Teirumnieka, Ērika

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Teirumnieka, Ērika
Official Name
Teirumnieka, Ērika
Alternative Name
Ērika Teirumnieka
Erika Teirumnieka
Teirumnieka, Erika
Main Affiliation
Email
erika.teirumnieka@rta.lv
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Scopus Author ID
56323862400
Researcher ID
EBG-0589-2022

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  • Publication
    SPECIAL SPLINE APPROXIMATION FOR THE SOLUTION OF THE NON-STATIONARY 3-D MASS TRANSFER PROBLEM
    (2021)
    Kangro, Ilmārs 
    ;
    Harijs Kalis
    ;
    Teirumnieks, Edmunds 
    ;
    Teirumnieka, Ērika 
    In this paper we consider the conservative averaging method (CAM) with special spline approximation for solving the non-stationary 3-D mass transfer problem. The special hyperbolic type spline, which interpolates the middle integral values of piece-wise smooth function is used. With the help of these splines the initial-boundary value problem (IBVP) of mathematical physics in 3-D domain with respect to one coordinate is reduced to problems for system of equations in 2-D domain. This procedure allows reduce also the 2-D problem to a 1-D problem and thus the solution of the approximated problem can be obtained analytically. The accuracy of the approximated solution for the special 1-D IBVP is compared with the exact solution of the studied problem obtained with the Fourier series method. The numerical solution is compared with the spline solution. The above-mentioned method has extensive physical applications, related to mass and heat transfer problems in 3-D domains.
  • Publication
    SPECIAL HPERBOLIC TYPE APPROXIMATION FOR SOLVING OF 3-D TWO LAYER STATIONARY DIFFUSION PROBLEM
    (2019)
    Kangro, Ilmārs 
    ;
    Harijs Kalis
    ;
    Teirumnieka, Ērika 
    ;
    Teirumnieks, Edmunds 
    In this paper we examine the conservative averaging method (CAM) along the vertical z-coordinate for solving the 3-D boundary-value 2 layers diffusion problem. The special parabolic and hyperbolic type approximation (splines), that interpolate the middle integral values of piece-wise smooth function, is investigated. With the help of these splines the problems of mathematical physics in 3-D with respect to one coordinate are reduced to problems for system of equations in 2-D in every layer. This procedure allows reduce also the 2-D problem to a 1-D problem and the solution of the approximated problem can be obtained analytically. As the practical application of the created mathematical model, we are studying the calculation of the concentration of heavy metal calcium (Ca) in a two-layer peat block.
    Scopus© Citations 1
  • 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