Space and Time Adaptivity

.gitignore

@@ -1,36 +1,37 @@
-## C++ #########################################################################
-
-# Prerequisites
-*.d
-
-# Compiled Object files
-*.slo
-*.lo
-*.o
-*.obj
-
-# Precompiled Headers
-*.gch
-*.pch
-
-# Compiled Dynamic libraries
-*.so
-*.dylib
-*.dll
-
-# Fortran module files
-*.mod
-*.smod
-
-# Compiled Static libraries
-*.lai
-*.la
-*.a
-*.lib
-
-# Executables
-*.exe
-*.out
-*.app
-
-*/build/*
+## C++ #########################################################################
+
+# Prerequisites
+*.d
+
+# Compiled Object files
+*.slo
+*.lo
+*.o
+*.obj
+
+# Precompiled Headers
+*.gch
+*.pch
+
+# Compiled Dynamic libraries
+*.so
+*.dylib
+*.dll
+
+# Fortran module files
+*.mod
+*.smod
+
+# Compiled Static libraries
+*.lai
+*.la
+*.a
+*.lib
+
+# Executables
+*.exe
+*.out
+*.app
+
+build/
+.vscode

CMakeLists.txt

@@ -1,7 +1,10 @@
-cmake_minimum_required(VERSION 3.12.0)
-project(project_title LANGUAGES CXX C)
-
-include(../common/cmake-common.cmake)
-
-add_executable(lab-01 src/lab-01.cpp src/Poisson1D.cpp)
-deal_ii_setup_target(lab-01)
+cmake_minimum_required(VERSION 3.12.0)
+project(project_title LANGUAGES CXX C)
+
+include(common/cmake-common.cmake)
+
+add_executable(H_Heat src/homogeneous/main.cpp src/homogeneous/H_Heat.cpp src/timing/Timing.cpp)
+deal_ii_setup_target(H_Heat)
+
+add_executable(STA_Heat src/adaptive/main.cpp src/adaptive/STA_Heat.cpp src/homogeneous/H_Heat.cpp src/timing/Timing.cpp)
+deal_ii_setup_target(STA_Heat)

README.md

@@ -1,23 +1,78 @@
-### Organizing the source code
-Please place all your sources into the `src` folder.
-
-Binary files must not be uploaded to the repository (including executables).
-
-Mesh files should not be uploaded to the repository. If applicable, upload `gmsh` scripts with suitable instructions to generate the meshes (and ideally a Makefile that runs those instructions). If not applicable, consider uploading the meshes to a different file sharing service, and providing a download link as part of the building and running instructions.
-
-### Compiling
-To build the executable, make sure you have loaded the needed modules with
-```bash
-$ module load gcc-glibc dealii
-```
-Then run the following commands:
-```bash
-$ mkdir build
-$ cd build
-$ cmake ..
-$ make
-```
-The executable will be created into `build`, and can be executed through
-```bash
-$ ./executable-name
-```
+# Space-Time Adaptivity
+
+## Project Information
+
+- **Course:** Numerical Methods for Partial Differential Equations
+- **Authors:** Giacomo Maglio, Francesca Morciano, Giuseppe Hares
+- **Advisor:** Alfio Maria Quarteroni
+- **Co-Advisor:** Michele Bucelli
+- **Academic year:** 2025/2026
+- **Institution:** Politecnico di Milano
+
+This project contains two deal.II-based solvers for the heat equation:
+
+- `H_Heat`: homogeneous reference solver
+- `STA_Heat`: adaptive space-time solver
+
+The code is organized under `src/` and builds with CMake.
+
+## Repository layout
+
+- `src/homogeneous/`: reference solver implementation
+- `src/adaptive/`: adaptive solver implementation
+- `src/timing/`: profiling utilities
+
+## Requirements
+
+You need a working C++ toolchain and deal.II with MPI support.
+
+Environment setup:
+
+```bash
+$ apptainer shell *.sif
+$ source /u/sw/etc/bash.bashrc
+$ module load gcc-glibc dealii
+```
+
+## Build
+
+From the repository root:
+
+```bash
+$ mkdir build
+$ cd build
+$ cmake ..
+$ make
+```
+
+This creates the executables inside `build/`.
+
+## Run
+
+Available executables:
+
+- `build/H_Heat`
+- `build/STA_Heat`
+
+Run them from the build directory, for example:
+
+```bash
+$ cd build
+$ mpirun -n <number of threads> ./H_Heat  # to run the homogenous solver
+$ mpirun -n <number of threads> ./STA_Heat # to run the adaptive solver
+```
+
+Both executables currently use hardcoded parameters in their respective `main.cpp` files.
+To change time step, final time, or forcing term, edit:
+
+- `src/homogeneous/main.cpp`
+- `src/adaptive/main.cpp`
+
+## Output
+
+The solvers write output files in the build directory.
+
+## Notes
+
+- The adaptive executable contains an optional baseline-comparison path behind the `COMPARE_WITH_BASE` macro.
+- If you want to compare adaptive and homogeneous results, enable that macro in `src/adaptive/main.cpp` and ensure the baseline mesh is available.

common/cmake-common.cmake

@@ -0,0 +1,34 @@
+set(CMAKE_CXX_STANDARD 17)
+set(CMAKE_CXX_STANDARD_REQUIRED "ON")
+set(CMAKE_CXX_FLAGS "-O3 -march=native -ffast-math")
+
+# Set default build type to Release.
+if(NOT CMAKE_BUILD_TYPE OR "${CMAKE_BUILD_TYPE}" STREQUAL "")
+  set(CMAKE_BUILD_TYPE "Release" CACHE STRING "" FORCE)
+endif()
+message(STATUS)
+message(STATUS "Build type: ${CMAKE_BUILD_TYPE}")
+message(STATUS)
+if("${CMAKE_BUILD_TYPE}" STREQUAL "Debug")
+  add_definitions(-DBUILD_TYPE_DEBUG)
+endif()
+
+# Locate MPI compiler.
+find_package(MPI REQUIRED)
+set(CMAKE_CXX_COMPILER "${MPI_CXX_COMPILER}")
+
+# Locate Boost.
+find_package(Boost 1.72.0 REQUIRED
+  COMPONENTS filesystem iostreams serialization
+  HINTS ${BOOST_DIR} $ENV{BOOST_DIR} $ENV{mkBoostPrefix})
+message(STATUS "Using the Boost-${Boost_VERSION} configuration found at ${Boost_DIR}")
+message(STATUS)
+include_directories(${Boost_INCLUDE_DIRS})
+
+# Locate deal.II and initialize its variables.
+find_package(deal.II 9.3.1 REQUIRED
+  HINTS ${DEAL_II_DIR} $ENV{DEAL_II_DIR} $ENV{mkDealiiPrefix})
+deal_ii_initialize_cached_variables()
+
+# Add useful compiler flags.
+set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wfloat-conversion -Wmissing-braces -Wnon-virtual-dtor")

experiments_results/baseline_comparison.txt

@@ -0,0 +1,110 @@
+=======================================================================
+                    Space and Time Adaptivity
+=======================================================================
+
+Baseline Results
+Number of steps: 40
+Elapsed Time:
+---------------------------------------------------------------
+Timer             Calls     Min(s)    Avg(s)    Max(s)    Total(s)
+---------------------------------------------------------------
+update-ghost      40        1.17e-04  1.92e-04  4.22e-04  7.69e-03
+solve             40        6.74e-02  8.87e-02  1.37e-01  3.55e+00
+output            40        7.12e-02  8.70e-02  1.39e-01  3.48e+00
+assemble          40        1.82e-01  2.13e-01  2.61e-01  8.50e+00
+setup             1         3.13e-01  3.13e-01  3.13e-01  3.13e-01
+---------------------------------------------------------------
+Number of DoFs: 35937
+
+Adaptivity Results
+Number of steps: 42
+Elapsed Time:
+---------------------------------------------------------------
+Timer             Calls     Min(s)    Avg(s)    Max(s)    Total(s)
+---------------------------------------------------------------
+refine            12        1.96e-01  3.56e-01  8.15e-01  4.28e+00
+time-adap         28        1.06e-01  1.41e-01  2.12e-01  3.95e+00
+solve             42        2.27e-01  3.12e-01  4.82e-01  1.31e+01
+output            28        1.06e-01  1.40e-01  2.11e-01  3.93e+00
+assemble          42        1.87e-01  3.26e-01  5.21e-01  1.37e+01
+update-ghost      73        1.10e-05  3.20e-04  1.20e-03  2.34e-02
+setup             1         1.79e-01  1.79e-01  1.79e-01  1.79e-01
+---------------------------------------------------------------
+Max number of DoFs: 82891
+
+Computing L2 against baseline
+L2_error = 1.33e-03
+
+=======================================================================
+                         Only Space Adaptivity
+=======================================================================
+
+Baseline Results
+Number of steps: 40
+Elapsed Time:
+---------------------------------------------------------------
+Timer             Calls     Min(s)    Avg(s)    Max(s)    Total(s)
+---------------------------------------------------------------
+update-ghost      40        1.19e-04  1.92e-04  5.98e-04  7.67e-03
+solve             40        7.31e-02  8.91e-02  1.33e-01  3.56e+00
+output            40        7.35e-02  8.89e-02  1.15e-01  3.56e+00
+assemble          40        1.84e-01  2.14e-01  2.98e-01  8.55e+00
+setup             1         3.38e-01  3.38e-01  3.38e-01  3.38e-01
+---------------------------------------------------------------
+Number of DoFs: 35937
+
+Adaptivity Results
+Number of steps: 20
+Elapsed Time:
+---------------------------------------------------------------
+Timer             Calls     Min(s)    Avg(s)    Max(s)    Total(s)
+---------------------------------------------------------------
+refine            5         2.21e-01  5.87e-01  1.04e+00  2.93e+00
+time-adap         20        8.22e-02  1.60e-01  2.64e-01  3.20e+00
+solve             20        1.39e-01  3.44e-01  5.44e-01  6.89e+00
+output            20        8.19e-02  1.59e-01  2.62e-01  3.17e+00
+assemble          20        2.09e-01  3.70e-01  5.98e-01  7.40e+00
+update-ghost      43        1.39e-05  3.86e-04  1.42e-03  1.66e-02
+setup             1         2.55e-01  2.55e-01  2.55e-01  2.55e-01
+---------------------------------------------------------------
+Max number of DoFs: 99978
+
+Computing L2 against baseline
+L2_error = 6.56e-05
+
+
+=======================================================================
+                         Only Time Adaptivity
+=======================================================================
+
+Baseline Results
+Number of steps: 40
+Elapsed Time:
+---------------------------------------------------------------
+Timer             Calls     Min(s)    Avg(s)    Max(s)    Total(s)
+---------------------------------------------------------------
+update-ghost      40        1.09e-04  2.17e-04  5.24e-04  8.66e-03
+solve             40        6.77e-02  8.45e-02  1.17e-01  3.38e+00
+output            40        6.84e-02  8.88e-02  1.41e-01  3.55e+00
+assemble          40        1.83e-01  2.16e-01  2.72e-01  8.63e+00
+setup             1         1.80e-01  1.80e-01  1.80e-01  1.80e-01
+---------------------------------------------------------------
+Number of DoFs: 35937
+
+Adaptivity Results
+Number of steps: 40
+Elapsed Time:
+---------------------------------------------------------------
+Timer             Calls     Min(s)    Avg(s)    Max(s)    Total(s)
+---------------------------------------------------------------
+time-adap         27        7.31e-02  8.56e-02  1.12e-01  2.31e+00
+solve             40        1.28e-01  1.92e-01  2.57e-01  7.69e+00
+output            27        7.27e-02  8.51e-02  1.12e-01  2.30e+00
+assemble          40        1.72e-01  2.07e-01  2.49e-01  8.27e+00
+update-ghost      67        5.00e-05  2.39e-04  6.81e-04  1.60e-02
+setup             1         2.26e-01  2.26e-01  2.26e-01  2.26e-01
+---------------------------------------------------------------
+Max number of DoFs: 35937
+
+Computing L2 against baseline
+L2_error = 1.35e-03