Efficient and scalable data structures and algorithms for goal-oriented adaptivity of space-time FEM codes
arXiv:1812.08558 · doi:10.1016/j.softx.2019.100239
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.
References in corpus (2)
Cited by in corpus (7)
- Flexible goal-oriented adaptivity for higher-order space-time discretizations of transport problems with coupled flow
- Dual weighted residual based error control for nonstationary convection-dominated equations: potential or ballast?
- A Posteriori Single- and Multi-Goal Error Control and Adaptivity for Partial Differential Equations
- Numerical study of goal-oriented error control for stabilized finite element methods
- A Cost-Efficient Space-Time Adaptive Algorithm for Coupled Flow and Transport
- Hierarchical DWR Error Estimates for the Navier Stokes Equation: and Enrichment
- Anisotropic hp space-time adaptivity and goal-oriented error control for convection-dominated problems