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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.
The `equation-free toolbox empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable you to immediately use microscopic simulators to perform macro-scale system level tasks and analysis, because micro-scale simulati
We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations (PDEs) with pa
Goal-oriented dialogue systems typically rely on components specifically developed for a single task or domain. This limits such systems in two different ways: If there is an update in the task domain, the dialogue system usually needs to be updated
The design of online algorithms has tended to focus on algorithms with worst-case guarantees, e.g., bounds on the competitive ratio. However, it is well-known that such algorithms are often overly pessimistic, performing sub-optimally on non-worst-ca
In this paper, we design parallel write-efficient geometric algorithms that perform asymptotically fewer writes than standard algorithms for the same problem. This is motivated by emerging non-volatile memory technologies with read performance being