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math.NA2026
Finite Elements for Helmholtz Scattering with Infinity as a Computational Boundary
Markus Wess, Anıl ZenginoÄlu
Building on the null-infinity-layer construction, we develop an H1-conforming finite-element formulation of hyperboloidal compactification for the exterior Helmholtz equation. A ch…
math.NA2026
From Penrose to Melrose: Computing Scattering Amplitudes at Infinity for Unbounded Media
Anıl ZenginoÄlu
We develop a method to compute scattering amplitudes for the Helmholtz equation in variable, unbounded media with possibly long-range asymptotics. Combining Penrose's conformal com…
math.NA2024
Swarm-Based Gradient Descent Method for Non-Convex Optimization
Jingcheng Lu, Eitan Tadmor, Anil Zenginoglu
We introduce a new Swarm-Based Gradient Descent (SBGD) method for non-convex optimization. The swarm consists of agents, each is identified with a position, , and mass…