4 papers
Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inference
Luis Mandl, Dibyajyoti Nayak, Tim Ricken +1
Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning.…
Insights into experimental evaluation of the non-fourier heat transfer model in biological tissues
Mohammad Azhdari, Ghader Rezazadeh, Raghav Pathak +4
A comprehensive understanding of heat transfer mechanisms in biological tissues is essential for the advancement of thermal therapeutic techniques and the development of accurate b…
Least-Squares Finite Element Methods for nonlinear problems: A unified framework
Fleurianne Bertrand, Maximilian Brodbeck, Tim Ricken +1
This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A L…
Adaptive finite element methods based on flux and stress equilibration using FEniCSx
Maximilian Brodbeck, Fleurianne Bertrand, Tim Ricken
This contribution shows how a-posteriori error estimators based on equilibrated fluxes - H(div) functions fulfilling the underlying conservation law - can be implemented in FEniCSx…