Yazar "Ganzha, Victor G." seçeneğine göre listele

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    Object oriented finite element calculations using maple
    (Selcuk University Research Center of Applied Mathematics, 2003) Chibisov, Dmytro; Ganzha, Victor G.; Zenger, Christoph
    Modern Computer Algebra Systems (CAS), such as Maple or Mathematica, with their symbolic facilities and visualization possibilities are powerful tools to design data structures and algorithms used in numerical simulation, with significantly lower costs compared to straightforward implementation in ''real'' programming languages, such as, for example, C or Java. The present paper shows how the CAS Maple can be used to design finite element software using linear and hierarchical bases. As a computational example the two-dimensional Poisson-equation with Dirichlet boundary conditions is presented.
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    Support operator method for Laplace equation on unstructured triangular grid
    (Selcuk University Research Center of Applied Mathematics, 2002) Ganzha, Victor G.; Liska, Richard; Shashkov, Mikhail; Zenger, Christoph
    A finite difference algorithm for solution of generalized Laplace equation on unstructured triangular grid is constructed by a support operator method. The support operator method first constructs discrete divergence operator from the divergence theorem and then constructs discrete gradient operator as the adjoint operator of the divergence. The adjointness of the operators is based on the continuum Green formulas which remain valid also for discrete operators. Developed method is exact for linear solution and has second order convergence rate. It is working well for discontinuous diffusion coefficient and very rough or very distorted grids which appear quite often e.~g. in Lagrangian simulations. Being formulated on the unstructured grid the method can be used on the region of arbitrary geometry shape. Numerical results confirm these properties of the developed method.