Dear all, I am implementing a Maxwell harmonic simulation in FEniCS. I should also note from the outset that I am interested in PDE-constrained optimization of some material distribution, .
In wave scattering simulations one needs absorbing boundary conditions, e.g. the "perfectly matched layer" (a "frame" delimiting the simulation box in which some absorption parameter is smoothly increased). In general, the 3D harmonic equation in the magnetic field H, with vacuum wavevector k0, looks like this: rot(1/epsr rot( H )) = k0^2 H + Ji where Ji is a vector source current term and epsr is the (scalar, complex) dielectric permittivity. With the introduction of a PML, the previous eqn. looks as follows: rot( 1/epsr L^-1 rot( H )) = k0^2 L H + Ji where L is a 3x3 diagonal matrix, with (scalar, complex) distinct elements, each a function of position. One approximation is setting the contents of L to be constant within each element. QUESTION: can the elements of L be represented as scalar fields, just like any other field? how are smooth functions defined piecewise on the mesh? (in order to test whether higher order elements lead to smaller spurious reflections) Thank you in advance and kind regards, Marco
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