Discontinuous Galerkin Finite Element Methods for Maxwell\u27s Equations in Dispersive and Metamaterials Media

Discontinuous Galerkin Finite Element Method (DG-FEM) has been further developed in this dissertation. We give a complete proof of stability and error estimate for the DG-FEM combined with Runge Kutta which is commonly used in different fields. The proved error estimate matches those numerical results seen in technical papers. Numerical simulations of metamaterials play a very important role in the design of invisibility cloak, and sub-wavelength imaging. We propose a leap-frog discontinuous Galerkin Finite Element Method to solve the time-dependent Maxwell\u27s equations in metamaterials. The stability and error estimate are proved for this scheme. The proposed algorithm is implemented and numerical results supporting the analysis are provided. The wave propagation simulation in the double negative index metamaterials supplemented with perfectly matched layer (PML) boundary is given with one discontinuous Galerkin time difference method (DGTD), of which the stability and error estimate are proved as well in this dissertation. To illustrate the effectiveness of this DGTD, we present some numerical result tables which show the consistent convergence rate and the simulation of PML in metamaterials is tested in this dissertation as well. Also the wave propagation simulation in metamaterals by this DGTD scheme is consistent with those seen in other papers. Several techniques have appeared for solving the time-dependent Maxwell\u27s equations with periodically varying coefficients. For the first time, I apply the discontinuous Galerkin (DG) method to this homogenization problem in dispersive media. For simplicity, my focus is on obtaining a solution in two-dimensions (2D) using 2D corrector equations. my numerical results show the DG method to be both convergent and efficient. Furthermore, the solution is consistent with previous treatments and theoretical expectations

Topological Segmentation of 2D Vector Fields

Vector field topology has a long tradition as a visualization tool. The separatrices segment the domain visually into canonical regions in which all streamlines behave qualitatively the same. But application scientists often need more than just a nice image for their data analysis, and, to best of our knowledge, so far no workflow has been proposed to extract the critical points, the associated separatrices, and then provide the induced segmentation on the data level. We present a workflow that computes the segmentation of the domain of a 2D vector field based on its separatrices. We show how it can be used for the extraction of quantitative information about each segment in two applications: groundwater flow and heat exchange

Topological Segmentation of 2D Vector Fields

Vector field topology has a long tradition as a visualization tool. The separatrices segment the domain visually into canonical regions in which all streamlines behave qualitatively the same. But application scientists often need more than just a nice image for their data analysis, and, to best of our knowledge, so far no workflow has been proposed to extract the critical points, the associated separatrices, and then provide the induced segmentation on the data level. We present a workflow that computes the segmentation of the domain of a 2D vector field based on its separatrices. We show how it can be used for the extraction of quantitative information about each segment in two applications: groundwater flow and heat exchange

Topological Segmentation of 2D Vector Fields

Vector field topology has a long tradition as a visualization tool. The separatrices segment the domain visually into canonical regions in which all streamlines behave qualitatively the same. But application scientists often need more than just a nice image for their data analysis, and, to best of our knowledge, so far no workflow has been proposed to extract the critical points, the associated separatrices, and then provide the induced segmentation on the data level. We present a workflow that computes the segmentation of the domain of a 2D vector field based on its separatrices. We show how it can be used for the extraction of quantitative information about each segment in two applications: groundwater flow and heat exchange

Health-status outcomes with invasive or conservative care in coronary disease

BACKGROUND In the ISCHEMIA trial, an invasive strategy with angiographic assessment and revascularization did not reduce clinical events among patients with stable ischemic heart disease and moderate or severe ischemia. A secondary objective of the trial was to assess angina-related health status among these patients. METHODS We assessed angina-related symptoms, function, and quality of life with the Seattle Angina Questionnaire (SAQ) at randomization, at months 1.5, 3, and 6, and every 6 months thereafter in participants who had been randomly assigned to an invasive treatment strategy (2295 participants) or a conservative strategy (2322). Mixed-effects cumulative probability models within a Bayesian framework were used to estimate differences between the treatment groups. The primary outcome of this health-status analysis was the SAQ summary score (scores range from 0 to 100, with higher scores indicating better health status). All analyses were performed in the overall population and according to baseline angina frequency. RESULTS At baseline, 35% of patients reported having no angina in the previous month. SAQ summary scores increased in both treatment groups, with increases at 3, 12, and 36 months that were 4.1 points (95% credible interval, 3.2 to 5.0), 4.2 points (95% credible interval, 3.3 to 5.1), and 2.9 points (95% credible interval, 2.2 to 3.7) higher with the invasive strategy than with the conservative strategy. Differences were larger among participants who had more frequent angina at baseline (8.5 vs. 0.1 points at 3 months and 5.3 vs. 1.2 points at 36 months among participants with daily or weekly angina as compared with no angina). CONCLUSIONS In the overall trial population with moderate or severe ischemia, which included 35% of participants without angina at baseline, patients randomly assigned to the invasive strategy had greater improvement in angina-related health status than those assigned to the conservative strategy. The modest mean differences favoring the invasive strategy in the overall group reflected minimal differences among asymptomatic patients and larger differences among patients who had had angina at baseline