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AlexandersenEtAl2026
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<span id="AlexandersenEtAl2026">J. Alexandersen and M. Appel, “Large-scale topology optimisation of time-dependent thermal conduction using space-time finite elements and a parallel space-time multigrid preconditioner,” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 450, p. 118605, Mar. 2026, doi: 10.1016/j.cma.2025.118605. [Online]. Available at: <a href="http://dx.doi.org/10.1016/j.cma.2025.118605" target="_blank">http://dx.doi.org/10.1016/j.cma.2025.118605</a></span>
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<pre class="abstract">@article{AlexandersenEtAl2026,
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author = {Alexandersen, Joe and Appel, Magnus},
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doi = {10.1016/j.cma.2025.118605},
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issn = {0045-7825},
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journal = {Computer Methods in Applied Mechanics and Engineering},
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month = mar,
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pages = {118605},
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publisher = {Elsevier BV},
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title = {Large-scale topology optimisation of time-dependent thermal conduction using space-time finite elements and a parallel space-time multigrid preconditioner},
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url = {http://dx.doi.org/10.1016/j.cma.2025.118605},
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volume = {450},
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<span id="AluthgeEtAl2026">D. Aluthge, I. Jeffrey, S. Filizadeh, and D. Muthumuni, “Accelerating electromagnetic transient simulations using graphical processing units,” <i>Electric Power Systems Research</i>, vol. 252, p. 112314, Jan. 2026, doi: 10.1016/j.epsr.2025.112314. [Online]. Available at: <a href="http://dx.doi.org/10.1016/j.epsr.2025.112314" target="_blank">http://dx.doi.org/10.1016/j.epsr.2025.112314</a></span>
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<pre class="abstract">@article{AluthgeEtAl2026,
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author = {Aluthge, Devin and Jeffrey, Ian and Filizadeh, Shaahin and Muthumuni, Dharshana},
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doi = {10.1016/j.epsr.2025.112314},
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issn = {0378-7796},
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journal = {Electric Power Systems Research},
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month = jan,
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pages = {112314},
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publisher = {Elsevier BV},
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title = {Accelerating electromagnetic transient simulations using graphical processing units},
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url = {http://dx.doi.org/10.1016/j.epsr.2025.112314},
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volume = {252},
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<span id="HeEtAl2026">T. He, T. Zhai, X. Huang, and M. Li, “The parareal algorithm based on a new local time-integrator for nonlinear Caputo–Hadamard fractional differential equations,” <i>Communications in Nonlinear Science and Numerical Simulation</i>, vol. 152, p. 109183, Jan. 2026, doi: 10.1016/j.cnsns.2025.109183. [Online]. Available at: <a href="http://dx.doi.org/10.1016/j.cnsns.2025.109183" target="_blank">http://dx.doi.org/10.1016/j.cnsns.2025.109183</a></span>
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author = {He, Tingting and Zhai, Tianle and Huang, Xuhang and Li, Min},
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doi = {10.1016/j.cnsns.2025.109183},
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issn = {1007-5704},
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journal = {Communications in Nonlinear Science and Numerical Simulation},
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month = jan,
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pages = {109183},
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publisher = {Elsevier BV},
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title = {The parareal algorithm based on a new local time-integrator for nonlinear Caputo–Hadamard fractional differential equations},
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url = {http://dx.doi.org/10.1016/j.cnsns.2025.109183},
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volume = {152},
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<span id="LiEtAl2025b">Z. Li, A. Onwunta, and B. Sousedík, “Stochastic Galerkin Method and Hierarchical Preconditioning for PDE-constrained Optimization,” arXiv:2512.23804v1 [math.OC], 2025 [Online]. Available at: <a href="https://arxiv.org/abs/2512.23804v1" target="_blank">https://arxiv.org/abs/2512.23804v1</a></span>
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author = {Li, Zhendong and Onwunta, Akwum and Sousedík, Bedřich},
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howpublished = {arXiv:2512.23804v1 [math.OC]},
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title = {Stochastic Galerkin Method and Hierarchical Preconditioning for PDE-constrained Optimization},
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url = {https://arxiv.org/abs/2512.23804v1},
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year = {2025}
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We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element discretization, stochastic Galerkin approximation, and advanced time-discretization schemes, the approach addresses the challenge of large-scale, ill-conditioned linear systems arising in uncertainty quantification. By exploiting the sparsity inherent in generalized polynomial chaos expansions, we derive hierarchical preconditioners based on truncated stochastic expansion that strike an effective balance between computational cost and preconditioning quality. Numerical experiments demonstrate that the proposed preconditioners significantly accelerate the convergence of iterative solvers compared to existing methods, providing robust and efficient solvers for both steady-state and time-dependent optimal control applications under uncertainty.
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