相关论文: The auxiliary space preconditioner for the de Rham…

The fourth derivative models for two dimensional gravity are shown to be equivalent to the special version of the nonlinear sigma models coupled to 2d quantum gravity. The reduction consists in the introduction of the auxiliary scalar…

We design in this work a discrete de Rham complex on manifolds. This complex, written in the framework of exterior calculus, has the same cohomology as the continuous de Rham complex, is of arbitrary order of accuracy and, in principle, can…

In this second part of our series of papers, we develop an abstract framework suitable for de Rham complexes that depend on a parameter belonging to an arbitrary Banach space. Our primary focus is on spectral perturbation problems and the…

We examine the five-dimensional super-de Rham complex with $N = 1$ supersymmetry. The elements of this complex are presented explicitly and related to those of the six-dimensional complex in $N = (1, 0)$ superspace through a specific notion…

We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological…

Given a domain $\Omega \subset \mathbb{R}^n$, the de Rham complex of differential forms arises naturally in the study of problems in electromagnetism and fluid mechanics defined on $\Omega$, and its discretization helps build stable…

The goal of this paper is to propose preconditioners for the system of linear equations that arises from a discretization of fourth order elliptic problems using spectral element methods. These preconditioners are constructed using…

In this study, two-dimensional finite element complexes with various levels of smoothness, including the de Rham complex, the curldiv complex, the elasticity complex, and the divdiv complex, are systematically constructed. Smooth scalar…

We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…

This paper discusses the construction of local bounded commuting projections for discrete subcomplexes of the gradgrad complexes in two and three dimensions, which play an important role in the finite element theory of elasticity (2D) and…

This paper introduces a fully algebraic two-level additive Schwarz preconditioner for general sparse large-scale matrices. The preconditioner is analyzed for symmetric positive definite (SPD) matrices. For those matrices, the coarse space…

For globally subanalytic manifolds we define de Rham complexes of globally subanalytic differential forms and of constructible differential forms. Whereas the de Rham theorem does not hold for the former in the non-compact case, it does…

Many coupled problems in engineering and science can be described by elliptic partial differential equations on adjacent domains, where the coupling can be considered either as a thin equidimensional overlap between the model domains, or as…

We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the range of a weighted sum of two fractional differential…

We study a thermo-poroelasticity model which describes the interaction between the deformation of an elastic porous material and fluid flow under non-isothermal conditions. The model involves several parameters that can vary significantly…

Criteria and constructive methods for the completion of an incomplete basis of, or context in, a four-dimensional Hilbert space by (in)decomposable vectors are given.

Introducing $h$- and $h'$-deformations of ${\mathbb Z}_2$-graded (1+2)- and (2+1)-spaces, denoted by ${\mathbb A}_h^{1|2}$ and ${\mathbb A}_{h'}^{2|1}$, a two-parameter first order differential calculus, de Rham complex, on ${\mathbb…

We investigate the super-de Rham complex of five-dimensional superforms with $N=1$ supersymmetry. By introducing a free supercommutative algebra of auxiliary variables, we show that this complex is equivalent to the Chevalley-Eilenberg…

Parafermions of order two and three are shown to be the fundamental tool to construct superspaces related to cubic and quartic extensions of the Poincar\'e algebra. The corresponding superfields are constructed, and some of their main…

Using the framework of operator or Calder\'on preconditioning, uniform preconditioners are constructed for elliptic operators discretized with continuous finite (or boundary) elements. The preconditioners are constructed as the composition…