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A time-dependent coordinate transformation of a constant coeffcient hyperbolic equation which results in a variable coeffcient problem is considered. By using the energy method, we derive well-posed boundary conditions for the continuous problem. It is shown that the number of boundary conditions depend on the coordinate transformation. By using Summation-by-Parts (SBP) operators for the space discretization and weak boundary conditions, an energy stable finite dieffrence scheme is obtained. We also show how to construct a time-dependent penalty formulation that automatically imposes the right number of boundary conditions. Numerical calculations corroborate the stability and accuracy of the approximations

Higher order finite difference schemes for the magnetic induction equations

We describe high order accurate and stable finite difference schemes for the initial-boundary value problem associated with the magnetic induction equations. These equations model the evolution of a magnetic field due to a given velocity field. The finite difference schemes are based on Summation by Parts (SBP) operators for spatial derivatives and a Simultaneous Approximation Term (SAT) technique for imposing boundary conditions. We present various numerical experiments that demonstrate both the stability as well as high order of accuracy of the schemes.Comment: 20 page

Stability issues of entropy-stable and/or split-form high-order schemes -- Analysis of local linear stability

The focus of the present research is on the analysis of local linear stability of high-order (including split-form) summation-by-parts methods, with e.g. two-point entropy-conserving fluxes, approximating non-linear conservation laws. Our main finding is that local linear stability is not guaranteed even when the scheme is non-linearly stable and that this has grave implications for simulation results. We show that entropy-conserving two-point fluxes are inherently locally linearly unstable, as they can be dissipative or anti-dissipative. Unfortunately, these fluxes are at the core of many commonly used high-order entropy-stable extensions, including split-form summation-by-parts discontinuous Galerkin spectral element methods (or spectral collocation methods). For the non-linear Burgers equation, we demonstrate numerically that such schemes cause exponential growth of errors. Furthermore, we demonstrate a similar abnormal behaviour for the compressible Euler equations. Finally, we demonstrate numerically that other commonly used split-forms, such as the Kennedy and Gruber splitting, are also locally linearly unstable

New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions

We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the truncation error on the boundary points, the spectral radius, or a combination of these. We examine in detail a set of operators that are up to tenth order accurate in the interior, and we surprisingly find that a combination of these optimizations can improve the operators' spectral radius and accuracy by orders of magnitude in certain cases. We also construct high-order dissipation operators that are compatible with these new finite difference operators and which are semi-definite with respect to the appropriate summation by parts scalar product. We test the stability and accuracy of these new difference and dissipation operators by evolving a three-dimensional scalar wave equation on a spherical domain consisting of seven blocks, each discretized with a structured grid, and connected through penalty boundary conditions.Comment: 16 pages, 9 figures. The files with the coefficients for the derivative and dissipation operators can be accessed by downloading the source code for the document. The files are located in the "coeffs" subdirector

Demarcating the Right to Gather News: A Sequential Interpretation of the First Amendment

In this paper we construct well-posed boundary conditions for the compressible Euler and Navier-Stokes equations in two space dimensions. When also considering the dual equations, we show how to construct the boundary conditions so that both the primal and dual problems are well-posed. By considering the primal and dual problems simultaneously, we construct energy stable and dual consistent finite difference schemes on summation-by-  parts form with weak imposition of the boundary conditions. According to linear theory, the stable and dual consistent discretization can be used to compute linear integral functionals from the solution at a superconvergent rate. Here we evaluate numerically the superconvergence property for the non-linear Euler and Navier{ Stokes equations with linear and non-linear integral functionals

Towards Verification of Unstructured-Grid Solvers

New methodology for verification of computational methods using unstructured grids is presented. The discretization order properties are studied in computational windows, easily constructed within a collection of grids or a single grid. The windows can be adjusted to isolate the interior discretization, the boundary discretization, or singularities. A major component of the methodology is the downscaling test, introduced previously for studying the convergence rates of truncation and discretization errors of finite-volume discretization schemes on general unstructured grids. Demonstrations of the method are shown, including a comparative accuracy assessment of commonly-used schemes on general mixed grids and the identification of local accuracy deterioration at intersections of tangency and inflow/outflow boundaries. Recommendations for the use of the methodology in large-scale computational simulations are given

A genomic survey of the fish parasite Spironucleus salmonicida indicates genomic plasticity among diplomonads and significant lateral gene transfer in eukaryote genome evolution

BACKGROUND: Comparative genomic studies of the mitochondrion-lacking protist group Diplomonadida (diplomonads) has been lacking, although Giardia lamblia has been intensively studied. We have performed a sequence survey project resulting in 2341 expressed sequence tags (EST) corresponding to 853 unique clones, 5275 genome survey sequences (GSS), and eleven finished contigs from the diplomonad fish parasite Spironucleus salmonicida (previously described as S. barkhanus). RESULTS: The analyses revealed a compact genome with few, if any, introns and very short 3' untranslated regions. Strikingly different patterns of codon usage were observed in genes corresponding to frequently sampled ESTs versus genes poorly sampled, indicating that translational selection is influencing the codon usage of highly expressed genes. Rigorous phylogenomic analyses identified 84 genes – mostly encoding metabolic proteins – that have been acquired by diplomonads or their relatively close ancestors via lateral gene transfer (LGT). Although most acquisitions were from prokaryotes, more than a dozen represent likely transfers of genes between eukaryotic lineages. Many genes that provide novel insights into the genetic basis of the biology and pathogenicity of this parasitic protist were identified including 149 that putatively encode variant-surface cysteine-rich proteins which are candidate virulence factors. A number of genomic properties that distinguish S. salmonicida from its human parasitic relative G. lamblia were identified such as nineteen putative lineage-specific gene acquisitions, distinct mutational biases and codon usage and distinct polyadenylation signals. CONCLUSION: Our results highlight the power of comparative genomic studies to yield insights into the biology of parasitic protists and the evolution of their genomes, and suggest that genetic exchange between distantly-related protist lineages may be occurring at an appreciable rate in eukaryote genome evolution

Transcriptome analyses of the Giardia lamblia life cycle

Author Posting. © The Author(s), 2010. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Molecular and Biochemical Parasitology 174 (2010): 62-65, doi:10.1016/j.molbiopara.2010.05.010.We quantified mRNA abundance from 10 stages in the Giardia lamblia life cycle in vitro using Serial Analysis of Gene Expression (SAGE). 163 abundant transcripts were expressed constitutively. 71 transcripts were upregulated specifically during excystation and 42 during encystation. Nonetheless, the transcriptomes of cysts and trophozoites showed major differences. SAGE detected co-expressed clusters of 284 transcripts differentially expressed in cysts and excyzoites and 287 transcripts in vegetative trophozoites and encysting cells. All clusters included known genes and pathways as well as proteins unique to Giardia or diplomonads. SAGE analysis of the Giardia life cycle identified a number of kinases, phosphatases, and DNA replication proteins involved in excystation and encystation, which could be important for examining the roles of cell signaling in giardial differentiation. Overall, these data pave the way for directed gene discovery and a better understanding of the biology of Giardia lamblia.BJD, DSR, and FDG were supported by NIH grants AI42488, GM61896, DK35108, and AI051687. DP and SGS were supported by grants from the Swedish Natural Science Research Council, the Swedish Medical Research Council, and the Karolinska Institutet. AGM, SRB, SPP, and MJC were supported by NIH grant AI51089 and by the Marine Biological Laboratory’s Program in Global Infectious Diseases, funded by the Ellison Medical Foundation