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Computations of incompressible flows with velocity boundary conditions require solution of a Poisson equation for pressure with all Neumann boundary conditions. Discretization of such a Poisson equation results in a rank-deficient matrix of…
The natural orbital functional theory (NOFT) has emerged as an alternative formalism to both density functional (DF) and wavefunction methods. In NOFT, the electronic structure is described in terms of the natural orbitals (NOs) and their…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based…
Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…
Computation of electromagnetic fields due to point sources (Hertzian dipoles) in cylindrically stratified media is a classical problem for which analytical expressions of the associated tensor Green's function have been long known. However,…
In this paper, we present a systematic study of the force-free field equation for simple axisymmetric configurations in spherical geometry and apply it to the solar active regions. The condition of separability of solutions in the radial…
This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
We describe a generalized algorithm for evaluating the steady-state solution of the density matrix equation of motion, for the pump-probe scheme, when two fields oscillating at different frequencies couple the same set of atomic transitions…
We introduce a novel parametrization scheme for the Hilbert space of a spin-1/2 Heisenberg antiferromagnet (AFM) based on an octapartite description of the square lattice. Our formulation provides an efficient yet systematic way to model…
Using the complete orthonormal sets of radial parts of nonrelativitistic exponential type orbitals (2,1, 0, 1, 2, ...) and spinor type tensor spherical harmonics of rank s the new formulae for the 2(2s+1)-component relativistic spinors…
Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set…
We compute the structure of a self-gravitating torus with polytropic equation-of-state (EOS) rotating in an imposed centrifugal potential. The Poisson-solver is based on isotropic multigrid with optimal covering factor (fluid…
Analytic gradient routines are a desirable feature for quantum mechanical methods, allowing for efficient determination of equilibrium and transition state structures and several other molecular properties. In this work, we present…
We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential…
We have implemented the single-site density matrix renormalization group algorithm for the variational optimization of SU(2) \times U(1) (spin and particle number) invariant matrix product states for general spin and particle number…
AC-OPF (Alternative Current Optimal Power Flow)aims at minimizing the operating costs of a power gridunder physical constraints on voltages and power injections.Its mathematical formulation results in a nonconvex polynomial…
Over the past decade, the high-contrast observation of disks and gas giant planets around nearby stars has been made possible on ground-based instruments using extreme adaptive optics (XAO). While these facilities produce images with a…
Based on a class of exactly solvable models of interacting bose and fermi liquids, we compute the single-particle propagators of these systems exactly for all wavelengths and energies and in any number of spatial dimensions. The field…