Convergence of Wachspress coordinates: from polygons to curved domains
Given a smooth, strictly convex planar domain, we investigate point-wise convergence of the sequence of Wachspress coordinates defined over finer and finer inscribed polygonal approximations of the domain. Based on a relation between the discrete ...
Subdivision schemes, network flows and linear optimization
We link regularity and smoothness analysis of multivariate vector subdivision schemes with network flow theory and with special linear optimization problems. This connection allows us to prove the existence of what we call optimal difference masks that ...
Efficient sum-of-exponentials approximations for the heat kernel and their applications
In this paper, we show that efficient separated sum-of-exponentials approximations can be constructed for the heat kernel in any dimension. In one space dimension, the heat kernel admits an approximation involving a number of terms that is of the order ...
Mixed finite elements for elasticity on quadrilateral meshes
We present stable mixed finite elements for planar linear elasticity on general quadrilateral meshes. The symmetry of the stress tensor is imposed weakly and so there are three primary variables, the stress tensor, the displacement vector field, and the ...
On error bounds of Filon-Clenshaw-Curtis quadrature for highly oscillatory integrals
In this paper, we aim to derive some error bounds for Filon-Clenshaw-Curtis quadrature for highly oscillatory integrals. Thanks to the asymptotics of the coefficients in the Chebyshev series expansions of analytic functions or functions of limited ...
Approximation of the multi-dimensional Stokes system with embedded pressure discontinuities
Surface tension in multi-phase fluid flow engenders pressure discontinuities on phase interfaces. In this work we present a finite element method to solve viscous incompressible flows problems, especially designed to cope with such a situation. Taking ...
Geometric multigrid for an implicit-time immersed boundary method
The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the deformations and resulting forces of the structure and Eulerian variables to describe the motion and forces of the fluid. ...
Multilevel approximation of the gradient operator on an adaptive spherical geodesic grid
This work presents a new adaptive multilevel approximation of the gradient operator on a recursively refined spherical geodesic grid. The multilevel structure provides a simple way to adapt the computation to the local structure of the gradient operator ...
Variants of an explicit kernel-split panel-based Nyström discretization scheme for Helmholtz boundary value problems
The incorporation of analytical kernel information is exploited in the construction of Nyström discretization schemes for integral equations modeling planar Helmholtz boundary value problems. Splittings of kernels and matrices, coarse and fine grids, ...
An anisotropic directional subdivision and multiresolution scheme
In order to handle directional singularities, standard wavelet approaches have been extended to the concept of discrete shearlets in Kutyniok and Sauer (SIAM J. Math. Anal. 41, 1436---1471, 2009). One disadvantage of this extension, however, is the ...