# directory

PDEPartial differential equations.

### Contents

- Reference

This directory contains implementations of spatial discretizations for *partial* differential equations (PDE). (*Partial* as opposed to *ordinary* differential equations in `src/DiffEq`

). At this time, all of these PDEs are used exclusively by Inciter.

`Configure<eq>.[Ch]`

contain functionality related to registration and querying user-configuration information on specific equation types.

All specific equation types "inherit" from a common "base" so that user-configured instances of multiple specific equations (as a potentially coupled system) can be integrated in a generic fashion. This is done using concept-based runtime polymorphism.

The specific equation types are registered into a factory, which leads to generic code for configuring and using existing equation types and adding new ones.

Currently, there are two families of spatial discretizations (or *schemes*) implemented: *continuous* and *discontinuous* Galerkin (CG, DG) finite element methods (FEM). Correspondingly, there are two factories into which PDEs are registered, inciter::

CG discretization in space is combined with a time stepping scheme that is equivalent to the Lax-Wendroff (LW) scheme adopted to the unstructured-mesh finite element context and treats discontinuities with flux-corrected transport (FCT).

DG discretization in space is combined with Runge-Kutta time stepping.

## Directories

## Files

- file CGPDE.h
- Partial differential equation base for continuous Galerkin PDEs.
- file ConfigureCompFlow.C
- Register and compile configuration for compressible flow PDE.
- file ConfigureCompFlow.h
- Register and compile configuration for compressible flow PDE.
- file ConfigureMultiMat.C
- Register and compile configuration for multi-material compressible flow PDE.
- file ConfigureMultiMat.h
- Register and compile configuration for multi-material compressible flow PDE.
- file ConfigureTransport.C
- Register and compile configuration on the transport PDE.
- file ConfigureTransport.h
- Register and compile configuration on the Transport PDE.
- file DGPDE.h
- Partial differential equation base for discontinuous Galerkin PDEs.
- file FunctionPrototypes.h
- Function prototypes used in PDE classes.
- file Limiter.C
- Limiters for DG.
- file Limiter.h
- Limiters for discontinous Galerkin methods.
- file PDEFactory.h
- Differential equations factory.
- file PDEStack.C
- Stack of partial differential equations.
- file PDEStack.h
- Stack of differential equations.