NGSDiffGeo

NGSDiffGeo extends NGSolve with differential-geometry operations, with a focus on Riemannian manifolds. Start with the geometry foundations below, then follow the Regge and curvature tutorials or use the calculus notebooks as references.

We gratefully acknowledge support by the Austrian Science Foundation FWF through project J4824, Numerical analysis of curvatures from Regge finite elements.

Getting Started

• Installation
• License

Geometry foundations

• Riemannian Manifolds
• Covariant Derivatives
• Curvature quantities on Riemannian manifolds
• Gauss-Bonnet theorem

Regge metrics and Gauss curvature

• Regge finite elements and Regge metrics
• Distributional Gauss curvature
• Distributional Gauss curvature (analysis)
• Gauss curvature approximation on embedded surfaces

Higher-dimensional curvature and linearization

• Distributional scalar curvature
• Distributional Einstein curvature
• Distributional Riemann curvature tensor
• Linearization of curvature quantities

Exterior calculus and hypersurfaces

• Alternating k-forms, wedge product, Hodge star, and exterior (co-) derivative
• Double forms
• Exterior covariant derivatives of double forms
• Differential operators and curvature on hypersurfaces

Developer Guide

• Developer guide