Efficient space-time adaptivity for parabolic evolution equations using wavelets in time and finite elements in space

This repository contains the implementation that was used to generate the numerics in arXiv:2104.08143 and arXiv:2101.03956.

This project provides a linear complexity implementation of a space-time adaptive solver for parabolic evolution equations. Aiming at a truly linear-complexity implementation, we implemented this algorithm using tree-based algorithms, without the use of hash maps.

Requirements

• A C++17 compliant compiler
• CMake, version >= 3.15

Install instructions

Download the release or clone this repository. Then, build using CMake:

cd spacetime
cmake -S src -B build
cmake --build build

The tests can be run using make -C build test. The adapative method, used for the numerical results in the paper, is given in src/applications/adaptive.cpp. It can be run using the flags specified in the source, e.g.

build/applications/adaptive --problem singular --mark_theta 0.5 --domain l-shape

License

This project is licensed under the terms of the MIT license.