An open-source framework for large-scale transient topology optimization using PETSc

Hansotto Kristiansen*, Niels Aage

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


This paper presents a fully parallelized and open-source C++/MPI framework for large-scale transient topology optimization using the density method. The framework comes with two often used time-stepping schemes: the Newmark and the backward Euler methods built-in. By a generalized representation of the temporal residuals as well as the velocity and acceleration approximations, it is easy to extend the framework with additional time-stepping schemes. Four different objective functions are included in the distribution, including kinetic and potential energies. The framework utilizes the fully-discrete adjoint temporal sensitivity analysis to facilitate gradient-based optimization, which ensures easy incorporation of non-zero initial conditions from the forward problem in the adjoint problem. Moreover, the provided sensitivity analysis comes with support for an optional check-pointing scheme in order to reduce the memory requirements for large-scale, non-reduced problems. The option to use a second-order Krylov reduction method with moment matching Gram–Schmidt orthonormalization (SOMMG) is included to increase the computational efficiency of the transient analysis. The framework’s capabilities are demonstrated on numerical examples and the full source code is available at
Original languageEnglish
Article number295
JournalStructural and Multidisciplinary Optimization
Issue number10
Number of pages15
Publication statusPublished - 2022


  • Topology optimization
  • Transient
  • Parallel computing
  • Reduced-order methods
  • Large-scale


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