Abstract
Numerical simulations based on partial differential equations are applied to different knowledge areas. There was a motivation for the use of computational tools to perform real and numerical simulations, however many of these are restricted to a software installation and limiting processing, mainly in mobile devices. The aim of this study was to develop a web system which is able to solve real problems involving partial differential equations in 2D generalized coordinates, by the finite difference discretization. The system consists of web service for client-server communication, a database, a module of processing calculation (back-end) and a graphical user interface (front-end). The system can be executed on devices regardless their performance, such as personal computers and mobile devices, since the calculations are made on a remote server. The contribution is the availability of a web architecture for including other types of differential equations and consequently, for real problems and situations, such as energy conduction and pollutant transportation.
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References
Tonti, E.: Why starting from differential equations for computational physics? Journal of Computational Physics 257, 1260–1290 (2014)
Romeiro, N.M., Castro, R.G., Cirilo, E.R., Natti, P.L.: Local calibration of coliforms parameters of water quality problem at Igapó I Lake, Londrina, Paraná, Brazil. Ecological Modelling 222(11), 1888–1896 (2011)
Gupta, P.K., Singh, J., Rai, K., Rai, S.: Solution of the heat transfer problem in tissues during hyperthermia by finite difference-decomposition method. Applied Mathematics and Computation 219(12), 6882–6892 (2013)
Reimer, A.S., Cheviakov, A.F.: A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions. Computer Physics Communications 184(3), 783–798 (2013)
Grande, A., Gonzalez, O., Pereda, J.A., Vegas, A.: Educational Computer Simulations for Visualizing and Understanding the Interaction of Electromagnetic Waves with Metamaterials. In: IEEE EDUCON Education Engineering, vol. (1), pp. 543–547 (2010)
Dumont, C., Mourlin, F.: A Mobile Computing Architecture for Numerical Simulation. In: International Conference on Mobile Ubiquitous Computing, Systems, Services and Technologies (UBICOMM 2007), pp. 68–74. IEEE (November 2007)
Weng, W.C.: Web-based post-processing visualization system for finite element analysis. Advances in Engineering Software 42(6), 398–407 (2011)
Isbasoiu, E.C.: Numerical Calculation, Web Services and Principles for Physics Applications. In: 2010 Fourth UKSim European Symposium on Computer Modeling and Simulation, pp. 387–390. IEEE (November 2010)
Walker, J.D., Chapra, S.C.: A client-side web application for interactive environmental simulation modeling. Environmental Modelling & Software 55, 49–60 (2014)
Wriedt, T.: Mie theory 1908, on the mobile phone 2008. Journal of Quantitative Spectroscopy and Radiative Transfer 109(8), 1543–1548 (2008)
Matsunaga, F.T., Vilas Boas, J.L., Romeiro, N.M.L., Brancher, J.D.: CloudPDE: a web solver of differential equations by finite difference discretization. In: IADIS - International Conference on Applied Computing (prelo). (2013)
Cirilo, E.R., Bortoli, A.L.D.: Cubic Splines for Trachea and Bronchial Tubes Grid Generation. Semina: Ciências Exatas e Tecnológicas 27, 147–155 (2006)
da Silva, W.P., Precker, J.W., Silva, D.D., Silva, C.D., de Lima, A.G.B.: Numerical simulation of diffusive processes in solids of revolution via the finite volume method and generalized coordinates. International Journal of Heat and Mass Transfer 52(21-22), 4976–4985 (2009)
Maliska, C.R.: Transferência de Calor e Mecânica dos Fluidos Computacional, 2a edn. Editora Livros Técnicos e Científicos Editora, Rio de Janeiro (2004)
Romeiro, N.M.L., Cirilo, E.R., Natti, P.L.: Estudo do escoamento e da dispersão de poluentes na superfície do Lago Igapó I. In: Anais do II Seminário Nacional sobre Regeneração Ambiental de Cidades - Águas Urbanas II, pp. 1–17 (2007)
Russell, M., Probert, S.: FDiff3: a finite-difference solver for facilitating understanding of heat conduction and numerical analysis. Applied Energy 79(4), 443–456 (2004)
Weibe, A.Y., Huisinga, W.: Error-controlled global sensitivity analysis of ordinary differential equations. Journal of Computational Physics 230(17), 6824–6842 (2011)
Singh, V., Dubey, R., Panigrahi, P.K., Muralidhar, K.: An educational website on interferometry. In: 2012 IEEE International Conference on Technology Enhanced Education (ICTEE), pp. 1–10 (January 2012)
Perus, I., Klinc, R., Dolenc, M., Dolsek, M.: A web-based methodology for the prediction of approximate IDA curves. Earthquake Engineering & Structural Dynamics 42(April 2012), 43–60 (2013)
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Matsunaga, F.T., Boas, J.L.V., Romeiro, N.M.L., Toda, A.M., Brancher, J.D. (2014). A Web System for Solving Real Problems Involving Partial Differential Equations in Generalized Coordinates. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8584. Springer, Cham. https://doi.org/10.1007/978-3-319-09153-2_50
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DOI: https://doi.org/10.1007/978-3-319-09153-2_50
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