Related papers: Discrete tensor product BGG sequences: splines and…
This paper deals with balanced domain decomposition by constraints (BDDC) method for solving large-scale linear systems of algebraic equations arising from the space-time finite element discretization of parabolic initial-boundary value…
Two types of finite element spaces on triangles are constructed for div-div conforming symmetric tensors. Besides the normal-normal continuity, the stress tensor is continuous at vertices and another trace involving combination of…
The paper is concerned with three types of cubic splines over a triangulation that are characterized by three degrees of freedom associated with each vertex of the triangulation. The splines differ in computational complexity, polynomial…
We introduce and study, for a process P delivering edges on the Cartesian product of the vertex sets of a given set of graphs, the P-product of these graphs, thereby generalizing many types of product graph. Analogous to the notion of a…
Spacetime discontinuous Galerkin (SDG) finite element methods are used to solve such PDEs involving space and time variables arising from wave propagation phenomena in important applications in science and engineering. To support an…
Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and…
To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along…
We present a generic algorithm for computing discrete logarithms in a finite abelian p-group H, improving the Pohlig-Hellman algorithm and its generalization to noncyclic groups by Teske. We then give a direct method to compute a basis for…
Let G be a connected reductive quasisplit algebraic group over a field L which is a finite extension of the p-adic numbers. We construct an exact sequence modelled on (the dual of) the BGG resolution involving locally analytic principal…
This paper focuses on the $GL_n$ tensor product algebra, which encapsulates the decomposition of tensor products of arbitrary finite dimensional irreducible representations of $GL_n$. We will describe an explicit basis for this algebra.…
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…
The relaxed micromorphic model is a generalized continuum model that is well-posed in the space $X = [H^1]^3 \times [H(\textrm{curl})]^3$. Consequently, finite element formulations of the model rely on $H^1$-conforming subspaces and…
We propose and analyze stable finite element approximations for Willmore flow of planar curves. The presented schemes are based on a novel weak formulation which combines an evolution equation for curvature with the curvature formulation…
In this article, we discuss the efficient implementation of powerful domain decomposition smoothers for multigrid methods for high order discontinuous Galerkin (DG) finite element methods. In particular, we study the inversion of matrices…
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac…
We study the discretisation of a uniaxial (rank-one) reduction of the Oldroyd-B model for dilute polymer solutions, in which the conformation tensor is represented as $\sig = \vec b \otimes \vec b$. Building on structural analogies with…
In this paper we study the Bernstein-Gel'fand-Gel'fand (BGG) correspondence linking sheaves on a projective space to graded modules over an exterior algebra. We give an explicit construction of a Beilinson monad for a sheaf on projective…
Gaussian fields (GFs) are frequently used in spatial statistics for their versatility. The associated computational cost can be a bottleneck, especially in realistic applications. It has been shown that computational efficiency can be…
Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such…
In this paper we describe a class of highly entangled subspaces of a tensor product of finite dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values…