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# Efficient space-time adaptivity for parabolic evolution equations using wavelets in time and finite elements in space
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This repository contains an implementation of arXiv:2101.03956, as described in.
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This repository contains the implementation that was used to generate the numerics in arXiv:2104.08143 and arXiv:2101.03956.
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This project provides a linear complexity implementation of a space-time
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adaptive solver for parabolic evolution equations. The trial spaces that
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we consider here are given as sparse tensor product approximations
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of wavelets-in-time and (locally refined) finite element spaces-in-space.
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Special care has to be taken to evaluate matrix-vector products, as the
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system-matrix w.r.t. such a multi-level type basis is not sparse. By restricting
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to bases that are spanned by tensor products having index sets that form double-trees,
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we can still evaluate the system matrices in linear complexity.
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Aiming at a truly linear-complexity implementation, we implemented this algorithm
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using tree-based algorithms, without the use of hash maps.
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adaptive solver for parabolic evolution equations. Aiming at a truly linear-complexity
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implementation, we implemented this algorithm using tree-based algorithms, without the use of hash maps.
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## Requirements
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- A C++17 compliant compiler

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