A general method is given for constructing sets of sufficient linear conditions that ensure convexity of a polynomial in Bernstein–Bézier form on a triangle. Using the linear conditions, computational methods based on macro-element spline spaces are developed to construct convexity preserving splines over triangulations that interpolate or approximate given scattered data.

We develop stable splitting of the minimal determining sets for the spaces of bivariate C splines on triangulations, including a modified Argyris space, Clough-Tocher, Powell-Sabin and quadrilateral macro-element spaces. This leads to the stable splitting of the corresponding bases as required in Böhmer’s method for solving fully nonlinear elliptic PDEs on polygonal domains.

We propose a parametric tensioned version of the FVS macro-element to control the shape of the composite surface and remove artificial oscillations, bumps and other undesired behaviour. In particular, this approach is applied to C1 cubic spline surfaces over a four-directional mesh produced by two-stage scattered data fitting methods.

Ductile fracture modeling still has to be improved at the macro and microscales. New numerical methods are applied to the limit analysis of cells containing one or several voids or void clusters. The results are compared with existing macroscopic models. Voids can also be introduced in analytical polycrystalline models, in order to combine plastic anisotropy and texture evolution with ductile f...

The presented study is motivated by the development of methods, algorithms, and software tools for μFE (micro finite element) simulation of human bones. The voxel representation of the bone microstructure is obtained from a high resolution computer tomography (CT) image. The considered numerical homogenization problem concerns isotropic linear elasticity models at micro and macro levels.

A UK-based grid computing project that merges two earthquake data modeling methods is one of the latest tools in earthquake prediction. The new technique provides a 2D data map of tectonic structures by combining a macro modeling method based on surface deformation measurements from satellite imagery with a micro method based on finite element analysis and simulation within local geophysical co...

The semantics of the times macro is given in [2] only for the case when the body of the macro is parahalting. We remedy this by defining a new times macro instruction in terms of while (see [9, 13]). The semantics of the new times macro is given in a way analogous to the semantics of while macros. The new times uses an anonymous variable to control the number of its executions. We present two e...

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This paper examines the blood chamber of a left ventricular assist device (LVAD) under static loading conditions and standard operating temperatures. The LVAD’s walls are made of a temperature-sensitive polymer (ChronoFlex C 55D) and are covered with a titanium nitride (TiN) nano-coating (deposited by laser ablation) to improve their haemocompatibility. A loss of cohesion may be observed near t...