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A new implementation of the GW approximation (GWA) based on the all-electron Projector-Augmented-Wave method (PAW) is presented, where the screened Coulomb interaction is computed within the Random Phase Approximation (RPA) instead of the…
By carefully choosing parameters and including more semi-core orbitals as valence electrons, we have constructed a high quality projected augmented wave (PAW) dataset that yields results comparable to existing full-potential linearized…
This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…
We devise 3-field and 4-field finite element approximations of a system describing the steady state of an incompressible heat-conducting fluid with implicit non-Newtonian rheology. We prove that the sequence of numerical approximations…
Layer-wise preconditioning methods are a family of memory-efficient optimization algorithms that introduce preconditioners per axis of each layer's weight tensors. These methods have seen a recent resurgence, demonstrating impressive…
In this work, we develop a novel multilevel Tau matrix-based preconditioned method for a class of non-symmetric multilevel Toeplitz systems. This method not only accounts for but also improves upon an ideal preconditioner pioneered by [J.…
We analyse a class of nonoverlapping domain decomposition preconditioners for nonsymmetric linear systems arising from discontinuous Galerkin finite element approximation of fully nonlinear Hamilton--Jacobi--Bellman (HJB) partial…
The rigorous coupled-wave analysis (RCWA) is one of the most successful and widely used methods for modeling periodic optical structures. It yields fast convergence of the electromagnetic far-field and has been adapted to model various…
We examine the challenge of performing accurate electronic structure calculations at high pressures by comparing the results of all-electron full potential linearized augmented-plane-wave calculations with those of the projector augmented…
The random phase approximation (RPA) is attracting renewed interest as a universal and accurate method for first-principles total energy calculations. The RPA naturally accounts for long-range dispersive forces without compromising accuracy…
In order to investigate electronic properties of recently discovered heavy fermion superconductors CeTIn$_5$ (T=Ir and Co), we employ the relativistic linear augmented-plane-wave (RLAPW) method to clarify the energy band structures and…
In [Dai et al, Multi. Model. Simul., 2020], a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory, based on which a linearized method was developed in [Hu, et al,…
Unless special conditions apply, the attempt to solve ill-conditioned systems of linear equations with standard numerical methods leads to uncontrollably high numerical error. Often, such systems arise from the discretization of operator…
The method based on fast Fourier transforms proposed by G. Rom\'an-P\'erez and J. M. Soler [Phys. Rev. Lett. 103, 096102 (2009)], which allows for a computationally fast implementation of the nonlocal van der Waals (vdW) functionals, has…
It was recently demonstrated that, in deep subwavelength gap resonators coupled to two-dimensional electron gases, coupling to propagating plasmons can lead to energy leakage and prevent the formation of polaritonic resonances. This…
We present a general numerical approach to construct local Kohn-Sham potentials from orbital-dependent functionals within the all-electron full-potential linearized augmented-plane-wave (FLAPW) method, in which core and valence electrons…
We consider multigrid methods for finite volume discretizations of the Reynolds Averaged Navier-Stokes (RANS) equations for both steady and unsteady flows. We analyze the effect of different smoothers based on pseudo time iterations, such…
This paper presents the sparsifying preconditioner for the time-harmonic Maxwell's equations in the integral formulation. Following the work on sparsifying preconditioner for the Lippmann-Schwinger equation, this paper generalizes that…
This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures,…
In this paper, we propose and evaluate the performance of a unified computational framework for preconditioning systems of linear equations resulting from the solution of coupled problems with monolithic schemes. The framework is composed…