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Computational Modeling: History
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Contributor: Jack Zhong

Computational modeling is the use of a mathematical description of a system, solved numerically on a computer, to predict behaviour that has not been measured. A model is built by choosing the governing equations, the constitutive laws and the geometry, and then discretising them; the finite element method turns a continuum boundary-value problem into a large algebraic system, and automating that step has long been the route to coupling design with analysis [1]. The parameters fed into the model matter as much as the equations: a finite element simulation of a cutting or forming operation is only as good as the flow stress and the friction model it is given [2]. At the atomic scale, molecular dynamics integrates the equations of motion for an ensemble of particles and yields diffusion coefficients, melting temperatures and mechanical response, with the accuracy of a computed melting point depending on the method used to locate it [3]. The accessible time and size are limited by the cost of evaluating the interactions, so faster algorithms for the long-range forces continue to be developed [4]. Electronic-structure calculation supplies parameters that the coarser models need, and linking the scales while tracking how input uncertainty reaches the prediction is still the central difficulty [5].

  • finite element method
  • molecular dynamics
  • multiscale modeling
  • numerical simulation
  • uncertainty

Mathematical and Computational Methods·Modeling and Simulation·Mathematics·Physical Sciences

References

  1. Shephard, M.S.; Yerry, M.A.; Toward automated finite element modeling for the unification of engineering design and analysis. Finite Elements in Analysis and Design 1986, 2, 143-160, 10.1016/0168-874x(86)90014-4.
  2. Sartkulvanich, P.; Altan, T.; Gocmen, A.; Effects of flow stress and friction models in finite element simulation of orthogonal cutting: a sensitivity analysis. Machining Science and Technology 2005, 9, 1-26, 10.1081/mst-200051211.
  3. Zou, Y.; Xiang, S.; Dai, C.; Investigation on the efficiency and accuracy of methods for calculating melting temperature by molecular dynamics simulation. Computational Materials Science 2020, 171, 109156, 10.1016/j.commatsci.2019.109156.
  4. Kurzak, J.; Pettitt, B.M.; Fast multipole methods for particle dynamics. Molecular Simulation 2006, 32, 775-790, 10.1080/08927020600991161.
  5. Ghosh, S.K.; Density functional theory and multiscale materials modeling. Bulletin of Materials Science 2003, 26, 3-12, 10.1007/bf02712781.
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