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The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...
We present a new class of self-adaptive higher-order finite element methods (-FEM) which are free of analytical
error estimates and thus work equally well for virtually all PDE problems ranging from simple linear elliptic equations to complex time-dependent nonlinear multiphysics coupled problems. The methods do not contain any tuning parameters and work reliably with both
low- and high-order finite elements. The methodology was used to solve various types of problems including thermoelasticity,...
We present a sparse grid/hyperbolic cross discretization for many-particle problems.
It involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the associated series expansion then results in a sparse grid discretization.
Here, depending on the norms involved, different variants of sparse grid techniques for many-particle spaces can be derived
that, in the best case, result in complexities and error estimates which are independent of the number of particles.
Furthermore...
The paper is concerned with the measurement of scalar physical quantities at nodes on the -dimensional unit sphere surface in the -dimensional Euclidean space and the spherical RBF interpolation of the data obtained. In particular, we consider . We employ an inverse multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 defined in Cartesian coordinates. We prove the existence of the interpolation formula of the type considered. The formula can be useful...
The paper is concerned with spherical radial basis function (SRBF) interpolation. We introduce particular SRBF interpolants employing several different geodesic metrics and a single trend function. Interpolation on a sphere is an important tool serving to processing data measured on the Earth's surface by satellites. Nevertheless, our model physical quantity is the magnetic susceptibility of rock measured in different directions. We construct a general SRBF formula and prove conditions sufficient...
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