Burgisser, F. James et S. Person in charge for the code development: C. Main developer: O. It solves a coupled system of two non-linear differential equations and a diffusion equation, modeling the growth of a single gas bubble in a viscous fluid and undergoing decompression and diffusion exsolution. This package for the R statistical software , provides a set of functions for analyzing a variety of finite mixture models.
Person in charge for the code development: D.
Main developers: D. Young, D.
Umashankar , B. Pergamon, Macmillan, New York, Buffa and S. Personalised recommendations. Google Scholar  V. Dauge , Singularities of Electromagnetic Fields?? The stress singularities and invariant integrals", Prikl.
Chauveau , D. Hunter Penn State. Solution for the Ficheras corner for homogeneous material top and for a bimaterial joint bottom. The reference solution small circles is Reference . In both cases the exponents are real in the whole --range. However, the parameter study shows a strong change in the gradient of the solution in this point, which is not typical for such problems. Moreover, it is clear that, if logarithmical terms are present, the true solution is slightly more singular than the numerical approximation.
As a consequence, to give an answer to the above question further investigations are necessary. The procedure is based on the Arnoldi method and uses the classical advantages of iterative techniques for large sparse systems—fast solutions with minimum hardware requirements. For large systems the required storage can be reduced using a preconditioned CG-method for the solution of a linear system, which have to be solved on each Arnoldi step.
For smaller systems the best strategy is to use one direct LU factorization in combination with multiple back-substitutions instead of the CG-method, so that a size-optimized strategy can be used, depending on the problem. With this solution technique several real-3D-problems were investigated.
In most cases a comparison with known solutions was possible only for special geometries or materials, because full parameter studies are quite rare in the literature. Kondratiev VA. Boundary problems for elliptic equations in domains with conical or angular points. Transactions of Moscow Mathematical Society ; — Leguillon D, Sanchez-Palencia E. Masson, Wiley: Paris, Dauge M.
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Randwertproblem der Elastizit5atstheorie f5ur Polyeder-Singularit5aten und Approximation mit Randelementmethoden. Thesis, Technische Hochschule Darmstadt, Williams ML. Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics ; — NoordhoD: Leiden, Singularities of rotationally symmetric solutions of boundary value problems for the LamUe equations.
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Nonlinear eigenvalue problems: A challenge for modern eigenvalue methods. By Heinrich Voss. Arding , Dirichlet's problem for linear elliptic partial differential equations. Geis, G. Mishuris, and A.
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