| 초록 |
In the well-established area of self-consistent mean field theory, the partition functions are evaluated by numerically solving the modified diffusion equation, but many numerical methods are known to have problems in keeping the amount of polymer materials in the system. For the purpose of checking material conservation of various numerical algorithms, we develop an algebraic method using matrix and bra-ket notation, which traces the symmetry of the product of the volume and evolution matrices. Algebraic tests reveal that when Crank-Nicolson method is adopted, finite volume method (FVM) is the only way to conserve material perfectly in the cylindrical and spherical coordinate systems. Alternating direction implicit method combined with FVM cannot conserve material, though it is still a good candidate after considering speed and accuracy simultaneously. I also confirm that in the Cartesian coordinate system, the widely used pseudospectral method has the ability to conserve material. |
