Numeerisen analyysin ja laskennallisen tieteen seminaari

13.3.2006 klo 14.15 U356

Matti Lassas, TKK, Matematiikan laitos

Absorbing boundary conditions in electromagnetism

We review absorbing boundary conditions, particularly so-called Perfectly Matched Layer (PML). Absorbing boundary conditions are used in computer simulations for scattering problems, for simulating radar or cellular phones etc. When simulating the waves in infinite space one faces the problem that any computer has only finite memory. Thus the domain of simulation has to be cut finite. The boundary of this new domain should cause as little echo as possible. The echo-less boundary structures implemented at the boundary are called absorbing boundary conditions. Mathematically, the PML-structure is equivalent for interpreting the real space as a submanifold of the complex space and stretching the real space into the complex direction. In the talk we give introduction to the PML method, show numerical results and explain the connection of PML to quantum mechanical resonances. Presented results are done in collaboration with Erkki Somersalo, Jukka Liukkonen and Seppo Järvenpää.