A constrained LLM front-end for FEniCS multi-physics simulations dispatches to human-written templates and achieves 100% valid parses plus 90-100% geometry success on benchmarks while avoiding LLM-generated solver code.
Unified form language: A domain-specific language for weak formulations of partial differential equations
9 Pith papers cite this work, alongside 582 external citations. Polarity classification is still indexing.
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A structure-preserving upwind DG scheme with convex splitting for the Cahn-Hilliard-Darcy tumor growth model that maintains mass conservation, pointwise bounds, and a discrete energy law.
A Bloch domain wall in a ferromagnetic racetrack between superconductors allows position-based control of the Josephson critical current with tunable 0-pi transitions and current loop formation.
Stochastic material heterogeneity modeled with Gaussian random fields in a nonlocal framework fundamentally changes phase nucleation, localization, and macroscopic mechanical response in architected metamaterials.
Numerical construction of Hayward boson stars shows that frozen states produce Schwarzschild-like shadows with no extra photon rings while non-frozen states show multiple photon rings inside the shadow.
Metriplectic systems converge to entropy extrema at fixed Hamiltonian under stated conditions; a Landau-inspired class reduces the check to two simpler conditions for use in equilibrium relaxation schemes.
A novel linear upwind DG method for local and nonlocal chemotaxis models with nonlinear diffusion, attraction/repulsion, logistic growth and damping that preserves positivity and prevents numerical blow-up.
A conformal finite element and implicit Euler discretization is proposed and analyzed for the Biot-contact variational problem, proving existence, uniqueness, stability, and a priori error estimates, with numerical verification of the rates.
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Influence of Heterogeneity on the Response of Architected Metamaterials
Stochastic material heterogeneity modeled with Gaussian random fields in a nonlocal framework fundamentally changes phase nucleation, localization, and macroscopic mechanical response in architected metamaterials.