Past Event: Oden Institute Seminar

Space-Time Methods and Goal-Oriented Adaptivity - A Game Changer?

Uwe Koecher, Professor, Helmut Schmidt University, Hamburg, Germany

Abstract

The accurate and efficient approximation in space and time is of fundamental importance for the simulation of dynamic poroelastic models which include coupled fluid flow, deformation, wave propagation and crack propagation. Dynamic poroelastic models appear for example Lithium-ion battery fast-charge simulations as well as in the subsurface considering dynamic problems near wells in which the characteristic reservoir time scale is in the order of the intrinsic characteristic time. They include sharp concentration and pressure gradients,high mechanical stresses, elastic wave propagation, memory-effects on the permeability, multi-phase behaviour and electro-chemical reactions. Space-time methods, in which problems from partial differential equations are discretised uniformly in space and time using finite element methods, attracting interdisciplinary researchers interest again. Space-time methods yield the opportunity for a-priori as well as a-posteriori error estimates and they are barely needed for goal-oriented space-time adaptivity based on duality techniques. Moreover, space-time methods allow naturally the local choice of the subdimensional time length. Therefore, they are for instance under current consideration of the ICES Center of Subsurface Modeling for phase-field crack-propagation simulators to gain computational efficiency. This contribution introduces high-order space-time variational discretisations for subsurface problems, the use of them in goal-oriented space-time adaptive simulations, presents challenging numerical simulations of physical relevance and starts the discussion if those methods will be a game changer in the current and future computational simulation research. References: [1] U. Koecher, M.P. Bruchhaeuser, M. Bause: Efficient and scalable data structures and algorithms for goal-oriented adaptivity of space-time FEM codes, SoftwareX, Elsevier, submitted, p. 1-6, arXiv:1812.08558, 2018. [2] U. Koecher, M. Bause: A mixed discontinuous-continuous Galerkin time discretisation for Biot's system, preprint, arXiv:1805.00771, 2018. [3] M. Bause, F. Radu, U. Koecher: Space-time finite element approximation of the Biot poroelasticity system with iterative coupling,Comput. Meth. Appl. Mech. Engrg. 320:745-768, 2017. Bio: 2019: Guest Visitor of Dr. M.F. Wheeler, Center of Subsurface Modeling (CSM) as J.T. Oden Faculty Fellow, ICES, University of Texas at Austin (Jan-Mar 2019) 2017: (Sep. - Nov.) Guest Visitor of Dr. F.A. Radu, Porous Media Group (PMG), Department of Mathematics, University of Bergen, Norway as E.ON Stipendienfonds Fellow since 2016: Postdoc working on a Habilitation at the chair of Prof. Markus Bause 2011-2015: PhD at the chair of Prof. Markus Bause, Numerical Methods for Computer Aided Engineering/Numerical Mathematics, Helmut-Schmidt-University Hamburg 2015: Doctoral Degree with the Monograph Thesis: "Variational Space-Time Methods for the Elastic Wave Equation and the Diffusion Equation". 2005-2011: Computer Sciences and Engineering (Diploma Degree) at the Technical University of Hamburg, Germany 2011: Diploma Thesis: "Adaptive Reduced Order Methods"