[Doc] Adding benchmark documentation

docs/pages/Kratos/For_Developers/General/Benchmarking.md

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+---
+title: Benchmarking in Kratos Multiphysics  
+keywords: Benchmarking, Google Benchmark, Performance Measurement  
+tags: [Benchmarking]  
+sidebar: kratos_for_developers
+summary:  Step-by-step guide on adding and executing benchmarks in Kratos Multiphysics using Google Benchmark.
+---
+
+## Introduction  
+
+Benchmarking is now supported in **Kratos Multiphysics**, enabling developers to measure and analyze the performance of their code effectively. The system integrates seamlessly with [Google Benchmark](https://github.com/google/benchmark), which is included as an external dependency, similar to the **GTest** suite.
+
+### Key Features:
+- Automatic generation of a binary per benchmark source file located in the `benchmark` directory.
+- Benchmark executables are compiled to the binary `benchmark` directory.
+- Activated using the `KRATOS_BUILD_BENCHMARK` CMake option (disabled by default).
+
+### What is Google Benchmark?
+
+[Google Benchmark](https://github.com/google/benchmark) is a library developed by *Google* for microbenchmarking C++ code. It provides:
+
+- Precision and reproducibility in measurements.
+- Built-in support for statistical analysis of timing data.
+- Customizable inputs to benchmarks for more flexible scenarios.
+- Support for benchmarking in multi-threaded and single-threaded environments.
+
+## Writing Benchmarks
+​
+### Overview of Google Benchmark API
+​
+A *Google Benchmark* consists of a **function** that performs repeated measurements of a specific code snippet. The framework automatically manages:
+​
+- Warm-up runs to stabilize performance.
+- Statistical aggregation of results (mean, median, standard deviation, etc.).
+- Handling of scaling issues with large inputs.
+​
+#### Essential Functions:
+​
+- `benchmark::State`: Represents the state of the benchmark, used to control iterations.
+- `BENCHMARK(...)`: Registers a function as a benchmark.
+- `BENCHMARK_MAIN()`: Main entry point for running benchmarks.
+​
+#### Benchmark Configuration Options:
+​
+1. **Repeats**: Specify the number of iterations with `--benchmark_repetitions=N`.
+2. **Time Limit**: Set the time for each benchmark with `--benchmark_min_time=N`.
+3. **Custom Arguments**: Pass custom inputs to benchmarks for parameterized testing.
+
+### Example Benchmark (C++ Code)
+
+Below is an example showcasing how to benchmark the nearest point calculation on a triangle in *Kratos*:
+
+~~~cpp
+// System includes
+
+// External includes
+#include <benchmark/benchmark.h>
+
+// Project includes
+#include "geometries/point.h"
+#include "geometries/triangle_3d_3.h"
+#include "utilities/geometry_utilities/nearest_point_utilities.h"
+
+namespace Kratos
+{
+
+// Sample data for benchmarking
+Point::Pointer p_point_1(make_shared<Point>( 0.0, 0.0, 0.0));
+Point::Pointer p_point_2(make_shared<Point>( 1.0, 0.0, 0.0));
+Point::Pointer p_point_3(make_shared<Point>( 0.0, 1.0, 0.0));
+
+Triangle3D3<Point> triangle(p_point_1, p_point_3, p_point_2);
+Point nearest_point(0.0, 0.0, 0.0);
+Point inside_point(0.2, 0.1, 0.00);
+
+static void BM_TriangleNearestPoint(benchmark::State& state) {
+    for (auto _ : state) {
+        NearestPointUtilities::TriangleNearestPoint(inside_point, triangle, nearest_point);
+    }
+}
+
+// Register the function as a benchmark
+BENCHMARK(BM_TriangleNearestPoint);
+
+}  // namespace Kratos
+
+BENCHMARK_MAIN();
+~~~
+
+### Advanced Features of Google Benchmark
+
+#### Custom Arguments
+
+Benchmarks can take custom arguments to test specific cases. Example:
+
+~~~cpp
+static void BM_CustomArguments(benchmark::State& state) {
+    for (auto _ : state) {
+        int input_size = state.range(0);
+        // Your code here, e.g., filling arrays of size input_size
+    }
+}
+
+BENCHMARK(BM_CustomArguments)->Arg(100)->Arg(1000)->Arg(10000);
+~~~
+
+#### Multithreading Support
+
+Google Benchmark can run benchmarks in multi-threaded mode:
+
+~~~cpp
+static void BM_MultiThreaded(benchmark::State& state) {
+    for (auto _ : state) {
+        // Thread-safe code
+    }
+}
+
+BENCHMARK(BM_MultiThreaded)->Threads(1)->Threads(2)->Threads(4);
+~~~
+
+## Running Benchmarks
+
+### Execution
+
+Once benchmarks are compiled, executables are created in the `benchmark` directory. Run them directly via the command line:
+
+```
+./benchmark_name
+```
+
+### Configuration Options
+
+- **JSON Output**: Export results in JSON format:
+
+```
+./benchmark_name --benchmark_format=json --benchmark_out=output.json
+```
+
+- **Statistical Runs**: Run benchmarks multiple times for statistical accuracy:
+
+```
+./benchmark_name --benchmark_repetitions=10
+```
+
+- **Custom Time Limits**: Specify time per benchmark:
+
+```
+./benchmark_name --benchmark_min_time=2.0
+```
+
+## Comparing Benchmark Results  
+
+The benchmark framework includes a Python utility script to compare results between multiple JSON outputs. This script, located in `kratos/python_scripts/benchmark/generate_plot_google_benchmark.py`, generates visualizations for easier comparison.
+
+### Example Usage:  
+To compare two JSON results:  
+```
+python generate_plot_google_benchmark.py --filenames result1.json result2.json
+```
+
+### Example Output:  
+A plot similar to the one below will be generated, showing the performance (in terms of CPU time and real time) of different benchmarks across the compared files.  
+
+![Benchmark Performance Graph](images/benchmark.png)
+
+## Python Script Explanation  
+
+### Purpose:
+The provided Python script consolidates and visualizes benchmarking data from multiple JSON files generated by Google Benchmark.  
+
+#### Script Functionality:  
+1. **Load JSON Outputs:** Extract benchmark results from each JSON file.  
+2. **Merge Data:** Combine results into a single pandas DataFrame for analysis.  
+3. **Generate Plot:** Create a grouped bar chart showing `cpu_time` and `real_time` for each benchmark.  
+
+## About the Google Benchmark Library
+
+### Benefits
+
+- Accurate Timing: Adjusts for background noise and other factors.
+- Reproducibility: Consistent and repeatable measurements.
+- Customizability: Configure inputs, threads, and scaling scenarios.
+
+### Useful Links
+
+- [Google Benchmark Documentation](https://github.com/google/benchmark)
+- [Google Benchmark Usage Guide](https://github.com/google/benchmark/blob/main/docs/user_guide.md)