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The common spatial pattern analysis (CSP) is a widely used signal processing technique in brain-computer interface (BCI) systems to increase the signal-to-noise ratio in electroencephalogram (EEG) recordings. Despite its popularity, the…
Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which…
Conventional optimal power flow (OPF) solvers assume full observability of the involved system states. However, in practice, there is a lack of reliable system monitoring devices in the distribution networks. To close the gap between the…
The optimal power flow (OPF) is a multi-valued, non-convex mapping from loads to dispatch setpoints. The variability of system parameters (e.g., admittances, topology) further contributes to the multiplicity of dispatch setpoints for a…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of…
Density functional theory (DFT) is the most promising method for calculating quantum properties of molecules and materials at moderate and large scales. However, commonly used density functional approximations (DFAs) have systematic…
Traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis (OB). For atoms with complicated shell structures, a large OB is needed to saturate all the…
Current Non-Orthogonal Configuration Interaction (NOCI) methods often use a set of Self-Consistent Field (SCF) states selected based on chemical intuition. However, it may be challenging to track these SCF states across a dissociation…
The advent of massively parallel supercomputers, with their distributed-memory technology using many processing units, has favored the development of highly-scalable local low-order solvers at the expense of harder-to-scale global very…
The spin density wave (SDW) state of the uniform electron gas is investigated in the exact exchange approximation of noncollinear spin density functional theory (DFT). Unlike in Hartree-Fock theory, where the uniform paramagnetic state of…
Kohn-Sham density functional theory (DFT) has long struggled with the accurate description of strongly correlated and open shell systems and improvements have been minor even in the newest hybrid functionals. In this Letter we treat the…
In this paper, we propose a mesh-free numerical method for solving elliptic PDEs on unknown manifolds, identified with randomly sampled point cloud data. The PDE solver is formulated as a spectral method where the test function space is the…
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…
Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-zeta (QZ) size are required to adequately converge Kohn-Sham density functional theory (DFT) calculations towards the complete basis set limit. However,…
Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these…
Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…
Linear-scaling implementations of density functional theory (DFT) reach their intended efficiency regime only when applied to systems having a physical size larger than the range of their Kohn-Sham density matrix (DM). This causes a problem…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compared with multiple precision arithmetic, and also be applied…