Displaying similar documents to “Geometric Aspects of the Space of Triangulations”

Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations

Siddhartha Mishra, Eitan Tadmor (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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We design efficient numerical schemes for approximating the MHD equations in multi-dimensions. Numerical approximations must be able to deal with the complex wave structure of the MHD equations and the divergence constraint. We propose schemes based on the genuinely multi-dimensional (GMD) framework of [S. Mishra and E. Tadmor, (2010) 688–710; S. Mishra and E. Tadmor, (2011) 1023–1045]. The schemes are formulated in terms of . A suitable choice of the...

Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for MHD equations

Siddhartha Mishra, Eitan Tadmor (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We design efficient numerical schemes for approximating the MHD equations in multi-dimensions. Numerical approximations must be able to deal with the complex wave structure of the MHD equations and the divergence constraint. We propose schemes based on the genuinely multi-dimensional (GMD) framework of [S. Mishra and E. Tadmor, (2010) 688–710; S. Mishra and E. Tadmor, (2011) 1023–1045]. The schemes are formulated in terms of . A suitable choice of the...

The discrete compactness property for anisotropic edge elements on polyhedral domains

Ariel Luis Lombardi (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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We prove the discrete compactness property of the edge elements of any order on a class of anisotropically refined meshes on polyhedral domains. The meshes, made up of tetrahedra, have been introduced in [Th. Apel and S. Nicaise, (1998) 519–549]. They are appropriately graded near singular corners and edges of the polyhedron.

The mixed regularity of electronic wave functions multiplied by explicit correlation factors

Harry Yserentant (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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The electronic Schrödinger equation describes the motion of electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3 variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, , Springer (2010)], the regularity of the solutions, which increases with the number of electrons,...

The geometry of dimer models

David Cimasoni (2014)

Winter Braids Lecture Notes

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This is an expanded version of a three-hour minicourse given at the winterschool held in Dijon in February 2014. The aim of these lectures was to present some aspects of the dimer model to a geometrically minded audience. We spoke neither of braids nor of knots, but tried to show how several geometric tools that we know and love (e.g. (co)homology, spin structures, real algebraic curves) can be applied to very natural problems in combinatorics and statistical physics. These lecture...

Convergence of gradient-based algorithms for the Hartree-Fock equations

Antoine Levitt (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large- result of [M. Griesemer and F. Hantsch, (2011) 170]. In this paper, we prove...