An Invitation to shape uncertainty quantification in Computational Electromagnetics
Event details
| Date | 05.11.2024 |
| Hour | 16:15 › 17:15 |
| Speaker | Prof. Carlos Jerez - Universidad Adolfo Ibanez |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Computational Mathematics Seminar
Abstract :
In this talk, we will consider solving time-harmonic electromagnetic wave scattering problems when the actual domains are not fully known but can be modeled as random perturbations departing from a nominal shape. Specifically, we will use the framework of affine-parametric shape parametrizations to describe the domain uncertainty. This setting is shown to be a reality for multiple applications ranging from telescope design to nano-photonics. Along the way, we will combine and derive several mathematical tools, some new and some old, ranging from shape derivatives, edge or Nédélec finite-elements and new Strang-type lemmas to domain-to-solutions maps, multilevel Monte Carlo methods, and multilevel sparse-grid quadratures. Fortunately, several numerical experiments will help us understand the problems at hand and confirm our error convergence rates and complexity bounds. These results will show that one can beat, to a certain extent, the dreaded curse of dimensionality while also opening new questions you may have the answer to!
Abstract :
In this talk, we will consider solving time-harmonic electromagnetic wave scattering problems when the actual domains are not fully known but can be modeled as random perturbations departing from a nominal shape. Specifically, we will use the framework of affine-parametric shape parametrizations to describe the domain uncertainty. This setting is shown to be a reality for multiple applications ranging from telescope design to nano-photonics. Along the way, we will combine and derive several mathematical tools, some new and some old, ranging from shape derivatives, edge or Nédélec finite-elements and new Strang-type lemmas to domain-to-solutions maps, multilevel Monte Carlo methods, and multilevel sparse-grid quadratures. Fortunately, several numerical experiments will help us understand the problems at hand and confirm our error convergence rates and complexity bounds. These results will show that one can beat, to a certain extent, the dreaded curse of dimensionality while also opening new questions you may have the answer to!
Practical information
- Informed public
- Free
Organizer
- Prof. Daniel Kressner
Contact
- Prof. Daniel Kressner