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DTSTART;TZID=Europe/Paris:20261021T140000
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DTSTAMP:20261002T161023Z
CREATED:20261002T161022Z
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UID:15719-1792591200-1792594800@gem.ec-nantes.fr
SUMMARY:Séminaire Martin Ladecký
DESCRIPTION:Jacobi-Accelerated FFT Solver for Topology Optimization of MetamaterialsMartin Ladeckýmartin.ladecky@imtek.uni-freiburg.deThe exotic properties of mechanical metamaterials arise from the geometry of their microstructure. Topology optimization of microstructures [1] is nontrivial and computationally expensive\, as it requires repeatedly solving homogenization problems. Solvers based on the fast Fourier transform (FFT) are a standard tool for homogenization problems [2\,3]\, offering quasilinear O(N log N) complexity and excellent performance on regular grids. However\, their convergence deteriorates markedly when the material coefficients are smooth and highly contrasted [4]\, a regime frequently encountered in density-based topology optimization.In my talk\, I will present the Jacobi-accelerated FFT (J-FFT) solver [4]\, designed specifically for this setting. The method augments the classical discrete Green operator [5] with a diagonal Jacobi scaling that captures local material contrast while preserving the O(N log N) complexity per iteration. Although the strict grid-size independence of the standard Green preconditioner is relaxed\, the J-FFT solver yields substantially faster convergence for smooth\, high-contrast coefficient fields. In phase-field topology optimization of mechanical metamaterials\, where the density field becomes smooth and highly contrasted\, J-FFT consistently outperforms the standard FFT-based solver.References[1] O. Sigmund\, Materials with prescribed constitutive parameters: An inverse homogenization problem\, Int. J. Solids Struct. 31(17) (1994) 2313–2329.[2] H. Moulinec and P. Suquet\, A fast numerical method for computing the linear and nonlinear mechanical properties of composites\, C. R. Acad. Sci. Paris\, Série II 318(11) (1994) 1417–1423.[3] M. Schneider\, A review of nonlinear FFT-based computational homogenization methods\, Acta Mechanica 232 (2021) 2051–2100.[4] M. Ladecký\, I. Pultarová\, F. Bignonnet\, I. Jödicke\, J. Zeman\, and L. Pastewka\, Jacobi-accelerated FFT-based solver for smooth high-contrast data\, Comput. Methods Appl. Mech. Engrg. 461 (2026) 119269.[5] M. Ladecký\, R. J. Leute\, A. Falsafi\, I. Pultarová\, L. Pastewka\, T. Junge\, and J. Zeman\, An optimal preconditioned FFT-accelerated finite element solver for homogenization\, Appl. Math. Comput. 446 (2023) 127835.
URL:https://gem.ec-nantes.fr/event/seminaire-martin-ladecky/
LOCATION:salle séminaire du Bat 17 sur le site d’Heinlex à Saint-Nazaire\, Rue Pierre-Marie Juret\, Saint-Nazaire\, 44600\, France
ATTACH;FMTTYPE=image/jpeg:https://gem.ec-nantes.fr/wp-content/uploads/2026/10/Martin-Ladecky.jpg
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