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Meshless methods are often used in numerical simulations of systems of partial differential equations (PDEs), particularly those which involve complex geometries or free surfaces. Here we present a novel compact scheme based on the local…
We present a novel energy-based localization procedure able to localize molecular orbitals into specific spatial regions. The method is applied to several cases including both conjugated and non-conjugated systems. The obtained localized…
We present a new linear scaling method for the energy minimization step of semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It is based on the self-consistent calculation of the optimum localized orbitals of any…
We present an implementation and analysis of a stochastic high performance algorithm to calculate the correlation energy of three dimensional periodic systems in second-order M{\o}ller-Plesset perturbation theory (MP2). In particular we…
As is known that wave equations have physically very important properties which should be respected by numerical schemes in order to predict correctly the solution over a long time period. In this paper, the long-time behaviour of momentum…
We present a fully variational generalization of the pseudo self-interaction correction (VPSIC) approach previously presented in two implementations based on plane-waves and atomic orbital basis set, known as PSIC and ASIC, respectively.…
The effective management of stochastic characteristics of renewable power generations is vital for ensuring the stable and secure operation of power systems. This paper addresses the task of optimizing the chance-constrained…
Variational optimization of orbitals in time-independent density functional calculations of excited electronic states presents a significant challenge, as excited states typically correspond to saddle points on the electronic energy…
The classic second-order average vector field (AVF) method can exactly preserve the energy for Hamiltonian ordinary differential equations and partial differential equations. However, the AVF method inevitably leads to fully-implicit…
Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational…
The Vlasov-Fokker-Planck equation describes the evolution of the probability density of the position and velocity of particles under the influence of external confinement, interaction, friction, and stochastic force. It is well-known that…
We have devised a variational sinc collocation method (VSCM) which can be used to obtain accurate numerical solutions to many strong-coupling problems. Sinc functions with an optimal grid spacing are used to solve the linear and non-linear…
We propose a scheme to perform the variational principle directly on the coherent pair condensate (VDPC). The result is equivalent to that of the so-called variation after particle-number projection, but now the particle number is always…
Wafer-level performance prediction has been attracting attention to reduce measurement costs without compromising test quality in production tests. Although several efficient methods have been proposed, the site-to-site variation, which is…
Lattice networks with dissipative interactions are often employed to analyze materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be modelled discretely. They are, however,…
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…
In this research work, let us focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave…
We introduce an algorithm that can be used to perform stochastic perturbation theory (sPT) to correct any non-linearly parametrized wavefunction that can be optimized using orbital space Variational Monte Carlo (VMC). Although the…
The self-energy-functional approach (SFA) is discussed in the context of different variational principles for strongly correlated electron systems. Formal analogies between static and dynamical variational approaches, different types of…
In a recent paper [Phys. Rev. Lett. \textbf{93}, 130401 (2004)], we proposed the idea of expanding the space of variations in variational calculations of the energy by considering the approximate wave function $\psi$ to be a functional of…