Related papers: Elliptic preconditioner for accelerating the self …
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
We are studying the efficient solution of the system of linear equation stemming from the mass conserving mixed stress (MCS) method discretization of the Stokes equations. To that end we perform static condensation to arrive at a system for…
Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient and highly parallelizable method to construct a set of, optionally orthogonal, localized basis functions for the associated subspace. Our…
A class of preconditioners is introduced to enhance geometry optimisation and transition state search of molecular systems. We start from the Hessian of molecular mechanical terms, decompose it and retain only its positive definite part to…
A preconditioned, multipole-accelerated, Krylov-subspace iterative algorithm for the electromagnetic scattering analysis of three dimensional (3D), arbitrary shaped dielectric structures composed of single and multi-layered dielectric…
We propose domain decomposition preconditioners for the solution of an integral equation formulation of forward and inverse acoustic scattering problems with point scatterers. We study both forward and inverse problems and propose…
In this work we propose a novel block preconditioner, labelled Explicit Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to address the sequence of non-symmetric systems of linear…
Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing…
The gas of the interacted electrons is usually described within Kohn-Sham approximation by the set of Poisson and Schr\"{o}dinger equations with an effective potential for the single-particle wave functions. The solution of these equations…
Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace…
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…
In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…
Solving optimization problems with transient PDE-constraints is computationally costly due to the number of nonlinear iterations and the cost of solving large-scale KKT matrices. These matrices scale with the size of the spatial…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…
In this paper preconditioners for the Conjugate Gradient method are studied to solve the Newton system with symmetric positive definite Jacobian. In particular, we define a sequence of preconditioners built by means of SR1 and BFGS low-rank…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to…
We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…
We describe a version of an algorithm for evolving self-gravitating collections of particles that should be nearly ideal for parallel architectures. Our method is derived from the ``self-consistent field'' (SCF) approach suggested…
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…