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- ItemMultiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods(Amsterdam [u.a.] : Elsevier Science, 1995) Hughes, Thomas J. R.An approach is developed for deriving variational methods capable of representing multiscale phenomena. The ideas are first illustrated on the exterior problem for the Helmholtz equation. This leads to the well-known Dirichlet-to-Neumann formulation. Next, a class of subgrid scale models is developed and the relationships to 'bubble function' methods and stabilized methods are established. It is shown that both the latter methods are approximate subgrid scale models. The identification for stabilized methods leads to an analytical formula for τ, the 'intrinsic time scale', whose origins have been a mystery heretofore. © 1995.
- ItemImplementation of an adaptive BDF2 formula and comparison with the MATLAB Ode15s(Amsterdam [u.a.] : Elsevier, 2014) Celaya, E. Alberdi; Aguirrezabala, J. J. Anza; Chatzipantelidis, P.After applying the Finite Element Method (FEM) to the diffusion-type and wave-type Partial Differential Equations (PDEs), a first order and a second order Ordinary Differential Equation (ODE) systems are obtained respectively. These ODE systems usually present high stiffness, so numerical methods with good stability properties are required in their resolution. MATLAB offers a set of open source adaptive step functions for solving ODEs. One of these functions is the ode15s recommended to solve stiff problems and which is based on the Backward Differentiation Formulae (BDF). We describe the error estimation and the step size control implemented in this function. The ode15s is a variable order algorithm, and even though it has an adaptive step size implementation, the advancing formula and the local error estimation that uses correspond to the constant step size formula. We have focused on the second order accurate and unconditionally stable BDF (BDF2) and we have implemented a real adaptive step size BDF2 algorithm using the same strategy as the BDF2 implemented in the ode15s, resulting the new algorithm more efficient than the one implemented in MATLAB. © The Authors. Published by Elsevier B.V.
- ItemThe finite volume-complete flux scheme for advection-diffusion-reaction equations(New York, NY [u.a.] : Springer Science + Business Media B.V., 2010) ten Thije Boonkkamp, J. H. M.; Anthonissen, M. J. H.We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional advection-diffusion-reaction equation, which is derived from the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying suitable quadrature rules to the integral representation gives the complete flux scheme. Extensions of the complete flux scheme to two-dimensional and time-dependent problems are derived, containing the cross flux term or the time derivative in the inhomogeneous flux, respectively. The resulting finite volume-complete flux scheme is validated for several test problems. © 2010 The Author(s).
- ItemThe systems biology format converter(London : BioMed Central, 2016) Rodriguez, Nicolas; Pettit, Jean-Baptiste; Dalle Pezze, Piero; Li, Lu; Henry, Arnaud; van Iersel, Martijn P.; Jalowicki, Gael; Kutmon, Martina; Natarajan, Kedar N.; Tolnay, David; Stefan, Melanie I.; Evelo, Chris T.; Le Novère, NicolasBackground: Interoperability between formats is a recurring problem in systems biology research. Many tools have been developed to convert computational models from one format to another. However, they have been developed independently, resulting in redundancy of efforts and lack of synergy. Results: Here we present the System Biology Format Converter (SBFC), which provide a generic framework to potentially convert any format into another. The framework currently includes several converters translating between the following formats: SBML, BioPAX, SBGN-ML, Matlab, Octave, XPP, GPML, Dot, MDL and APM. This software is written in Java and can be used as a standalone executable or web service. Conclusions: The SBFC framework is an evolving software project. Existing converters can be used and improved, and new converters can be easily added, making SBFC useful to both modellers and developers. The source code and documentation of the framework are freely available from the project web site.
- ItemThe Design of a Python Library for the Automatic Definition and Simulation of Transient Ionization Fronts(New York, NY : IEEE, 2023) Wong, Timothy; Timoshkin, Igor; MacGregor, Scott; Wilson, Mark; Given, MartinIn recent years, the interest in nonthermal plasma dynamics has grown significantly, within both industry and research. This has been driven by the development of several novel cold plasma technologies across a wide range of different fields, for example, for plasma medicine, chemical processing, pollution control, and surface treatment. The optimization of these technologies relies heavily upon the understanding of gas discharge plasmas: their generation, electrical characteristics, and interaction with their surroundings. Moreover, the manifestation of nonthermal plasmas in the form of streamers is of high relevance and critical importance to high voltage insulation technology, and has further significance to geophysical research concerning atmospheric discharges. The present work describes the development of the StrAFE (Streamers on Adaptive Finite Elements) package, a dedicated Python library built atop the popular open-source FEniCS finite element software, designed with the objective to simplify and to automate the solution of ionization front models. The library features support for mesh adaptivity, distributed memory parallelism, and an intuitive programming interface, while providing an exceptionally high level of user configurability. This article presents the software implementation, describes its features, and presents several code verification studies performed within simple and complex domains. It is concluded that the numerical results gained from this open-source framework are comparable to other well-established software in terms of accuracy. Therefore, it further demonstrates the great potential for open-source software to make significant contributions to technologies involving nonthermal plasmas, ionization fronts, and gas discharges.