Download Artificial Intelligence and Symbolic Mathematical Computing: by J. Calmet, J. A. Campbell (auth.), Jacques Calmet, John A. PDF

By J. Calmet, J. A. Campbell (auth.), Jacques Calmet, John A. Campbell (eds.)

This quantity comprises the papers, up-to-date at times, offered on the first AISMC (Artificial Intelligence and Symbolic Mathematical Computations)conference, held in Karlsruhe, August 3-6, 1992. This used to be the 1st convention to be dedicated to this sort of subject after a protracted interval whilst SMC made no visual appeal in AI meetings, notwithstanding it was once welcome within the early days of AI. a few meetings have been held lately on arithmetic and AI, yet none used to be at once similar in scope to this convention. end result of the novelty of the area, authors got longer allocations of time than ordinary within which to offer their paintings. accordingly, prolonged and fruitful discussions every one paper. The introductory bankruptcy during this ebook, which used to be now not provided throughout the convention, displays in lots of methods the flavour of those discussions and goals to set out the framework for destiny actions during this area of analysis. as well as the creation, the quantity comprises 20 papers.

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Extra info for Artificial Intelligence and Symbolic Mathematical Computing: International Conference AISMC-1 Karlsruhe, Germany, August 3–6, 1992 Proceedings

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Badia et al. − t∈Tjh VΔt 3 3 θc (xΔt ;q )σ (xΔt ;q ), ∇uh (xΔt ;q ) : ∇wjh (xΔt ;q ) q=1 θα,β fα,β · wjh (xα ) + =− t∈Tjh α∈Nj β∈Nα 3 VΔt θc (xΔt ;q )f e (xΔt ;q ) 3 q=1 − θα fαe · wjh (xα ) · wjh (xΔt ;q ) for j ∈ Sb . α∈Nj In 3D, one cannot use mid-face or mid-edge quadrature rules as one can in 1D and 2D, even for uncoupled continuum problems. Instead, one must use rules for which at least some of the quadrature points are in the interior of tetrahedra. Other than this, the development of a fully discretized method follows the same process as in the 2D case.

In many practical settings, the domain Ωb is a rectangle in 2D or is a rectangular parallelepiped in 3D. In such cases, one may simply choose θc (x) in the bridge region to be the tensor product of global 1D polynomials connecting the atomistic and continuum regions across the bridge region. One could choose linear polynomials in each direction such that their values are zero at the bridge/atomistic region interface and one at the bridge/continuum region interface. If one wishes to have a smoother transition from the atomistic to the bridge to the continuum regions, one can choose cubic polynomials in each direction such that they have zero value and zero derivative at the bridge/atomisitic region interface and value one and zero derivative at the bridge/continuum region interface.

A discretization technique based on central differences followed by Crank-Nicolson time-stepping is used in the advection-diffusion part. The non-linear chemical reactions are treated by the robust Backward Euler Formula. The performance of the combined numerical method (splitting procedure + numerical algorithms used in the advection-diffusion part and in the chemical part) is studied in connection with six test-problems. We are interested in both the accuracy of the results and the efficiency of the parallel computations.

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