13 citations · 34 across the 8 of their papers we have counts for
9 papers
A boundary-field formulation for elastodynamic scattering
George C. Hsiao, Tonatiuh Sánchez-Vizuet, Wolfgang L. Wendland
An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields sca…
Afternote to Coupling at a distance: convergence analysis and a priori error estimates
Nestor Sánchez, Tonatiuh Sánchez-Vizuet, Manuel E. Solano
In their article "Coupling at a distance HDG and BEM", Cockburn, Sayas and Solano proposed an iterative coupling of the hybridizable discontinuous Galerkin method (HDG) and the bou…
Surrogate Approximation of the Grad-Shafranov Free Boundary Problem via Stochastic Collocation on Sparse Grids
Howard C. Elman, Jiaxing Liang, Tonatiuh Sánchez-Vizuet
In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces…
Error analysis of an unfitted HDG method for a class of non-linear elliptic problems
Nestor Sánchez, Tonatiuh Sánchez-Vizuet, Manuel E. Solano
We study Hibridizable Discontinuous Galerkin (HDG) discretizations for a class of non-linear interior elliptic boundary value problems posed in curved domains where both the source…
Time-Dependent Wave-Structure Interaction Revisited: Thermo-piezoelectric Scatterers
George C. Hsiao, Tonatiuh Sánchez-Vizuet
In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body immersed in a compressible fluid. It is shown that the problem ca…
Boundary integral formulations for transient linear thermoelasticity with combined-type boundary conditions
George C. Hsiao, Tonatiuh Sánchez-Vizuet
We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic doma…
A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems
Nestor Sánchez, Tonatiuh Sánchez-Vizuet, Manuel E. Solano
We present a priori and a posteriori error analysis of a high order hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear elliptic problem posed on a piecewise…
Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad-Shafranov equation by extension from polygonal subdomains
Tonatiuh Sánchez-Vizuet, Manuel E. Solano, Antoine J. Cerfon
We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymmetric confinement devices. In t…
Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid
Thomas S. Brown, Tonatiuh Sánchez-Vizuet, Francisco-Javier Sayas
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear…