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vineet kshirsagar January 22, 2002 18:00

PML approximation

When we apply PML boundary there a a different set of equations along the PML and the main computational domain (and also different variables). Can any one please suggest to me how should i approximate the values required for the computations of these different variables and equations, along the PML main domain interaction. eg . if i am calculating at i'th grid point (in the main domain) and (i+1)'th gridpoint is in PML domain then how do i approximate the other variables(in the PML domain) for time marchiing for the grid point i, and vice -versa.

the PML equations considered by me are for linearised euler equations and i an using paper by Mr Fang Q Hu " on absorbing boundary conditions for linearised euler equations by a perfectly matched layer" as reference.

thanx in advance


undergraduate student

IIT bombay


paul January 25, 2002 22:43

Re: PML approximation
In Fang's paper, he splitted a variable into two variables. eg. u=u1+u2. But all the derivatives with respect to x and y are for the unsplitted variables. You don't need to use the splitted variables in the main domain. If you need the unsplitted variable u in the PML domain, you only need to add u1 and u2 together.

Hope it is helpful to you!

vineet kshirsagar January 27, 2002 01:59

Re: PML approximation
thanx, but i did not get ur point that i won't need the splitted variables in the main domain.... i understand that main domain doesnot have the splitted variables, but at the boundary ot the PML and the main domain to apply any kind of numerical scheme, i should require its adjecent values, i want to know what should i do in case of such a case, i have done the same as you mentioned when i required "u" in the PML domain, i just added the "u1" and "u2" but whaat should i do if i waht the reverse....

awaiting reply. thanx vineet

paul January 27, 2002 03:54

Re: PML approximation
I think you may solve the eight splitted equations with the absorbing coefficients \sigma equal to 0 in the main domain.

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