and analyzed on GC-MS. Commercially available ELISA kits were used to determine the serum inflammatory markers. Results: We demonstrated that total saturated FA (SFA) and total monounsaturated FA (MUFA) of serum lipids were positively correlated with serum hsCRP, whereas both n-3 and n-6 total polyunsaturated FA (PUFA) were negatively correlated with serum hsCRP. Serum interleukin-6 correlated positively with some SFA and MUFA, whereas negatively with some of PUFA. Positive correlation between serum hsCRP and specific SFA and MUFA or negative correlation with PUFA decreased with the increased FA chain length. The number and localization of double bonds also had impact on these correlations. Conclusion: Our findings suggest that individual serum lipid FA levels, depending on the length of FA chain, number and the localization of double bonds are distinctly associated with hsCRP in morbidly obese subjects