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Advanced Numerical Methods in the Mathematical Sciences

Yingwei Wang, Purdue University
Efficient Spectral Galerkin Methods for Electronic Structure Calculations


Two efficient spectral Galerkin methods, based on Legendre and Laguerre polynomials, respectively, are derived for direct discretization of the electronic Schrödinger equation in one spatial dimension. In order to treat the singularity in the Coulomb potentials, the set of basis functions is composed of orthogonal polynomials in subdomains and a joint function in the global domain. Sparse grid spectral methods based on hyperbolic cross approximations are employed for treating high-dimensional problems. With the help of Slater determinant, the basis functions are constructed to obey the antisymmetry relations of the fermionic wavefunctions. Numerical tests show the efficiency and accuracy of our methods.