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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 Discontinuous Galerkin Methods for Variational Inequalities
Alexandre Ern, Brendan Keith, Dohyun Kim +2
We introduce a family of proximal discontinuous Galerkin methods for variational inequalities, focusing on the obstacle problem as a didactic example. Each member of this family is…
math.NA2026
The proximal Galerkin method for non-symmetric variational inequalities
Guosheng Fu, Brendan Keith, Dohyun Kim +2
We introduce the proximal Galerkin (PG) method for non-symmetric variational inequalities. The proposed approach is asymptotically mesh-independent and yields constraint-preserving…