#RBF-FD-Prototype

Overview: This is a prototype PDE solver. Supported time integration schemes are either RK3 or RK4. 
The model is designed to easily integate new systems of equations by creating a new rhs 
function f* in rhs.c.

Language. The code is written in C, but be advised it needs a lot of cleaning up.

Precision. The code supports easy toggling between float or double execution. 
To change precision, go to floating_types.h and toggle the fType typedef.

Compilers. The code has only been tested on the Clang 11 compiler.

Parallelism. It is serial - all MPI, OpenMP, OpenCL and OpenACC has been stripped out.

##Test Cases

There are three supported test cases: {simple, aero, swe}

{simple} is an system of one equation.

{aero} integrates two equations and simulates a falling body with a drag term.

{swe} integrates the Drake and Williamson Test Case 5 (flow over a mountain) for the 
shallow water equations on the sphere using the Radial Basis Function Finite Difference (RBD-FD) Method. 
The swe case requires an initialization file. The code builds the 10,242 "node" case on an 
icosahedral grid, although the code is completely unstructured. In RBFs terminology "node"
corresponds to the notion of a grid point. 

{straka} a nonhydrostatic atmospheric test case, again using RBF-FD. Strake is under 
development, not supported at this time.

## Build 

To compile the PDE solver:

```bash
make clean
make
```
## Run

To run the PDE solver:

```bash
./pdex case
```
Where case = {simple, aero, swe}

##Correctness

{swe} Only swe has a built in test verification. 

For single precision:

u L1 error = 9.143353e-05
v L1 error = 7.724762e-05
w L1 error = 6.432120e-05
h L1 error = 2.081906e-02

For double precision:

u L1 error = 7.660539e-14
v L1 error = 6.772360e-14
w L1 error = 5.123566e-14
h L1 error = 1.455192e-11

##Performance

Serial performance (Clang 11.0) on 2.6 GHz Intel Core i7:

time in rhs = 0.005265 Gflops = 8.233032
time in update = 0.000127 Gflops = 3.860712

## License

GNU General Public License v3.0