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  • 1
    Electronic Resource
    Electronic Resource
    Mixed explicit-implicit iterative finite element scheme for diffusion-type problems: II. Solution strategy and examples (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 325-344 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I1 of this paper we have established local stability and convergence criteria for the mixed explicit-implicit finite element scheme and have shown that the proposed iterative method converges under certain conditions. Part II describes various practical aspects of the solution strategy such as convergence criteria for terminating the iterations, automatic control of time step size, reclassification of nodes from explicit to implicit during execution, estimation of time derivatives, and automatic adjustment of the implicit weight factor. Several examples are included to demonstrate certain aspects of the theory and illustrate the capabilities of the new approach.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110208
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  • 2
    Electronic Resource
    Electronic Resource
    Mixed explicit-implicit iterative finite element scheme for diffusion-type problems: I. Theory (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 309-323 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Galerkin finite element formulation of diffusion processes based on a diagonal capacity matrix is analysed from the standpoint of local stability and convergence. The theoretical analysis assumes that the conductance matrix is locally diagonally dominant, and it is shown that one can always construct a finite element network of linear triangles satisfying this condition. Time derivatives are replaced by finite differences, leading to a mixed explicit-implicit system of algebraic equations which can be efficiently solved by a point iterative technique. In this work the accelerated point iterative method is adopted and is shown to converge when the conductance matrix is locally diagonally dominant. Several examples are included in Part II of this paper to demonstrate the efficiency of the new approach.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110207
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    Paper (German National Licenses)
    Fulltext
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