When citing computations performed with PETSc in a publication, plus run the application code with all the options you usually use and the option -citations optionalfilename This will generate a list of bibtex references appropriate for that computation.

If you utilize the TS ODE/DAE solvers please cite

     @article{abhyankar2018petsc,
       author={Abhyankar, Shrirang and Brown, Jed and Constantinescu, Emil M and Ghosh, Debojyoti and Smith, Barry F and Zhang, Hong},
       title={PETSc/TS: A Modern Scalable ODE/DAE Solver Library},
       journal={arXiv preprint arXiv:1806.01437},
       year={2018}
     }
  
Also please cite the following:
     @Misc{petsc-web-page,
       author = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Jed Brown and Peter Brune
                 and Kris Buschelman and Lisandro Dalcin and Alp Dener and Victor Eijkhout and William~D. Gropp
                 and Dinesh Kaushik and Matthew~G. Knepley and Dave~A. May and Lois Curfman McInnes
                 and Richard Tran Mills and Todd Munson and Karl Rupp and Patrick Sanan
                 and Barry~F. Smith and Stefano Zampini and Hong Zhang and Hong Zhang},
       title =  {{PETS}c {W}eb page},
       url =    {http://www.mcs.anl.gov/petsc},
       howpublished = {\url{http://www.mcs.anl.gov/petsc}},
       year = {2018}
     }

     @TechReport{petsc-user-ref,
       author = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Jed Brown and Peter Brune
                 and Kris Buschelman and Lisandro Dalcin and Alp Dener and Victor Eijkhout and William~D. Gropp
                 and Dinesh Kaushik and Matthew~G. Knepley and Dave~A. May and Lois Curfman McInnes
                 and Richard Tran Mills and Todd Munson and Karl Rupp and Patrick Sanan
                 and Barry~F. Smith and Stefano Zampini and Hong Zhang and Hong Zhang},
       title  = {{PETS}c Users Manual},
       institution = {Argonne National Laboratory},
       year   = 2018,
       number = {ANL-95/11 - Revision 3.10},
       url    = {http://www.mcs.anl.gov/petsc}
     }

     @InProceedings{petsc-efficient,
       Author = "Satish Balay and William D. Gropp and Lois Curfman McInnes and Barry F. Smith",
       Title = "Efficient Management of Parallelism in Object Oriented Numerical Software Libraries",
       Booktitle = "Modern Software Tools in Scientific Computing",
       Editor = "E. Arge and A. M. Bruaset and H. P. Langtangen",
       Pages = "163--202",
       Publisher = "Birkh{\"{a}}user Press",
       Year = "1997"
      }