Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator
نویسندگان
چکیده
منابع مشابه
Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator
We design and analyze variational and non-variational multigrid algorithms for the Laplace-Beltrami operator on a smooth and closed surface. In both cases, a uniform convergence for the V -cycle algorithm is obtained provided the surface geometry is captured well enough by the coarsest grid. The main argument hinges on a perturbation analysis from an auxiliary variational algorithm defined dire...
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We design and analyze variational and non-variational multigrid algorithms for the Laplace-Beltrami operator on a smooth and closed surface. In both cases, a uniform convergence for the V -cycle algorithm is obtained provided the surface geometry is captured well enough by the coarsest grid. The main argument hinges on a perturbation analysis from an auxiliary variational algorithm defined dire...
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We present a new AFEM for the Laplace-Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W 1 ∞ and piecewise in a suitable Besov class embedded in C1,α with α ∈ (0, 1]. The idea is to have the surface sufficiently well resolved in W 1 ∞ relative to the current resolution of the PDE in H1. This gives rise to a conditional contraction property of the PDE...
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We introduce a Laplace-Beltrami type operator on the Fock space of symmetric functions and show that the Jack symmetric functions are the only family of eigenvectors of the differential operator, thus giving a new characterization of Jack polynomials. This was achieved by explicit computation of its action on generalized homogeneous symmetric functions. Using this new method we give a combinato...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2012
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2011-02551-2