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Sparse bounds for the discrete spherical maximal functions
(2020)
We prove sparse bounds for the spherical maximal operator of Magyar, Stein and Wainger. The bounds are conjecturally sharp, and contain an endpoint estimate. The new method of proof is inspired by ones by Bourgain and ...
Sparse bounds for Bochner–Riesz multiplers
(2019)
The Bochner–Riesz multipliers are shown to satisfy a range of sparse bounds. The range of sparse bounds increases to the optimal range, as δ increases to the critical value, even assuming only partial information on the ...
Parallel Sums and Adaptive BDDC Deluxe
(2017)
There has recently been a considerable activity in developing adaptive methods for the selection of primal constraints for BDDC algorithms and, in particular, for BDDC deluxe variants. The primal constraints of a BDDC or ...
A new coarse space for overlapping Schwarz algorithms for H(curl) problems in three dimensions with irregular subdomains
(2019)
A new coarse space for a two-level overlapping Schwarz algorithm is presented for problems posed in three dimensions in the space H(curl, Ω). Previous studies for these methods are very restrictive about the geometry of ...
A BDDC algorithm with deluxe scaling for H(curl) in two dimensions with irregular subdomains
(2015)
A bound is obtained for the condition number of a BDDC algorithm for problems posed in H(curl) in two dimensions, where the subdomains are only assumed to be uniform in the sense of Peter Jones. For the primal variable ...
A partial differential equation model with age-structure and nonlinear recidivism: Conditions for a backward bifurcation and a general numerical implementation
(2019-12-15)
We formulate an age-structured three-staged nonlinear partial differential equation model that features nonlinear recidivism to the infected (infectious) class from the temporarily recovered class. Equilibria are computed, ...
Parameter estimates of the 2016-2017 Zika outbreak in Costa Rica: An Approximate Bayesian Computation (ABC) approach
(2019-03-28)
In Costa Rica, the first known cases of Zika were reported in 2016. We looked at the 2016-2017 Zika outbreak and explored the transmission dynamics using weekly reported data. A nonlinear differential equation single-outbreak ...
An overlapping Schwarz method for virtual element discretizations in two dimensions
(2019)
A new coarse space for domain decomposition methods is presented for nodal ellipticproblems in two dimensions. The coarse space is derived from the novel virtual elementmethods and therefore can accommodate quite irregular ...
Transmission dynamics of Dengue in Costa Rica: The role of hospitalizations
Dinámica de la transmisión de dengue en Costa Rica: El rol de las hospitalizaciones
(2019-12)
For decades, dengue virus has caused major problems for public health officials in tropical and subtropical countries around the world. We construct a compartmental model that includes the role of hospitalized individuals ...
Virtual Coarse Spaces for Irregular Subdomain Decompositions
(2020-10-25)
On the other hand, Virtual Element Methods (VEM) [1, 12, 13] allow to handle general polygonal elements. In the case of triangular elements, VEM reduces to the usual FEM. Thus, VEM is a natural choice for constructing space ...