I would like to pose a question that is relatively open. Computational simulation of fracture (crack initiation, crack growth and crack propagation including bifurcation and branching) is a very popular field in applied mechanics research. The complexities of the mechanics involved have prompted numerous approaches to modelling fracture such as eXtended FEM, Cohesive Zone Modelling etc., which have been applied to parallel simulations rather successfully.
For my part, I have been working on Continuum Mechanics based models, such as gradient modelling, phase field modelling, micromorphic modelling etc. The biggest advantage of using this type of approach is the possibility to develop a unified model that can simulate different mechanical processes as a material model (elasticity, plasticity, damage, heat transfer etc.), at various scales of the materials (nano-, micro-, meso- and macro-scale). Via my PhD work I am convinced that this approach to modelling is fairly robust in terms of handling coupled phenomena. Furthermore, it allows for a relatively easy implementation using standard FEM, with or without slightly modified elements (depending on the case).
The problem with these approaches lies in the parallelisation of the simulations. I am wondering if anyone in the RG community has had any experience, or has had any problems in attempting such parallelisation or has developed any algorithm to address this issue. If anyone has succeeded in parallel simulations, could you kindly indicate the numerical details of your simulations (if possible of course). For example, how many nodes, improvement in time observed, type of integration schemes used, elements used, global resolution algorithms used, time stepping techniques, error detection/correction, type of material tested etc. Looking forward to replies.
To be clear, by "parallelisation" I mean computing spread over different nodes on a cluster, which is not the same as "multi-threading", which is relatively straight forward to implement and is a completely different approach.
I also work on continuum modelling specifically in fracture. In methods like phase field modeling of crack (which converts moving boundary crack problem into fixed boundary problem at the expense of addition of new field called phase-field). taking efforts to code for parallisation is justifiable if you are using explicit scheme only. if you are using implicit scheme then don't waste your time because there are already very well developed FEM solvers which can handle explicit scheme far effectively than you could ever code.
I'm developing a multiscale matlab code based in the RVE concept to simulate materials with strong discontinuities (composites with debonded fibers and polycrystalline materials). To improve the time performance, I used the strategy of vectorizing (only available in Matlab, as far as i know), avoiding for loops over each element in both scales. The main advantage of this kind of strategy instead of parallelization, is that it take a really shot time to implement it, improving considerably the algorithm performance. For example, assemble the stiffness matrix (500.000 nodes) in my desk computer (i7, 16Gb ram), via a vectorized code takes 2-3 second. Without vectorization takes more than five minutes. My colleagues are using the same approach for other kind of models (second order plasticity, gradient dependent damage, topological optimization), also with great results.
The largest mesh i used in this code was a 6 million nodes one.
I wanted to share this experience because when i started, i thought in parallelizing as the unique way to improve a code. Later, i discovered that vertorization is a good alternative and it works relativelly fine in multi scale and fracture problems with less than 5 or 6 millon nodes.
I hope it helps
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