Thanks John for the information on skyline solvers. There was an issue about those here at Discourse, with the implementation coming from a textbook by K. J. Bathe, see Replacing legacy code with Julia - #16 by ivanpribec
S. W. Sloan (1954 - 2019), that you mentioned above, published several works on equation reordering,
- Sloan, S. W., & Randolph, M. F. (1983). Automatic element reordering for finite element analysis with frontal solution schemes. International Journal for Numerical Methods in Engineering , 19 (8), 1153-1181. https://doi.org/10.1002/nme.1620190805
- Sloan, S. W. (1986). An algorithm for profile and wavefront reduction of sparse matrices. International Journal for Numerical Methods in Engineering , 23 (2), 239-251. https://doi.org/10.1002/nme.1620230208
- Sloan, S. W. (1989). A FORTRAN program for profile and wavefront reduction. International Journal for Numerical Methods in Engineering , 28 (11), 2651-2679. https://doi.org/10.1002/nme.1620281111
- Sloan, S. W., & Ng, W. S. (1989). A direct comparison of three algorithms for reducing profile and wavefront. Computers & Structures , 33 (2), 411-419. Redirecting
He also published several other algorithms useful in implementing finite-element methods. For instance his sorting routines (joint work with Guy T. Houlsby - another professor of civil engineering) work very well. (Houlsby has published some software on GitHub - guyhoulsby/HyperDrive: HyperDrive and associated code)
Intel used to provide a skyline solver as part of MKL, but I recall reading that it was removed in favor of other direct and iterative methods.
Edit: the journals IJNME and AES contain a lot of useful algorithms, most implemented in Fortran if you look at the earlier issues.