Timeline for Green's function for wave equations in R² or R³
Current License: CC BY-SA 2.5
7 events
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| Sep 16, 2010 at 9:28 | comment | added | Anand | Dear Prof. Serre, that's true. Even when the domain has a conner such as edges of a box, there will be very complicated diffractions. That's why we impose the strong conditions that the domain is convex (to avoid tangent incident rays) plus sufficiently continuous (to avoid diffractions by conner). You said that it is "essentially"...., what do you mean by "essentially"? I am wondering under these conditions, whether we can prove strictly that ray-tracing plus ordinary reflexion can work. Thank you very much for your useful comments! :-) | |
| Sep 16, 2010 at 8:24 | comment | added | Denis Serre | Well, geometric optics is a vast topic. It is impossible to give even a flavour of it in a few lines, because it involves the theory of pseudo-differential operators, even for a domain without boundary (${\mathbb R}^n$, compact manifolds). In presence of a boundary, it can be a nightmare when rays reach the boundary tangentially. Fortunately, this does not happen if the domain is convex, and thus the theory is essentially ray-tracing plus ordinary reflexion. | |
| Sep 16, 2010 at 7:01 | vote | accept | Anand | ||
| Sep 15, 2010 at 14:15 | comment | added | Anand | Yes. Like interior of a ball. :-) | |
| Sep 15, 2010 at 13:33 | comment | added | Denis Serre | Do you mean smooth convex close domain ? | |
| Sep 15, 2010 at 13:23 | comment | added | Anand | Thanks Prof. Serre. I am wondering whether the geometric optics would work under our assumptions on the boundaries (smooth concave closed domain). From geometric optics, people use ray-tracing method in computer graphics and acoustics as well. It is an approximation to the real physics phenomenon. But under our assumptions, we hope that there was no diffraction and hence the approximation was indeed accurate. | |
| Sep 15, 2010 at 13:05 | history | answered | Denis Serre | CC BY-SA 2.5 |