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A least-squares method with direct minimization for the solution of the breakage–coalescence population balance equation

Author

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  • Zhu, Zhengjie
  • Dorao, C.A.
  • Jakobsen, H.A.

Abstract

A least-squares method with a direct minimization algorithm is introduced to solve the non-linear population balance equation that consists of both breakage and coalescence terms. The least-squares solver, direct minimization solver together with a finite difference solver are implemented for comparisons. It is shown that the coalescence term introduces a strong non-linear behavior which can affect the robustness of the numerical solvers. In the comparison with the least-squares method, the direct minimization method is proved to be capable of producing equally accurate results, while its formulation is better conditioned. In the case of a non-linear population balance equation system, the direct minimization method converges faster than the standard least-squares method.

Suggested Citation

  • Zhu, Zhengjie & Dorao, C.A. & Jakobsen, H.A., 2008. "A least-squares method with direct minimization for the solution of the breakage–coalescence population balance equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 716-727.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:3:p:716-727
    DOI: 10.1016/j.matcom.2008.05.001
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    Cited by:

    1. Rogolino, P. & Cimmelli, V.A., 2020. "Fitting thermal conductivity and optimizing thermoelectric efficiency in SicGe1−c nanowires," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 279-291.

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