I am trying simulate an infinite domain so I need to use non-reflective boundary conditions. While searching, I came across PML method, but I have certain doubts.
1) How to decide the dimensions of the PML layer?
2) What effect does PML mesh size have on the reflected waves?
I am using TNO DIANA and I simulated a block of soil of 50 m subjected to an impulse load and tried to see the wave travel. I used PML lengths of 10 to 50 m . However, I can still see waves reflecting back. I also tried to increase the function values assigned at the PML boundaries, but after one point I see that the PML behaves like a clamped or fixed boundary. Can someone point me to a source where PML is explained clearly?
Thank you very much.
In my opinion PML are very well explained here:
http://math.mit.edu/~stevenj/18.369/pml.pdf
I hope you find it useful.
Best.
We have tried to develop a novel approach for semi-infinite domains in this paper
http://onlinelibrary.wiley.com/doi/10.1002/fld.3768/full
maybe similar ideas can be useful for your application as well.
Dear Nischal Sehrawat,
I don't know much about TNO DIANA, but usually the length of PML 8-10 times lamda (wavelength) and width 2 time lamda is enough. In such type of simulation the mesh quality should be very fine about lamda/100 (for 2D model).
I suggest you, built your model with dimensions in term of lamda and assign mesh size also as function of the lamda. This might work for you. My paper is under review, I cannot share but work given below may give you rough insight. I hope it helps
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Hi Nischal,
I know the question is old and with some help you managed in DIANA. For future reference the link to our tutorial :
https://dianafea.com/system/files/tutorial-machinefoundation103.pdf
(and good luck on your new job) Ab
The general idea is that PML once discretized and implemented in a numerical scheme results into a number of finite layers and is no longer defined as a continuous medium as depicted in the original theory.
The decision of the various control parameters of the PML (e.g number of layers/ dimensions of PML , theoretical reflection factor, mesh discretization e.t.c) is tricky and in my experience requires a bit of trial and error. Ideally you want to introduce a grading into the layer which prevents high reflections at the first layer. The higher the number of layers for a particular grading then the less reflections are generated at the first layer.
For guidance I would suggest 10-15 layers for your first trials. I would then trial various conductivity values ( or theoretical reflection factors) to see which generates the lowest reflections.
Once you find a good range then you can carry out more variations in the control parameters.
All in all, the PML requires some tuning and finding the best value varies for each experiments.
Hope this is helpful.
Dear Nischal Sehrawat, The PML mathematical implementation consists of the introduction of a modified coordinate system, where an expansion coefficient is a complex number with an evanescent imaginary part. This generalization is achieved through the substitution provided in the screenshot:
Article Perfectly matched layers simulation in two-dimensional VTI media
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