Related papers: Elliptic preconditioner for accelerating the self …
The discretization of the double-layer potential integral equation for the interior Dirichlet Laplace problem in a domain with smooth boundary results in a linear system that has a bounded condition number. Thus, the number of iterations…
The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem i.e. H({{\psi}}){\psi} = E{\psi}. This new scheme is derived from a…
The convergence property of a stochastic algorithm for the self-consistent field (SCF) calculations of electron structures is studied. The algorithm is formulated by rewriting the electron charges as a trace/diagonal of a matrix function,…
Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for mixed-dimensional…
The Poisson pressure solve resulting from the spectral element discretization of the incompressible Navier-Stokes equation requires fast, robust, and scalable preconditioning. In the current work, a parallel scaling study of…
The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistence searching method involves…
Kohn-Sham Density Functional Theory (KS-DFT) has been traditionally solved by the Self-Consistent Field (SCF) method. Behind the SCF loop is the physics intuition of solving a system of non-interactive single-electron wave functions under…
The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this…
In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…
We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and…
In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…
In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…
We introduce a domain decomposition-based nonlinear preconditioned iteration for solving nonlinear, nonsmooth elliptic optimal control problems, with a nonlinear reaction term, $L^1$ regularization and box constraints on the control…
In this paper, we consider flow simulation in highly heterogeneous media that has many practical applications in industry. To enhance mass conservation, we write the elliptic problem in a mixed formulation and introduce a robust two-grid…
The eXtended Finite Element Method (XFEM) is an approach for solving problems with non-smooth solutions. In the XFEM, the approximate solution is locally enriched to capture discontinuities without requiring a mesh which conforms to the…
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
We present a modification of the $\Delta$SCF method of calculating energies of excited states, in order to make it applicable to resonance calculations of molecules adsorbed on metal surfaces, where the molecular orbitals are highly…
The computational efficiency and rapid convergence of fast Fourier transform (FFT)-based solvers render them a powerful numerical tool for periodic cell problems in multiscale modeling. On regular grids, they tend to outperform traditional…
The paper suggests a preconditioning type method for fast solving of elliptic equations with oscillating quasiperiodic coefficients $A_\epsilon$ specified by the small parameter $\epsilon>0$. We use an iteration method generated by an…