The following article covers all three versions: serial, sharedmemory, and
distributedmemory, with a little more emphasis on users aspects:
@article{li05,
AUTHOR = {Xiaoye S. Li},
TITLE = {An Overview of {SuperLU}: Algorithms, Implementation,
and User Interface},
journal = toms,
volume = {31},
number = {3},
month = {September},
year = {2005},
pages = {302325},
}
The Users Guide:
@techreport{superlu_ug99,
AUTHOR = {X.S. Li and J.W. Demmel and J.R. Gilbert and iL. Grigori and M. Shao and
I. Yamazaki},
INSTITUTION = {Lawrence Berkeley National Laboratory},
NUMBER = {LBNL44289},
TITLE = {{SuperLU Users' Guide}},
MONTH = {September},
YEAR = {1999},
NOTE = "\url{https://portal.nersc.gov/project/sparse/superlu/ug.pdf}
Last update: June 2018"
}

If you use sequential SuperLU, please cite the Users Guide and the following article:
@article{superlu99,
author = {James W. Demmel and Stanley C. Eisenstat and
John R. Gilbert and Xiaoye S. Li and Joseph W. H. Liu},
title = {A supernodal approach to sparse partial pivoting},
journal = {SIAM J. Matrix Analysis and Applications},
year = {1999},
volume = {20},
number = {3},
pages = {720755}
}

If you use ILU routines in SuperLU, please cite the following article:
@article{lishao10,
AUTHOR = {Xiaoye S. Li and Meiyue Shao},
TITLE = {A Supernodal approach to incomplete {LU} factorization
with partial pivoting},
JOURNAL = "ACM Trans.\ Mathematical Software",
YEAR = 2010,
VOLUME = {37},
NUMBER = {4},
}

If you use SuperLU_MT (for sharedmemory parallel machines),
please cite the Users Guide and the following article:
@article{superlu_smp99,
author = {James W. Demmel and John R. Gilbert and Xiaoye S. Li},
title = {An Asynchronous Parallel Supernodal Algorithm for
Sparse Gaussian Elimination},
journal = {SIAM J. Matrix Analysis and Applications},
volume = {20},
number = {4},
pages = {915952},
year = {1999}
}

If you use SuperLU_DIST (for distributedmemory parallel machines),
please cite the Users Guide and the following article:
@article{lidemmel03,
author = {Xiaoye S. Li and James W. Demmel},
title = {{SuperLU_DIST}: A Scalable DistributedMemory Sparse Direct
Solver for Unsymmetric Linear Systems},
journal = {ACM Trans. Mathematical Software},
month = {June},
volume = {29},
number = {2},
pages = {110140},
year = 2003
}
If you use the parallel symbolic factorization functionality in SuperLU_DIST,
please also cite the following article:
@article{grigoridemmelli07,
Author = {Laura Grigori and James W. Demmel and Xiaoye S. Li},
Title = {Parallel Symbolic Factorization for Sparse {LU} with
Static Pivoting},
journal = {SIAM J. Scientific Computing},
volume = 29,
number = 3,
pages = {12891314},
year = 2007
}
If you use the parallel heavyweight perfect matching for row permutation
(numerical pivoting in SuperLU_DIST), please also cite the following article:
@article{hwpm,
author = {A. Azad and A. Buluc and X.S. Li and X. Wang and J. Langguth},
title = {{A DistributedMemory Algorithm for Computing a HeavyWeight Perfect Matching
on Bipartite Graphs}},
journal = sisc,
volume = {42},
number = {4},
pages = {C143C168},
year = 2020
}