Update README

Author: felsenhower

README.md

@@ -1 +1,60 @@
-# partdiff
+# partdiff
+
+partdiff is an application to solve partial differential equations using the Gauß-Seidel and Jacobi methods.
+
+It is mainly used for teaching and research purposes.
+
+partdiff was originally created by Thomas Ludwig, Thomas A. Zochler, and Andreas C. Schmidt in Fortran and has since been ported to C.
+
+## Usage
+
+```shell
+$ git clone
+$ cd partdiff
+$ make
+$ ./partdiff
+Usage: ./partdiff [num] [method] [lines] [func] [term] [acc/iter]
+
+  - num:       number of threads (1 .. 1024)
+  - method:    calculation method (1 .. 2)
+                 1: Gauß-Seidel
+                 2: Jacobi
+  - lines:     number of interlines (0 .. 100000)
+                 matrixsize = (interlines * 8) + 9
+  - func:      interference function (1 .. 2)
+                 1: f(x,y) = 0
+                 2: f(x,y) = 2 * pi^2 * sin(pi * x) * sin(pi * y)
+  - term:      termination condition ( 1.. 2)
+                 1: sufficient accuracy
+                 2: number of iterations
+  - acc/iter:  depending on term:
+                 accuracy:   1e-4 .. 1e-20
+                 iterations:    1 .. 200000
+
+Example: ./partdiff 1 2 100 1 2 100
+
+$ ./partdiff 1 2 100 1 2 100
+Calculation time:   0.035731 s
+Memory usage:       9.986588 MiB
+Calculation method: Jacobi
+Interlines:         100
+Inference function: f(x,y) = 0
+Termination:        Number of iterations
+Number iterations:  100
+Residuum:           3.544251e-03
+
+Matrix:
+ 1.0000 0.8750 0.7500 0.6250 0.5000 0.3750 0.2500 0.1250 0.0000
+ 0.8750 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1250
+ 0.7500 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2500
+ 0.6250 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.3750
+ 0.5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.5000
+ 0.3750 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.6250
+ 0.2500 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.7500
+ 0.1250 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.8750
+ 0.0000 0.1250 0.2500 0.3750 0.5000 0.6250 0.7500 0.8750 1.0000
+```
+
+## Regression testing
+
+We use [partdiff_tester](https://github.com/parcio/partdiff_tester) to perform automatic regression tests.