Uwe Köcher

Helmut Schmidt University / University of the Federal Armed Forces Hamburg | HSU · Numerical Mathematics (Department of Mechanical Engineering)

In this work we present some new variational space-time discretisations for the scalar-valued acoustic wave equation as a prototype model for the vector-valued elastic wave equation. The second-order hyperbolic equation is rewritten as a first-order in time system of equations for the displacement and velocity field. For the discretisation in time...

This paper presents a multirate in time approach for coupled flow and transport problems combined with goal-oriented error control based on the Dual Weighted Residual (DWR) method. The focus is on the implementation of the multirate concept regarding different time scales for the underlying subproblems. Key ingredients are an arbitrary degree disco...

In this work, the dual-weighted residual method is applied to a space-time formulation of nonstationary Stokes and Navier-Stokes flow. Tensor-product space-time finite elements are being used to discretize the variational formulation with discontinuous Galerkin finite elements in time and inf-sup stable Taylor-Hood finite element pairs in space. To...

In this work, a multirate in time approach resolving the different time scales of a convection-dominated transport and coupled fluid flow is developed and studied in view of goal-oriented error control by means of the Dual Weighted Residual (DWR) method. Key ingredients are an arbitrary degree discontinuous Galerkin time discretization of the under...

We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modelling poro- and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in space and time with inf-sup stable pa...

This paper provides an overview of the new features of the finite element library deal.II, version 9.3.

In this work, a flexible higher-order space–time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated transport is a challenging subproblem in poromechanics in which coupled transport with flow, chemical reaction and mechanical response in porous media is cons...

In this work, a flexible, fully space-time adaptive finite element approximation of a prototype multi-physics system coupling fluid flow and convection-dominated transport is developed and studied. By some minor generalization, the model becomes feasible for the simulation of a poroelasticity system. Automatic mesh adaptation is based on the Dual W...

The cost- and memory-efficient finite element simulation of multi-physics problems remains a challenging task. Goal-oriented space and time adaptive methods derived from the dual weighted residual method appear to be a shiny key technology. They offer to generate optimal sequences of space–time meshes to minimise costs. This work contributes to the...

We study the numerical solution of the quasi-static linear Biot equations solved iteratively by the fixed-stress splitting scheme. In each iteration the mechanical and flow problems are decoupled, where the flow problem is solved by keeping an artificial mean stress fixed. This introduces a numerical tuning parameter which can be optimized. We inve...

Interior penalty discontinuous Galerkin discretisations (IPDG) and especially the symmetric variant (SIPG) for time-domain wave propagation problems are broadly accepted and widely used due to their advantageous properties. Linear systems with block structure arise by applying space-time discretisations and reducing the global system to time-slab p...

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 techno...

We study higher-order space-time variational discretisations for modeling complex processes in porous media that include fluid and structure interactions which are of fundamental importance in many engineering fields with applications in subsurface processes, battery-design and biomechanics. For the discretisation in time we deploy discontinuous Ga...

We study higher-order space-time variational discretisations for modeling complex processes in porous media that include fluid and structure interactions which are of fundamental importance in many engineering fields with applications in subsurface processes, battery-design and biomechanics. For the discretisation in time we deploy discontinuous Ga...

We introduce and analyze a post-processing for a family of variational space-time approximations to wave problems. The discretization in space and time is based on continuous finite element methods. The post-processing lifts the fully discrete approximations in time from continuous to continuously differentiable ones. Further, it increases the orde...

We study the numerical solution of the quasi-static linear Biot's equations solved iteratively by the fixed-stress splitting scheme. In each iteration the mechanical and flow problems are decoupled, where the flow problem is solved by keeping an artificial mean stress fixed. This introduces a numerical tuning parameter which can be optimized. We in...

We study the numerical solution of the quasi-static linear Biot's equations solved iteratively by the fixed-stress splitting scheme. In each iteration the mechanical and flow problems are decoupled, where the flow problem is solved by keeping an artificial mean stress fixed. This introduces a numerical tuning parameter which can be optimized. We in...

The accurate, reliable and efficient numerical approximation of multi-physics processes in heterogeneous porous media with varying media coefficients that include fluid flow and structure interactions is of fundamental importance in energy, environmental, petroleum and biomedical engineering applications fields for instance. Important applications...

Interior penalty discontinuous Galerkin discretisations (IPDG) and especially the symmetric variant (SIPG) for time-domain wave propagation problems are broadly accepted and widely used due to their advantageous properties. Linear systems with block structure arise by applying space-time discretisations and reducing the global system to time-slab p...

Variational space-time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods for simulating transport processes in heterogeneous and anisotropic (porous) media have been demonstrated in a wide class of works. We conside...

In this work we analyze an optimized artificial fixed-stress iteration scheme for the numerical approximation of the Biot system modelling fluid flow in deformable porous media. The iteration is based on a prescribed constant artificial volumetric mean total stress in the first half step. The optimization comes through the adaptation of a numerical...

In this work we present an iterative coupling scheme for the quasi-static Biot system of poroelasticity. For the discretization of the subproblems describing mechanical deformation and single-phase flow space-time finite element methods based on a discontinuous Galerkin approximation of the time variable are used. The spatial approximation of the f...

My contribution to this work was to extend my software DTM++, which is based on the deal.II FEM-toolbox, in a way to study the H(div;\Omega) convergence behaviour of higher order time discretisations. The used model is a mass-conservative diffusion equation which is discretised with a mixed finite element method in space. The work is submitted to a...

We develop and study numerically two families of variational time discretization schemes for mixed finite element approximations applied to nonstationary diffusion problems. Continuous and discontinuous approximations of the time variable are encountered. The solution of the arising algebraic block system of equations by a Schur complement techniqu...

Keywords: parallel variational space–time methods, higher order space–time finite element methods. Abstract The accurate and reliable numerical approximation of the hyperbolic wave equation is of fundamental impor-tance to the simulation of acoustic, electromagnetic and elastic wave propagation phenomena. Here, we present families of variational sp...

Composites are one of the most promising materials to build light-weight structures for several fields of application, e.g. for wind energy plants and aerospace applications. Piezo-electric induced ultrasonic waves can be used for the development of structural health mon-itoring (SHM) systems. But, there are still a lot of open questions, especiall...

The numerical solution of hyperbolic second-order wave equations is of fundamental importance to the simulation of time dependent acoustic, electromagnetic of elastic wave prop-agation phenomena. In this work we study numerically higher order continuous and discon-tinuous finite element approximations of the acoustic and elastic wave equation. In p...

Graphic processing units provide a low-cost parallel computing architecture. Only recently emerged their employment in scientific computation as an area of research. We present an implementation of the QR decomposition on the NVDIA GeForce 8800 GT unit using the CUBLAS library made available by the manufacturer and analyze its performance.