Mapping between local and global coordinates is an important issue in finite element method, as all calculations are performed in local coordinates. The concern arises when subparametric are used, in which the shape functions of the field variable and the geometry of the element are not the same. This is particularly the case for * C elements in which the extra degrees of freedoms added to the ...

We consider linear algebraic equations, where the elements of the matrix and of the right-hand side vector are linear functions of interval parameters, and their parametric AE-solution sets, which are defined by universal and existential quantifiers for the parameters. We present how some sufficient conditions for a parametric AE-solution set to have linear boundary can be exploited for obtaini...

Mathematical concepts of multivariate parametric solids, their description by a B-spline basis functions are discussed. Parametric solids can model both the shape and unisotropic interior. Three types of parametric solids i.e. Coons body 0, 1 and 2 are used to demonstrate the interior modelling often used as initial or boundary conditions in numerical simulation. Multiple parametric solids elem...

This paper concerns semiparametric regression models with additive nonparametric components and high dimensional parametric components under sparsity assumptions. To achieve simultaneous model selection for both nonparametric and parametric parts, we introduce a penalty that combines the adaptive empirical L2-norms of the nonparametric component functions and the SCAD penalty on the coefficient...