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math.NA2026
The SiMPL Method for Multi-Material Topology Optimization
Peter Gangl, Brendan Keith, Dohyun Kim +2
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal desi…
math.NA2026
Proximal Galerkin for Phase Field Fracture
Miguel Castillón, Biswajit Khara, Jørgen S. Dokken +3
The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of…
math.NA2024
Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints
Brendan Keith, Thomas M. Surowiec
The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise…