The Bubble Transform and the de Rham ComplexSpringer Science and Business Media LLC - - Trang 1-49 - 2022
Richard S. Falk, Ragnar Winther
The purpose of this paper is to discuss a generalization of the bubble transform to differential forms. The bubble transform was discussed in Falk and Winther (Found Comput Math 16(1):297–328, 2016) for scalar valued functions, or zero-forms, and represents a new tool for the understanding of finite element spaces of arbitrary polynomial degree. The present paper contains a similar study for diffe...... hiện toàn bộ
Constrained Diffeomorphic Shape EvolutionSpringer Science and Business Media LLC - Tập 12 - Trang 295-325 - 2011
Laurent Younes
We design optimal control strategies in spaces of diffeomorphisms and shape spaces in which the Eulerian velocities of the evolving deformations are constrained to belong to a suitably chosen finite-dimensional space, which is also following the motion. This results in a setting that provides a great flexibility in the definition of Riemannian metrics, extending previous approaches in which shape ...... hiện toàn bộ
Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary TimescalesSpringer Science and Business Media LLC - Tập 20 - Trang 1505-1547 - 2020
Assyr Abdulle, Timothée Pouchon
A family of effective equations for wave propagation in periodic media for arbitrary timescales
$$\mathcal {O}(\varepsilon ^{-\alpha })$$
, where
$$\varepsilon \ll 1$$
is the period of the tensor describing the medium, is proposed. The well-posedness of the effective equations of the family is ensured without requiring a regularization process as in previous models (Benoit and Gloria in Long-...... hiện toàn bộ
A Necessary and Sufficient Proximity Condition for Smoothness Equivalence of Nonlinear Subdivision SchemesSpringer Science and Business Media LLC - Tập 16 - Trang 1069-1114 - 2015
Tom Duchamp, Gang Xie, Thomas Yu
In the recent literature on subdivision methods for approximation of manifold-valued data, a certain “proximity condition” comparing a nonlinear subdivision scheme to a linear subdivision scheme has proved to be a key analytic tool for analyzing regularity properties of the scheme. This proximity condition is now well known to be a sufficient condition for the nonlinear scheme to inherit the regul...... hiện toàn bộ
The Geometry of Off-the-Grid Compressed SensingSpringer Science and Business Media LLC - Tập 23 - Trang 241-327 - 2021
Clarice Poon, Nicolas Keriven, Gabriel Peyré
Compressed sensing (CS) ensures the recovery of sparse vectors from a number of randomized measurements proportional to their sparsity. The initial theory considers discretized domains, and the randomness makes the physical positions of the grid nodes irrelevant. Most imaging devices, however, operate over some continuous physical domain, and it makes sense to consider Dirac masses with arbitrary ...... hiện toàn bộ
Computing the Homology of Semialgebraic Sets. I: Lax FormulasSpringer Science and Business Media LLC - Tập 20 - Trang 71-118 - 2019
Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto
We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of closed semialgebraic sets given by Boolean formulas without negations over lax polynomial inequalities. The algorithm works in weak exponential time. This means that outside a subset of data having exponentially small measure, the cost of the algorithm is single exponential in the size of th...... hiện toàn bộ