Abstract
For the inhomogeneous Helmholtz equation in the plane, with a Gaussian random field coefficient, we derive and characterize a singular system of the source-to-field measurement map. To this end we first analyze the case with a deterministic coefficient, and then incorporate stochastic integrals in the L2 sense into a representation of the solution of the Helmholtz equation. Our results are applicable in the uncertainty quantification and the analysis of the robustness of solution of inverse source problems in the presence of random media.
| Original language | English |
|---|---|
| Publication date | 2022 |
| Number of pages | 1 |
| Publication status | Published - 2022 |
| Event | SIAM Conference on Imaging Science 2022 - Virtual Meeting, Berlin, Germany Duration: 21 Mar 2022 → 25 Mar 2022 https://www.siam.org/conferences/cm/conference/is22 |
Conference
| Conference | SIAM Conference on Imaging Science 2022 |
|---|---|
| Location | Virtual Meeting |
| Country/Territory | Germany |
| City | Berlin |
| Period | 21/03/2022 → 25/03/2022 |
| Internet address |