Related papers: Molecular spectra calculations using an optimized …
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop…
We apply a recently developed quasiparticle self-consistent $GW$ method (QSGW) to Gd, Er, EuN, GdN, ErAs, YbN and GdAs. We show that QSGW combines advantages separately found in conventional $GW$ and LDA+$U$ theory, in a simple and fully…
Rue and Held (2005) proposed a method for efficiently computing the Gaussian likelihood for stationary Markov random field models, when the data locations fall on a complete regular grid, and the model has no additive error term. The…
A Continuous Galerkin method-based approach is presented to compute the seismic normal modes of rotating planets. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core using a polynomial…
We present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions,…
A new approach to large-scale nuclear structure calculations, based on the Density Matrix Renormalization Group (DMRG), is described. The method is tested in the context of a problem involving many identical nucleons constrained to move in…
We present a novel formulation of the vibrational density matrix renormalization group (vDMRG) algorithm tailored to strongly anharmonic molecules described by general high-dimensional model representations of potential energy surfaces. For…
We present a subspace projection technique to conduct large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization. The proposed method treats both metallic and insulating materials in a single…
We study the intermediate statistics of the spectrum of quasi-energies and of the eigenfunctions in the kicked rotator, in the case when the corresponding system is fully chaotic while quantally localized. As for the eigenphases, we find…
This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical…
Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. However, the unfavorable scaling and the resulting high computational cost…
This work is concerned with the construction of Gaussian Beam (GB) solutions for the numerical approximation of wave equations, semi-discretized in space by finite difference schemes. GB are high-frequency solutions whose propagation can be…
We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This…
Most numerical schemes proposed for solving BGK models for rarefied gas dynamics are based on the discrete velocity approximation. Since such approach uses fixed velocity grids, one must secure a sufficiently large domain with fine velocity…
We present the second-order multidimensional Staggered Grid Hydrodynamics Residual Distribution (SGH RD) scheme for Lagrangian hydrodynamics. The SGH RD scheme is based on the staggered finite element discretizations as in [Dobrev et al.,…
This paper is devoted to the study of generalized subdifferentials of spectral functions over Euclidean Jordan algebras. Spectral functions appear often in optimization problems playing the role of "regularizer", "barrier", "penalty…
We describe a method for imposing the correct electron-nucleus (e-n) cusp in molecular orbitals expanded as a linear combination of (cuspless) Gaussian basis functions. Enforcing the e-n cusp in trial wave functions is an important asset in…
We study linear spectral statistics of high dimensional sample covariance matrices in a regime where the empirical spectral distribution remains governed by the classical sample covariance law but the fluctuation theory is nonclassical. Our…