131,131 research outputs found

    A Second-Order Formulation of Non-Termination

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    We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is generally undecidable. However, by restricting the language to known decidable cases, we exhibit new classes of loops, the non-termination of which is decidable. We present a bunch of examples.Comment: 8 page

    Application of edge-based finite elements and vector ABCs in 3D scattering

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    A finite element absorbing boundary condition (FE-ABC) solution of the scattering by arbitrary 3-D structures is considered. The computational domain is discretized using edge-based tetrahedral elements. In contrast to the node-based elements, edge elements can treat geometries with sharp edges, are divergence-less, and easily satisfy the field continuity condition across dielectric interfaces. They do, however, lead to a higher unknown count but this is balanced by the greater sparsity of the resulting finite element matrix. Thus, the computation time required to solve such a system iteratively with a given degree of accuracy is less than the traditional node-based approach. The purpose is to examine the derivation and performance of the ABC's when applied to 2-D and 3-D problems and to discuss the specifics of our FE-ABC implementation

    Numerical Methods for a Nonlinear BVP Arising in Physical Oceanography

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    In this paper we report and compare the numerical results for an ocean circulation model obtained by the classical truncated boundary formulation, the free boundary approach and a quasi-uniform grid treatment of the problem. We apply a shooting method to the truncated boundary formulation and finite difference methods to both the free boundary approach and the quasi-uniform grid treatment. Using the shooting method, supplemented by the Newton's iterations, we show that the ocean circulation model cannot be considered as a simple test case. In fact, for this method we are forced to use as initial iterate a value close to the correct missing initial condition in order to be able to get a convergent numerical solution. The reported numerical results allow us to point out how the finite difference method with a quasi-uniform grid is the less demanding approach and that the free boundary approach provides a more reliable formulation than the classical truncated boundary formulation.Comment: 25 pages, 12 figures, 5 table
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