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:

$ apptainer shell *.sif
$ source /u/sw/etc/bash.bashrc
$ module load gcc-glibc dealii

Build

From the repository root:

$ 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:

$ 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.