The discrete model so defined is usually inserted into a prototype code, often by using again an algebraic manipulator but the use of compiled programming languages is also possible if not common.
MATLAB® is certainly one of the state-of-the-art mathematical softwares available for performing numeric or symbolic analyses, but it is not the only one and a quite long list, see, of packages offering very similar features is available. This phase is characterised by the evaluation and the analysis of these operators through an algebraic manipulator such as MATLAB®. For example, in the case of the analysis of solid mechanics problems by FEM, important discrete operators are the mechanical response vector of the finite element and its tangent stiffness matrix. This operation leads to the identification of the needed discrete operators which define the computational model. The most popular technique is the Finite Element Method (FEM), see, but now the number of computational approximation techniques is very large and a synthetic summary can be tried only by citing some of these less conventional methods: mixed finite element methods partition of unity-based discontinuous finite elements meshless methods discontinuous Galerkin methods.
The subsequent step is the introduction of a numerical approximation technique. At present time the definition of a mathematical model is at the basis of any serious attempt to obtain previsions in any engineering application, but not only in the engineering field. The typical starting point is the formulation of a mathematical model where the main physical or real world phenomena to be described are established.
The developing of finite element formulations, standard or new ones, requires a lengthy process which involves several steps.
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