The development of BEM has gone through the process of traditional BEM, fast multipolar BEM, isogeometric BEM, etc. However, when solving complex problems with source terms and heterogeneous materials, no matter which BEM can not avoid the trouble brought by fundamental solutions, such as the transformation of domain integrals. Where do you think the boundary element method should go now? Where is the spring of the boundary element method? Does the boundary element method end up solving problems that are simple and do not involve domain integrals?
I select the method (FDM, FEM, FVM, FIM, BEM, etc.) depending on which one works best for the particular problem I am investigating. I use all of these methods. I choose the method based on the problem, not the problem based on the method. I don't expect BEM to solve every type of problem. I can see no reason to endlessly modify the BEM just to solve ever differing problems, as this would be an inefficient use of time and resources. BEM is a very clever and efficient way of solving a class of problems. I can run all 20 of problems illustrated in the above gif and output the graphics in 80 sec using BEM (not 80 seconds each, 80 seconds for all of them plus create the gif). [sorry, you have to download the file to "play" through the frames, as RG no longer animates gifs]
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