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References

The papers and manuals behind this wiki, grouped by what they justify. One line each on why it is cited. To cite this software, see how to cite on the home page.

The package and its lineage

  • Hamada, G. Y. R. and Frantz, R. A. S. linstabpy: open-source compressible stability and resolvent analysis. Theor. Comput. Fluid Dyn. (in preparation, 2026). The paper for this codebase. Prefer it when citing results.
  • Martini, E. and Schmidt, O. T. (2024). LinStab2D: stability and resolvent analysis of compressible viscous flows in MATLAB. Theor. Comput. Fluid Dyn. 38, 665–685. doi:10.1007/s00162-024-00706-0. The methodology ancestor: linearized equations, SBP discretization, metrics, boundary conditions, filtering. Cite alongside the linstabpy paper.
  • Padovan, A., Anantharaman, V., Rowley, C. W., Vollmer, B., Colonius, T. and Bodony, D. J. (2025). resolvent4py: a parallel Python package for analysis, model reduction and control of large-scale linear systems. SoftwareX 31, 102286. doi:10.1016/j.softx.2025.102286. Operator-handling design influence.

Stability and transition theory

  • Schmid, P. J. and Henningson, D. S. (2001). Stability and Transition in Shear Flows. Springer. The textbook companion for modal spectra, branches, and transition physics.
  • Schmid, P. J. (2007). Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129–162. Transient growth, optimal perturbations, and the finite-time viewpoint behind gain maps.
  • Trefethen, L. N., Trefethen, A. E., Reddy, S. C. and Driscoll, T. A. (1993). Hydrodynamic stability without eigenvalues. Science 261, 578–584. Why spectra alone mislead for nonnormal operators; the founding case for pseudospectra thinking.
  • Frantz, R. A. S., Loiseau, J.-Ch. and Robinet, J.-Ch. (2023). Krylov methods for large-scale dynamical systems: application in fluid dynamics. Appl. Mech. Rev. 75(3), 030802. doi:10.1115/1.4056808. Arnoldi factorization, Ritz convergence, modal vs non-modal bounds, Krylov practice. The review behind the solver glossary.
  • Hanifi, A., Schmid, P. J. and Henningson, D. S. (1996). Transient growth in compressible boundary layer flow. Phys. Fluids 8, 826–837. doi:10.1063/1.868864. Compressible transient growth; the wall-normal mapping parameter in the Blasius example follows this work.

Resolvent and adjoint methods

  • McKeon, B. J. and Sharma, A. S. (2010). A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382. Resolvent framing for amplifier flows.
  • Luchini, P. and Bottaro, A. (2014). Adjoint equations in stability analysis. Annu. Rev. Fluid Mech. 46, 493–. The adjoint machinery behind receptivity and wavemaker fields.
  • Chu, B.-T. (1965). On the energy transfer to small disturbances in fluid flow (Part I). Acta Mech. 1(3), 215–234. The compressible energy inner product used for every gain and norm here.

Discretization

  • Strand, B. (1994). Summation by parts for finite difference approximations for d/dx. J. Comput. Phys. 110(1), 47–67. First-derivative SBP operators.
  • Mattsson, K. and Nordstrom, J. (2004). Summation by parts operators for finite difference approximations of second derivatives. J. Comput. Phys. 199(2), 503–540. Second-derivative SBP operators.
  • Mattsson, K., Svard, M. and Nordstrom, J. (2004). Stable and accurate artificial dissipation. J. Sci. Comput. 21, 57–79. doi:10.1023/B:JOMP.0000027955.75872.3f. The dissipation operator behind the epsilon knob.
  • Linders, V., Lundquist, T. and Nordstrom, J. (2018). On the order of accuracy of finite difference operators on diagonal norm based summation-by-parts form. SIAM J. Numer. Anal. 56, 1048–1063. doi:10.1137/17M1139333. Why diagonal-norm boundary closures lose order — and why only even orders 2, 4, 6, 8 ship here.
  • Lele, S. K. (1992). Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42. Centered stencils annihilate the sawtooth mode at any order; the reason grid-scale content needs watching.
  • Fornberg, B. (1988). Generation of finite difference formulas on arbitrarily spaced grids. Math. Comp. 51, 699–706. Weight generation behind the mesh operators.

Solver stack

  • Balay, S. et al. (2025). PETSc/TAO Users Manual (ANL-21/39, Rev. 3.24). Argonne National Laboratory. doi:10.2172/2998643. Distributed matrices, KSP/PC, the runtime under every solve.
  • Hernandez, V., Roman, J. E. and Vidal, V. (2005). SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Software 31(3), 351–362. doi:10.1145/1089014.1089019. EPS eigensolvers and spectral transformations.
  • Amestoy, P. R., Duff, I. S., Koster, J. and L'Excellent, J.-Y. (2001). A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23(1), 15–41. MUMPS, the default sparse-direct backend.