相关论文: Auxiliary iterative schemes for the discrete opera…
The main difficulty in solving the discrete constrained problem is its poor and even ill condition. In this paper, we transform the discrete constrained problems on de Rham complex to Laplace-like problems. This transformation not only make…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…
Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace--Beltrami operator, for example, are fundamental for methods in shape analysis and mesh processing. The…
An algebraic multilevel iteration method for solving system of linear algebraic equations arising in $H(\mathrm{curl})$ and $H(\mathrm{div})$ spaces are presented. The algorithm is developed for the discrete problem obtained by using the…
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving…
The aim of the present work is to derive a error estimates for the Laplace eigenvalue problem in mixed form, by means of a virtual element method. With the aid of the theory for non-compact operators, we prove that the proposed method is…
The eigenvalue problem of the Laplace-Beltrami operators on curved surfaces plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve this…
In this work, following the Discrete de Rham (DDR) paradigm, we develop an arbitrary-order discrete divdiv complex on general polyhedral meshes. The construction rests 1) on discrete spaces that are spanned by vectors of polynomials whose…
Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discrete variational methods appropriate for boundary value…
In this work, following the discrete de Rham (DDR) approach, we develop a discrete counterpart of a two-dimensional de Rham complex with enhanced regularity. The proposed construction supports general polygonal meshes and arbitrary…
In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…
A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…
The standard mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex are based on proper discrete subcomplexes. As a consequence, the exterior derivatives, which are local operators, are computed…
We introduce an iterative scheme for discrete convex minimization problems of $p$-Laplace type such as variational graph $p$-Laplace problems and $\ell^p$ regression. In each iteration, the scheme solves only a weighted least-squares…
We propose a new monotone finite difference discretization for the variational $p$-Laplace operator, \[ \Delta_p u=\text{div}(|\nabla u|^{p-2}\nabla u), \] and present a convergent numerical scheme for related Dirichlet problems. The…
A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the $H^2$ space in three dimensions is proposed, involving an $H^2$-nonconforming finite element space, a new tangentially continuous…
An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with…
Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…