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