On the Treatment of Field Quantities and Elemental Continuity in FEM Solutions

As the finite element method (FEM) and the finite volume method (FVM), both traditional and high-order variants, continue their proliferation into various applied engineering disciplines, it is important that the visualization techniques and corresponding data analysis tools that act on the results produced by these methods faithfully represent the underlying data. To state this in another way: the interpretation of data generated by simulation needs to be consistent with the numerical schemes that underpin the specific solver technology. As the verifiable visualization literature has demonstrated: visual artifacts produced by the introduction of either explicit or implicit data transformations, such as data resampling, can sometimes distort or even obfuscate key scientific features in the data. In this paper, we focus on the handling of elemental continuity, which is often only C0 continuous or piecewise discontinuous, when visualizing primary or derived fields from FEM or FVM simulations. We demonstrate that traditional data handling and visualization of these fields introduce visual errors. In addition, we show how the use of the recently proposed line-SIAC filter provides a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous

Doctor of Philosophy

dissertationSmoothness-increasing accuracy-conserving (SIAC) filters were introduced as a class of postprocessing techniques to ameliorate the quality of numerical solutions of discontinuous Galerkin (DG) simulations. SIAC filtering works to eliminate the oscillations in the error by introducing smoothness back to the DG field and raises the accuracy in the L2-n o rm up to its natural superconvergent accuracy in the negative-order norm. The increased smoothness in the filtered DG solutions can then be exploited by simulation postprocessing tools such as streamline integrators where the absence of continuity in the data can lead to erroneous visualizations. However, lack of extension of this filtering technique, both theoretically and computationally, to nontrivial mesh structures along with the expensive core operators have been a hindrance towards the application of the SIAC filters to more realistic simulations. In this dissertation, we focus on the numerical solutions of linear hyperbolic equations solved with the discontinuous Galerkin scheme and provide a thorough analysis of SIAC filtering applied to such solution data. In particular, we investigate how the use of different quadrature techniques could mitigate the extensive processing required when filtering over the whole computational field. Moreover, we provide detailed and efficient algorithms that a numerical practitioner requires to know in order to implement this filtering technique effectively. In our first attempt to expand the application scope of this filtering technique, we demonstrate both mathematically and through numerical examples that it is indeed possible to observe SIAC filtering characteristics when applied to numerical solutions obtained over structured triangular meshes. We further provide a thorough investigation of the interplay between mesh geometry and filtering. Building upon these promising results, we present how SIAC filtering could be applied to gain higher accuracy and smoothness when dealing with totally unstructured triangular meshes. Lastly, we provide the extension of our filtering scheme to structured tetrahedral meshes. Guidelines and future work regarding the application of the SIAC filter in the visualization domain are also presented. We further note that throughout this document, the terms postprocessing and filtering will be used interchangeably

One-sided smoothness-increasing accuracy-conserving filtering for enhanced streamline integration through discontinuous fields

The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. One of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high-order discretizations on an inter-element level while allowing discontinuities between elements. This flexibility, however, generates a plethora of difficulties when one attempts to use DG fields for feature extraction and visualization, as most post-processing schemes are not designed for handling explicitly discontinuous fields. This work introduces a new method of applying smoothness-increasing, accuracy-conserving filtering on discontinuous Galerkin vector fields for the purpose of enhancing streamline integration. The filtering discussed in this paper enhances the smoothness of the field and eliminates the discontinuity between elements, thus resulting in more accurate streamlines. Furthermore, as a means of minimizing the computational cost of the method, the filtering is done in a one-dimensional manner along the streamline.United States. Army Research Office (Grant no. W911NF-05-1-0395)National Science Foundation (U.S.) (Career Award NSF-CCF0347791

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields

Journal ArticleStreamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators - integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated, which is not available at the interelement level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by interelement discontinuities

Bayesian atmospheric correction over land: Sentinel-2/MSI and Landsat 8/OLI

Mitigating the impact of atmospheric effects on optical remote sensing data is critical for monitoring intrinsic land processes and developing Analysis Ready Data (ARD). This work develops an approach to this for the NERC NCEO medium resolution ARD Landsat 8 (L8) and Sentinel 2 (S2) products, called Sensor Invariant Atmospheric Correction (SIAC). The contribution of the work is to phrase and solve that problem within a probabilistic (Bayesian) framework for medium resolution multispectral sensors S2/MSI and L8/OLI and to provide per-pixel uncertainty estimates traceable from assumed top-of-atmosphere (TOA) measurement uncertainty, making progress towards an important aspect of CEOS ARD target requirements. A set of observational and a priori constraints are developed in SIAC to constrain an estimate of coarse resolution (500 m) aerosol optical thickness (AOT) and total column water vapour (TCWV), along with associated uncertainty. This is then used to estimate the medium resolution (10–60 m) surface reflectance and uncertainty, given an assumed uncertainty of 5 % in TOA reflectance. The coarse resolution a priori constraints used are the MODIS MCD43 BRDF/Albedo product, giving a constraint on 500 m surface reflectance, and the Copernicus Atmosphere Monitoring Service (CAMS) operational forecasts of AOT and TCWV, providing estimates of atmospheric state at core 40 km spatial resolution, with an associated 500 m resolution spatial correlation model. The mapping in spatial scale between medium resolution observations and the coarser resolution constraints is achieved using a calibrated effective point spread function for MCD43. Efficient approximations (emulators) to the outputs of the 6S atmospheric radiative transfer code are used to estimate the state parameters in the atmospheric correction stage. SIAC is demonstrated for a set of global S2 and L8 images covering AERONET and RadCalNet sites. AOT retrievals show a very high correlation to AERONET estimates (correlation coefficient around 0.86, RMSE of 0.07 for both sensors), although with a small bias in AOT. TCWV is accurately retrieved from both sensors (correlation coefficient over 0.96, RMSE <0.32 g cm−2). Comparisons with in situ surface reflectance measurements from the RadCalNet network show that SIAC provides accurate estimates of surface reflectance across the entire spectrum, with RMSE mismatches with the reference data between 0.01 and 0.02 in units of reflectance for both S2 and L8. For near-simultaneous S2 and L8 acquisitions, there is a very tight relationship (correlation coefficient over 0.95 for all common bands) between surface reflectance from both sensors, with negligible biases. Uncertainty estimates are assessed through discrepancy analysis and are found to provide viable estimates for AOT and TCWV. For surface reflectance, they give conservative estimates of uncertainty, suggesting that a lower estimate of TOA reflectance uncertainty might be appropriate

Smoothness-increasing accuracy-conserving (SIAC) line filtering: effective rotation for multidimensional fields

Over the past few decades there has been a strong effort towards the development of Smoothness-Increasing Accuracy-Conserving (SIAC) filters for Discontinuous Galerkin (DG) methods, designed to increase the smoothness and improve the convergence rate of the DG solution through this post-processor. The applications of these filters in multidimension have traditionally employed a tensor product kernel, allowing a natural extension of the theory developed for one-dimensional problems. In addition, the tensor product has always been done along the Cartesian axis, resulting in a filter whose support has fixed shape and orientation. This thesis has challenged these assumptions, leading to the investigation of rotated�filters: tensor product filters with variable orientation. Combining this approach with previous experiments on lower-dimension filtering, a new and computationally efficient subfamily for post-processing multidimensional data has been developed: SIAC Line filters. These filters transform the integral of the convolution into a line integral. Hence, the computational advantages are immediate: the simulation times become significantly shorter and the complexity of the algorithm design reduces to a one-dimensional problem. In the thesis, a solid theoretical background for SIAC Line �filters has been established. Theoretical error estimates have been developed, showing how Line filtering preserves the properties of traditional tensor product �filtering, including smoothness recovery and improvement in the convergence rate. Furthermore, different numerical experiments were performed, exhibiting how these filters achieve the same accuracy at significantly lower computational costs. This affords great advantages towards the applications of these filters during flow visualization; one important limiting factor of a tensor product structure is that the filter grows in support as the field dimension increases, becoming computationally expensive. SIAC Line filters have proven effi�ciency in computational performance, thus overcoming the limitations presented by the tensor product filter. The experiments carried out on streamline visualization suggest that these filters are a promising tool in scientific visualisation

Capnocytophaga canimorsus : genomic characterization of a specialised host-dependent lifestyle and implications in pathogenesis

Here is presented the complete 2,571,405-bp genome sequence of Capnocytophaga canimorsus strain 5 (Cc5), a strain that was isolated from a fatal septicaemia. Phylogenetic analysis of conserved genes supports the inclusion of C. canimorsus into the Cytophaga-Flavobacteria-Bacteroides (CFB) phylum and indicates close relationships with environmental flavobacteria as Flavobacterium johnsoniae and Gramella forsetii. In addition, relative phylogenetic topology of Capnocytophaga species shows that C. canimorsus share more sequence similarities with human host associated Capnocytophaga species than species from the latter group among themselves (e.g. C. gingivalis and C. ochracea). As compared to other Capnocytophaga, C.canimorsus seems to have differentiated by large-scale horizontal gene transfer compensated by gene losses. Consistently with a relatively reduced genome size, genome scale metabolic modelling suggested a reduced global pleiotropy as it is illustrated by the presence of a split TCA cycle or by the metabolic uncoupling of the hexoses and N-acetylhexosamines pathways. In addition and in agreement with the high content in HCO3- and Na+ ions in saliva, we predicted a CO2-dependent fumarate respiration coupled to a Na+ ions gradient based respiratory chain in Cc5. All together these observations draw the picture of an organism with a high degree of specialization to a relatively homeostatic host environment. Unexpectedly, the genome of Cc5 did not encode classical complex virulence functions as T3SSs or T4SSs. However it exhibits a very high relative number of predicted surface-exposed lipoproteins. Many of them are encoded within 13 different putative polysaccharide utilization loci (PULs), a hallmark of the CFB group, discovered in the gut commensal Bacteroides thetaiotaomicron. When Cc5 bacteria were grown on Hek293 cells, at least 12 PULs were expressed and detected by mass spectrometry. Semi-quantitative analysis of the Cc5 surfome identified 73 surface exposed proteins among which 40 were lipoproteins and accounted for 76% of the total quantification. Interestingly, 28 proteins (38%) were encoded by 9 different PULs and corresponded to more than 54% of total MS-flying peptides detected. A systematic knockout analysis of the 13 PULs revealed that 6 PULs are involved in growth during cell culture infections with most dramatic effect observed for ΔPUL5. Proteins encoded by PUL5, one of the most abundant PULs (12%), turned out to be devoted to foraging glycans from N-linked glycoproteins as fetuin but also IgG. It was not only essential for growth on cells but also for survival in mice and in fresh human serum therefore representing a new type of virulence factor. Further characterization of the PUL5 deglycosylation mechanism revealed that deglycosylation is achieved by a large surface complex spanning the outer membrane and consisting of five PUL5 encoded Gpd proteins and the Siac sialidase. GpdCDEF contribute to the binding of glycoproteins at the bacterial surface while GpdG is a β-endo-glycosidase cleaving the N-linked oligosaccharide after the first N-linked GlcNAc residue. We demonstrate that GpdD, -G, -E and -F are surface-exposed outer membrane lipoproteins while GpdC resembles a TonB-dependent OM transporter and presumably imports oligosaccharides into the periplasm after cleavage from glycoproteins. Terminal sialic acid residues of the oligosaccharide are then removed by SiaC in the periplasm. Finally, degradation of the oligosaccharide proceeds sequentially from the desialylated non reducing end by the action of periplasmic exoglycosidases, including β-galactosidases, β-N-Acetylhexosaminidases and α-mannosidases. Genome sequencing of additional C. canimorsus strains have been performed with the only use of second generation sequencing methods (Solexa and 454). Two assembling approaches were developed in order to enhance assembly capacities of pre-existing tools. Draft assemblies of the three pathogenic human blood isolates C. canimorsus 2 (three contigs), C. canimorsus 11 (152 contigs) and C. canimorsus 12 (63 contigs) are presented here. Comparative genomics including genomes of four available human hosted Capnocytophaga species stressed C. canimorsus exclusively conserved features as an oxidative respiratory chain and an oxidative stress resistance or the presence of a Cc5 specific PULs content. Therefore we propose these features as potential factors involved in the pathogenesis of C. canimorsus