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1. Equivalence between the DPG method and the exponential integrators for linear parabolic problems

   https://doi.org/10.1016/j.jcp.2020.110016  

   Munoz-Matute, J.; Pardo, D.; Demkowicz, L. (July 2021, Journal of computational physics)

   The Discontinuous Petrov-Galerkin (DPG) method and the exponential integrators are two well establishednumerical methods for solving Partial Differential Equations (PDEs) and stiff systems of Ordinary Differential Equations (ODEs), respectively. In this work, we apply the DPG method in the time variable for linear parabolic problems and we calculate the optimal test functions analytically. We show that the DPG method in time is equivalent to exponential integrators for the trace variables, which are decoupled from the interior variables. In addition, the DPG optimal test functions allow us to compute the approximated solutions in the time element interiors. This DPG method in time allows to construct a posteriori error estimations in order to perform adaptivity. We generalize this novel DPG-based time-marching scheme to general first order linear systems of ODEs. We show the performance of the proposed method for 1D and 2D +time linear parabolic PDEs after discretizing in space by the finite element method. 

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2. Adaptive Quotient Filters

   https://doi.org/10.1145/3677128  

   Wen, Richard; McCoy, Hunter; Tench, David; Tagliavini, Guido; Bender, Michael A; Conway, Alex; Farach-Colton, Martin; Johnson, Rob; Pandey, Prashant (October 2024, Proceedings of the ACM on Management of Data)

   Filters trade off accuracy for space and occasionally return false positive matches with a bounded error. Numerous systems use filters in fast memory to avoid performing expensive I/Os to slow storage. A fundamental limitation in traditional filters is that they do not change their representation upon seeing a false positive match. Therefore, the maximum false positive rate is only guaranteed for a single query, not for an arbitrary set of queries. We can improve the filter's performance on a stream of queries, especially on a skewed distribution, if we can adapt after encountering false positives. Adaptive filters, such as telescoping quotient filters and adaptive cuckoo filters, update their representation upon detecting a false positive to avoid repeating the same error in the future. Adaptive filters require an auxiliary structure, typically much larger than the main filter and often residing on slow storage, to facilitate adaptation. However, existing adaptive filters are not practical and have not been adopted in real-world systems for two main reasons. First, they offer weak adaptivity guarantees, meaning that fixing a new false positive can cause a previously fixed false positive to come back. Secondly, the sub-optimal design of the auxiliary structure results in adaptivity overheads so substantial that they can actually diminish overall system performance compared to a traditional filter. In this paper, we design and implement the \sysname, the first practical adaptive filter with minimal adaptivity overhead and strong adaptivity guarantees, which means that the performance and false-positive guarantees continue to hold even for adversarial workloads. The \sysname is based on the state-of-the-art quotient filter design and preserves all the critical features of the quotient filter such as cache efficiency and mergeability. Furthermore, we employ a new auxiliary structure design which results in considerably low adaptivity overhead and makes the \sysname practical in real systems. We evaluate the \sysname by using it to filter queries to an on-disk B-tree database and find no negative impact on insert or query performance compared to traditional filters. Against adversarial workloads, the \sysname preserves system performance, whereas traditional filters incur 2× slowdown from adversaries representing as low as 1% of the workload. Finally, we show that on skewed query workloads, the \sysname can reduce the false-positive rate 100× using negligible (1/1000th of a bit per item) space overhead. 

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3. Analysis of Robust Hybridized Discontinuous Galerkin Methods for Viscoacoustic Wave Equations

   https://doi.org/10.1007/s10915-025-02818-z  

   Lee, Jeonghun_J; Ruiz_Bolanos, Jesus_Indalecio (February 2025, Journal of Scientific Computing)

   Abstract In this paper we study hybridized discontinuous Galerkin methods for viscoacoustic wave equations with a general number of viscosity terms. For viscoacoustic equations rewritten as a first order symmetric hyperbolic system, we develop a hybridized local discontinuous Galerkin method which is robust for the number of viscosity terms. We show that the method satisfies a discrete energy estimate such that the implicit constants in the energy estimate are independent of the number of viscosity terms and the length of simulation time. Furthermore, we show that the sizes of reduced system after static condensation are independent of the number of viscosity terms. Optimal a priori error estimates with the Crank–Nicolson scheme are proved and numerical test results are included. 

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4. Interdisciplinary knowledge combinations and emerging technological topics: Implications for reducing uncertainties in research evaluation

   https://doi.org/10.1093/reseval/rvaa029  

   Kwon, Seokbeom; Youtie, Jan; Porter, Alan L (December 2020, Research Evaluation)

   null (Ed.)

   Abstract This article puts forth a new indicator of emerging technological topics as a tool for addressing challenges inherent in the evaluation of interdisciplinary research. We present this indicator and test its relationship with interdisciplinary and atypical research combinations. We perform this test by using metadata of scientific publications in three domains with different interdisciplinarity challenges: Nano-Enabled Drug Delivery, Synthetic Biology, and Autonomous Vehicles. Our analysis supports the connection between technological emergence and interdisciplinarity and atypicality in knowledge combinations. We further find that the contributions of interdisciplinary and atypical knowledge combinations to addressing emerging technological topics increase or stay constant over time. Implications for policymakers and contributions to the literature on interdisciplinarity and evaluation are provided. 

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5. Discontinuous Galerkin approximations to elliptic and parabolic problems with a Dirac line source

   https://doi.org/10.1051/m2an/2022095  

   Masri, Rami; Shen, Boqian; Riviere, Beatrice (March 2023, ESAIM: Mathematical Modelling and Numerical Analysis)

   The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence of the method by deriving a priori error estimates in the L 2 norm and in weighted energy norms. In addition, we prove almost optimal local error estimates in the energy norm for any approximation order. Further, almost optimal local error estimates in the L 2 norm are obtained for the case of piecewise linear approximations whereas suboptimal error bounds in the L 2 norm are shown for any polynomial degree. For the time-dependent case, convergence of semi-discrete and of backward Euler fully discrete scheme is established by proving error estimates in L 2 in time and in space. Numerical results for the elliptic problem are added to support the theoretical results. 

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