- NRPy+: Introduction & Motivation ([email protected] web page)
- Basic C Code Output, NRPy+'s Parameter Interface
- Numerical Grids
- Indexed Expressions (e.g., tensors, pseudotensors, etc.)
- Finite Difference Derivatives
- Instructional module: How NRPy+ Computes Finite Difference Derivative Coefficients
**Start-to-Finish Example**: Finite-Difference Playground: A Complete C Code for Validating NRPy+-Based Finite Differences

- Application: The Scalar
**Wave Equation**in Cartesian Coordinates, with Plane-Wave Initial Data**Start-to-Finish Example**: Numerically Solving the Scalar Wave Equation: A Complete C Code- Solving the Wave Equation with the **Einstein Toolkit** (
*Courtesy Patrick Nelson*)

- Application (in progress): Two Formulations of
**Maxwell's Equations**in Cartesian Coordinates. (Formulations based on Illustrating Stability Properties of Numerical Relativity in Electrodynamics by Knapp, Walker, and Baumgarte.) (*Courtesy Patrick Nelson*)

- Application: The
**Weyl Scalars and Invariants**in Cartesian Coordinates (*Courtesy Patrick Nelson*)- **WeylScal4NRPy**: An **Einstein Toolkit** Diagnostic Thorn (
*Courtesy Patrick Nelson*)

- **WeylScal4NRPy**: An **Einstein Toolkit** Diagnostic Thorn (

- Moving beyond Cartesian Grids: Reference Metrics
- Application: The Scalar Wave Equation in Curvilinear Coordinates, using a Reference Metric
**Start-to-Finish Example**: Numerically Solving the Scalar Wave Equation in Curvilinear Coordinates: A Complete C Code

**Start-to-Finish Example**: Implementation of Curvilinear Boundary Conditions, Including for Tensorial Quantities- Application: Maxwell's Equations in Curvilinear Coordinates, using a Reference Metric (
*Courtesy Ian Ruchlin*)

**Overview: Covariant BSSN formulation of general relativity in curvilinear coordinates****Initial data modules**. Initial data are set in terms of standard ADM formalism spacetime quantities.- Non-Spinning ("static trumpet") black hole initial data (
*Courtesy Terrence Pierre Jacques & Ian Ruchlin*) - Spinning ("UIUC") Black Hole initial data (
*Courtesy Terrence Pierre Jacques & Ian Ruchlin*) - Brill-Lindquist initial data: Two-black-holes released from rest
- Neutron Star initial data: The Tolman-Oppenheimer-Volkoff (TOV) solution (
*Courtesy Phil Chang*)

- Non-Spinning ("static trumpet") black hole initial data (
**ADM-to-curvilinear-BSSN initial data conversion****Exact**ADM Spherical/Cartesian to BSSN Curvilinear Initial Data Conversion (Use this module for initial data conversion if the initial data are known*exactly*. The BSSN quantity $\lambda^i$ will be computed exactly using SymPy from given ADM quantities.)**Start-to-Finish initial data validation modules**:

**Numerical**ADM Spherical/Cartesian to BSSN Curvilinear Initial Data Conversion (Use this module for initial data conversion if the initial data are provided by an initial data solver, and are thus known to roundoff error at best. The BSSN quantity $\lambda^i$ will be computed using finite-difference derivatives from given ADM quantities.)**Start-to-Finish initial data validation modules**: (Note that UIUC black hole initial data are*exact*; however we choose to set them up as though they were only known numerically, as a validation test for the**numerical**ADM-Spherical-to-BSSN-Curvilinear initial data conversion module. TOV initial data on the other hand are generated via the solution of a system of ODEs, thus are truly known only numerically):

**Start-to-Finish curvilinear BSSN simulation examples**: