相关论文: Preconditioning orbital minimization method for pl…
This paper discusses lowest-order nonstandard finite element methods for space discretization and explicit and implicit schemes for time discretization of the biharmonic wave equation with clamped boundary conditions. A modified Ritz…
The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and…
In this paper we are concerned with fast algorithms for the systems arising from the plane wave discretizations for two-dimensional Helmholtz equations with large wave numbers. We consider the plane wave weighted least squares (PWLS) method…
For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is naturally related to properties of the underlying model. This is particularly so for…
When solving linear systems arising from PDE discretizations, iterative methods (such as Conjugate Gradient, GMRES, or MINRES) are often the only practical choice. To converge in a small number of iterations, however, they have to be…
We consider a modification of the OMM energy functional which contains an $\ell^1$ penalty term in order to find a sparse representation of the low-lying eigenspace of self-adjoint operators. We analyze the local minima of the modified…
We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular…
The projection of the eigenfunctions obtained in standard plane-wave first-principle calculations is used for analyzing atomic-orbital basis sets. The "spilling" defining the error in such a projection allows the evaluation of the quality…
We propose an operator preconditioner for general elliptic pseudodifferential equations in a domain $\Omega$, where $\Omega$ is either in $\mathbb{R}^n$ or in a Riemannian manifold. For linear systems of equations arising from low-order…
Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show…
This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the…
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…
A mimetic spectral element discretization, utilizing a novel Galerkin projection Hodge star operator, of the macroscopic Maxwell equations in Hamiltonian form is presented. The idea of splitting purely topological and metric dependent…
Solution methods for the nonlinear partial differential equation of the Rudin-Osher-Fatemi (ROF) and minimum-surface models are fundamental for many modern applications. Many efficient algorithms have been proposed. First order methods are…
This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…
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…
We present and compare three generically applicable signal processing methods for periodic orbit quantization via harmonic inversion of semiclassical recurrence functions. In a first step of each method, a band-limited decimated periodic…
Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudo-spectral method is implemented by assuming that the grid, used to represent the…
In this paper we present a unified framework for constructing spectrally equivalent low-order-refined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in $H^1$, $H({\rm curl})$, and…