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My main research interests lie in the areas of numerical analysis, scientific computing and computational physics. Currently I work developing numerical methods for problems arising in the computational simulation of magnetically confined plasmas. I have also interest in the application of integral equation techniques for the study of time domain wave propagation, in the applications and theoretical development of the Boundary Element Method (BEM) and the Hybridizable Discontinuous Galerkin Method (HDG), and in formulations that involve the coupling of integral and partial differential equations.Show Less
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Courses
- ISCIntroduction to Statistical Computing
- ISMIntroduction to Statistical Methods
- TSTheory of Statistics
- AODEAnalysis of Ordinary Differential Equations
- ISBIntroduction to Statistics and Biostatistics
- CICalculus I
Grants
- LEAPS-MPS: Hybridizable Discontinuous Galerkin Methods for Non-Linear Integro-Differential Boundary Value Problems in Magnetic Plasma Confinement
Principal Investigator (PI)
2021
$250.0K
Active
Publications (21)
Recent
- A boundary-field formulation for elastodynamic scattering
2023
- Afternote to “Coupling at a Distance”: Convergence Analysis and A Priori Error Estimates
2022
- High Performance Equilibrium Solvers for Integrated Magnetic Fusion Simulations
2022
- Afternote to Coupling at a distance: convergence analysis and a priori error estimates .
2022
- Time-Dependent Wave-Structure Interaction Revisited: Thermo-Piezoelectric Scatterers
2021
- Error analysis of an unfitted HDG method for a class of non-linear elliptic problems
2021
- A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems
2021
- Surrogate Approximation of the Grad-Shafranov Free Boundary Problem via Stochastic Collocation on Sparse Grids
2021
- Boundary integral formulations for transient linear thermoelasticity with combined-type boundary conditions
2021
- Adaptive hybridizable discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains
2020
- Time-domain boundary integral methods in linear thermoelasticity
2020
- A hybridizable discontinuous Galerkin solver for the Grad–Shafranov equation
2019
- The Mathematics of Cathleen Synge Morawetz
2018
- A new and improved analysis of the time domain boundary integral operators for the acoustic wave equation
2017
- Boundary and coupled boundary ndash;finite element methods for transient wave ndash;structure interaction
2017
- Pseudo spectral collocation with Maxwell polynomials for kinetic equations with energy diffusion
2017
- Symmetric Boundary-Finite Element Discretization of Time Dependent Acoustic Scattering by Elastic Obstacles with Piezoelectric Behavior
2017
- Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid
2017
- Integral and coupled integral-volume methods for transient problems in wave-structure interaction
2016
- Boundary and coupled boundary–finite element methods for transient wave–structure interaction
2016
- A fully discrete Calderón calculus for the two-dimensional elastic wave equation
2015