I am developing a MATLAB code for shock problem and want to divide the FE domain into explicit and implicit elements (region of domain at vicinity to shock is meshed into explicit elements and region of domain farther from shock into implicit elements) so as to apply Explict-Implicit time integration scheme developed by Hughes and Liu 'Implicit-Explicit Finite Elements in Transient Analysis: Implementation and Numerical Examples'. So, if the domain is of certain length, how can I estimate up to what certain length of the domain should be meshed with explicit elements and rest with implicit elements?
I don't know about your problem domain, but I got the gist about your requirement. Do tell me if it helps.
For a problem involving traveling waves or discontinuity, you can always trace them and put tag on those element to get a curve of discontinuity. They are easy to detect as state of domain on either side of shockwave are different(for gases, it's pressure; for tsunami, it's hydraulic elevation). You can involve a conditional statement like: if (d(pressure) > epsilon) then tag it for discontinuity.
Shocks usually involves non-linearity in domain which makes it dificult to stabilize. The region to involve in explicit domain could be according to your choice and try comparing it to standard results by any other simulation.
Or you can always find entropy solution for your problem. Entropy solutions are used for adaptive mesh refinement near the waves and can give you enough idea about what regions to consider in explcit region.
Thank you, @ Abhishek Singh for your suggestions. The problem domain is a structural member, a 1-D uniform long bar with one end fixed subjected to suddenly applied load at its free end. I will look into your suggestions and will let you know.
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