Browsing by Subject "3-D boundary-value problem"

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  • Publication
    ON MATHEMATICAL MODELLING OF METALS DISTRIBUTION IN PEAT LAYERS
    (2014)
    Kangro, Ilmārs 
    ;
    Harijs Kalis
    ;
    Aigars Gedroics
    ;
    Teirumnieka, Ērika 
    ;
    Teirumnieks, Edmunds 
    In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in multilayered domain. We consider the metals Fe and Ca concentration in the layered peat blocks. Using experimental data the mathematical model for calculation of concentration of metals in different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations (PDEs) of second order with piece-wise diffusion coefficients in the layered domain. We develop here a finite-difference method for solving of a problem of one, two and three peat blocks with periodical boundary condition in x direction. This procedure allows to reduce the 3-D problem to a system of 2-D problems by using circulant matrix.
    Scopus© Citations 7
  • Publication
    THE MATHEMATICAL MODELING OF METALS CONTENT IN PEAT
    (2009)
    Teirumnieks, Edmunds 
    ;
    Harijs Kalis
    ;
    Teirumnieka, Ērika 
    ;
    Kangro, Ilmārs 
    Metals deposition in peat can aid to evaluate impact of atmospheric or wastewaters pollution and thus can be a good indicator of recent and historical changes in the pollution loading. For peat using in agriculture, industrial, heat production etc. knowledge of peat metals content is important. Experimental determination of metals in peat is very long and expensive work. Using experimental data the mathematical model for calculation of concentrations of metals in different points for different layers is developed. The values of the metals (Ca, Mg, Fe, Sr, Cu, Zn, Mn, Pb, Cr, Ni, Se, Co, Cd, V, Mo) concentrations in different layers in peat taken from Knavu peat bog from four sites are determined using inductively coupled plasma optical emission spectrometer. Mathematical model for calculation of concentrations of metal has been described in the paper. As an example, mathematical models for calculation of Pb concentrations have been analyzed.
    Scopus© Citations 1