# Efficient and scalable data structures and algorithms for goal-oriented adaptivity of space-time FEM codes

## TL;DR

This paper introduces efficient data structures and algorithms to enhance goal-oriented space-time adaptivity in FEM codes, improving scalability and performance for complex multi-physics simulations.

## Contribution

It presents a novel, modular approach for embedding DWR-based adaptive methods into FEM tools, addressing extensibility and memory issues.

## Key findings

- Improved scalability of adaptive FEM algorithms.
- Reduced memory consumption in goal-oriented adaptivity.
- Demonstrated efficiency on challenging multi-physics problems.

## Abstract

The cost- and memory-efficient numerical simulation of coupled volume-based multi-physics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goal-oriented space and time adaptive methods derived from the dual weighted residual (DWR) method appear to be a shiny key technology to generate optimal space-time meshes to minimise costs. Current implementations for challenging problems of numerical screening tools including the DWR technology broadly suffer in their extensibility to other problems, in high memory consumption or in missing system solver technologies. This work contributes to the efficient embedding of DWR space-time adaptive methods into numerical screening tools for challenging problems of physically relevance with a new approach of flexible data structures and algorithms on them, a modularised and complete implementation as well as illustrative examples to show the performance and efficiency.