In this paper we revisit the cells-and-portals visibility methods, originally developed for the special case of architectural interiors. We define an effectiveness measure for a cells-and-portals partition, and introduce ...

The modern group analysis of differential equations is used to study a class of two-dimensional variable coefficient Burgers equations. The group classification of this class is performed. Equivalence transformations are ...

We study the reconstruction of the missing thermal and mechanical fields on an inaccessible part of the boundary for two-dimensional linear isotropic thermoelastic materials from over-prescribed noisy (Cauchy) data on the ...

We consider the numerical approximation of the boundary and internal thermoelastic fields in the case of two-dimensional isotropic linear thermoelastic solids by combining the method of fundamental solutions (MFS) with the ...

We consider the most general two dimensional linear parabolic equations. Motivated by the recent work of Ibragimov et al. [1-3] we construct differential invariants, semi-invariants and invariant equations. These results ...

The Singular Function Boundary Integral Method (SFBIM) for solving two-dimensional elliptic problems with boundary singularities is revisited. In this method the solution is approximated by the leading terms of the asymptotic ...

The time-dependent, compressible extrusion of a Carreau fluid is solved over the reservoir-die-extrudate region using finite elements in space and a fully implicit scheme in time. A nonmonotonic slip law based on experimental ...