ideal.II: a Galerkin Space-Time Extension to the Finite Element Library deal.II
Jan Philipp Thiele
TL;DR
ideal.II extends the deal.II library to facilitate the implementation of space-time finite element schemes for time-dependent problems, providing a unified framework for finite elements in both space and time.
Contribution
The paper introduces ideal.II, a new extension to deal.II that simplifies the development of space-time finite element methods for time-dependent problems.
Findings
Enables easier implementation of space-time finite element schemes.
Integrates with existing deal.II infrastructure for seamless use.
Supports complex space-time problem formulations.
Abstract
The C++ library deal.II provides classes and functions to solve stationary problems with finite elements on one- to threedimensional domains. It also supports the typical way to solve time-dependent problems using time-stepping schemes, either with an implementation by hand or through the use of external libraries like SUNDIALS. A different approach is the usage of finite elements in time as well, which results in space-time finite element schemes. The library ideal.II (short for instationary deal.II) aims to extend deal.II to simplify implementations of the second approach.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Advanced Numerical Methods in Computational Mathematics · Numerical methods in engineering