Meshfree modeling and analysis of physical fields in heterogeneous media Article

Tsukanov, I, Shapiro, V. (2005). Meshfree modeling and analysis of physical fields in heterogeneous media . Advances in Computational Mathematics, 23(1-2), 95-124. 10.1007/s10444-004-1835-3

cited authors

  • Tsukanov, I; Shapiro, V

abstract

  • Continuous and discrete variations in material properties lead to substantial difficulties for most mesh-based methods for modeling and analysis of physical fields. The meshfree method described in this paper relies on distance fields to boundaries and to material features in order to represent variations of material properties as well as to satisfy prescribed boundary conditions. The method is theoretically complete in the sense that all distributions of physical properties and all physical fields are represented by generalized Taylor series expansions in terms of powers of distance fields. We explain how such Taylor series can be used to construct solution structures - spaces of functions satisfying the prescribed boundary conditions exactly and containing the necessary degrees of freedom to satisfy additional constraints. Fully implemented numerical examples illustrate the effectiveness of the proposed approach. © Springer 2005.

authors

publication date

  • July 1, 2005

published in

Digital Object Identifier (DOI)

start page

  • 95

end page

  • 124

volume

  • 23

issue

  • 1-2