# Thomas WickLeibniz Universität Hannover · Institute of Applied Mathematics

Thomas Wick

Professor

My 2020 book has been translated into Chinese.

## About

245

Publications

43,707

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

5,613

Citations

Introduction

Thomas Wick is a Professor for Scientific Computing at the Leibniz Universität Hannover. His research interests are design, implementation and analysis of numerical methods and algorithms for computational fluid dynamics, solids, multiphysics and crack propagation. He is also interested in error estimation and adaptive methods such as local mesh adaptivity with emphasis on goal-oriented techniques, and numerical optimization, such as optimal control; please see also https://thomaswick.org/

Additional affiliations

October 2017 - February 2022

September 2016 - September 2017

April 2015 - September 2015

Education

November 2008 - December 2011

January 2007 - October 2008

October 2003 - December 2006

## Publications

Publications (245)

In this work, restricted additive Schwarz (RAS) and optimized restricted additive Schwarz (ORAS) preconditioners from the Trilinos package FROSch (Fast and Robust Overlapping Schwarz) are employed to solve model problems implemented using deal.II (differential equations analysis library). Therefore, a Tpetra-based interface for coupling deal.II and...

The mechanics of fracture propagation provides essential knowledge for the risk tolerance design of devices, structures, and vehicles. Techniques of free energy minimization provide guidance, but have limited applicability to material systems evolving away from equilibrium. Experimental evidence shows that the material response depends on driving f...

This contribution addresses the problem of controlling the Degree of Crosslinking (DoC) in printed hydrogels through feedback control as a product quality indicator from a modeling approach. We set up a simulation that resembles co‐axial printing of calcium‐alginate (Ca‐Alg) hydrogel as a case study. A well‐known Ca‐Alg gelation model composed of a...

Geothermal energy, a promising renewable source, relies on efficiently utilizing geothermal reservoirs, especially in Enhanced Geothermal Systems (EGS), where fractures in hot rock formations enhance permeability. Understanding fracture behavior, influenced by temperature changes, is crucial for optimizing energy extraction. To address this, we pro...

The take-home message of this paper is that solving optimal control problems can be computationally straightforward, provided that differentiable partial differential equation (PDE) solvers are available. Although this might seem to be a strong limitation and the development of differentiable PDE solvers might seem arduous, for many problems this i...

This works investigates the generalization capabilities of MeshGraphNets (MGN) [Pfaff et al. Learning Mesh-Based Simulation with Graph Networks. ICML 2021] to unseen geometries for fluid dynamics, e.g. predicting the flow around a new obstacle that was not part of the training data. For this purpose, we create a new benchmark dataset for data-drive...

This study explores reduced-order modeling for analyzing time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in which the chemical potential and displacements are coupled. This system is formulated in a monolithic fashion and so...

This contribution addresses the problem of controlling the Degree of Crosslinking (DoC) in printed hydrogels through feedback control as a product quality indicator from a modeling approach. We set up a simulation that resembles co-axial printing of calcium-alginate (Ca-Alg) hydrogel as a case study. A well-known Ca-Alg gelation model composed of a...

In this work, various high-accuracy numerical schemes for transport problems in fractured media are further developed and compared. Specifically, to capture sharp gradients and abrupt changes in time, schemes with low order of accuracy are not always sufficient. To this end, discontinuous Galerkin up to order two, Streamline Upwind Petrov-Galerkin,...

This work presents a comparative review and classification between some well-known thermodynamically consistent models of hydrogel behavior in a large deformation setting, specifically focusing on solvent absorption/desorption and its impact on mechanical deformation and network swelling. The proposed discussion addresses formulation aspects, gener...

In this work, the space-time MORe DWR ( M odel O rder Re duction with D ual- W eighted R esidual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the Biot system which consists of vector-valued displacements (geomechanics) coupled to a Darcy flow pres...

In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives are the development and analysis of space-time estimators, in which the localization is based on a weak form emp...

Acid fracturing is a technique to enhance productivity in carbonate formations. In this work, a thermal–hydraulic–mechanical–chemical (THMC) coupling model for acid fracture propagation is proposed based on a phase-field approach. The phase-field variable is utilized as an indicator function to distinguish the fracture and the reservoir, and to tra...

This monograph is centered on mathematical modeling, innovative numerical algorithms and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art phase-field fracture models are complemented with prototype explanations and rigorous numerical analysis. These developments are embedded into a carefully designed balance betwe...

Phase-field fracture (PFF) modeling is a popular approach to model and simulate fracture processes in solids. Accurate material parameters and boundary conditions are of utmost importance to ensure a good prediction quality of numerical simulations. In this work, an Integrated Digital Image Correlation (IDIC) algorithm is proposed to calibrate boun...

The time-harmonic Maxwell equations are of great interest in current research fields, e.g., [7, 8, 10, 14, 16].

Phase-field fracture models are employed to capture failure and cracks in structures, alloys, and poroelastic media. The coupled model is based on solving the elasticity equation and an Allen-Cahn-type phase-field equation. In hydraulic fracture, a Darcytype equation is solved to capture the pressure profile. Solving this coupled system of equation...

The Maxwell system describes the behaviour of electromagnetic fields. Nedelec’s edge finite element method is an efficient discretization technique to solve this equation which involves the curl-curl operator numerically [13, 10].

In this work, we couple a high-accuracy phase-field fracture reconstruction approach iteratively to fluid-structure interaction. The key motivation is to utilize phase-field modelling to compute the fracture path. A mesh reconstruction allows a switch from interface-capturing to interface-tracking in which the coupling conditions can be realized in...

We formulate variational material modeling in a space-time context. The starting point is the description of the space-time cylinder and the definition of a thermodynamically consistent Hamilton functional which accounts for all boundary conditions on the cylinder surface. From the mechanical perspective, the Hamilton principle then yields thermo-m...

In this work, space-time formulations and Galerkin discretizations for phase-field fracture optimal control problems are considered. The fracture irreversibility constraint is formulated on the time-continuous level and is regularized by means of penalization. The optimization scheme is formulated in terms of the reduced approach and then solved wi...

In this work, we propose and computationally investigate a monolithic space-time multirate scheme for coupled problems. The novelty lies in the monolithic formulation of the multirate approach as this requires a careful design of the functional framework, corresponding discretization, and implementation. Our method of choice is a tensor-product Gal...

In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary differential equations. We show that when the convective part of the system, the chemotactic term, is dominant, then st...

In-situ (tomography) experiments are generally based on scans reconstructed from a large number of projections acquired under constant deformation of samples. Standard digital volume correlation (DVC) methods are based on a limited number of scans due to acquisition duration. They thus prevent analyses of time-dependent phenomena. In this paper, a...

Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving directional differentiability of the coefficient to solution mapping for the obstacle problem. Further, considering a...

In this work, we examine a numerical phase-field fracture framework in which the crack irreversibility constraint is treated with a primal-dual active set method and a linearization is used in the degradation function to enhance the numerical stability. The first goal is to carefully derive from a complementarity system our primal-dual active set f...

While working with N\'ed\'elec elements on adaptively refined meshes with hanging nodes, the orientation of the hanging edges and faces must be taken into account. Indeed, for non-orientable meshes, there was no solution and implementation available to date. The problem statement and corresponding algorithms are described in great detail. As a mode...

In this contribution, we apply adaptive finite elements to the Boussinesq model. Adaptivity is achived with goal‐oriented error control and local mesh refinement. The principle goal is motivated from laser material processing and laser waveguide writing in which material starts to flow due to laser‐induced heat generation. Flow of the material is d...

In this work, we apply reduced-order modeling to the parametrized, time-dependent, incompressible, laminar Navier-Stokes equations. The major goal is to reduce the computational costs by replacing the high-fidelity system by a low-rank approximation, which preserves the solution behavior. We utilize projection-based reduced basis methods and carry...

In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains. The advantage is that the interface condition can be updated without recomputing...

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 paper, we study a cancer invasion model both theoretically and numerically. The model is a nonstationary, nonlinear system of three coupled partial differential equations modeling the motion of cancer cells, degradation of the extracellular matrix, and certain enzymes. We first establish existence of global classical solutions in both two-...

In this work, Bayesian inversion with global-local forwards models is used to identify the parameters based on hydraulic fractures in porous media. It is well-known that using Bayesian inversion to identify material parameters is computationally expensive. Although each sampling may take more than one hour, thousands of samples are required to capt...

In this work, the dual-weighted residual (DWR) method is applied to obtain a certified incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Rduction with Dual-Weighted Residual error estimates) is being introduced. It marries tensor-product space-time reduced-order modeling with...

In this work, we undertake additional computational performance studies of a recently developed space‐time phase‐field fracture optimal control framework. Therein, the phase‐field forward problem is formulated in a monolithic fashion. The optimal control problem is formulated with the help of the reduced approach in which the state variable is repr...

However, the numerical solution is challenging. This is specifically
true for high wave numbers. Various solvers and preconditioners have been
proposed, while the most promising are based on domain decomposition methods
(DDM) [16].

This work is devoted to the efficient solution of variational-monolithic fluid-structure interaction (FSI) initial-boundary value problems. Solvers for such monolithic systems were developed, e.g., in [2, 3, 5, 7, 9, 11–13, 15]. Due to the interface coupling conditions, the development of robust scalable parallel solvers remains a challenging task,...

In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains. The advantage is that the interface condition can be updated without recomputing...

In this paper, we consider a nonlinear PDE system governed by a parabolic heat equation coupled in a nonlinear way with a hyperbolic momentum equation describing the behavior of a displacement field coupled with a nonlinear elliptic equation based on an internal damage variable. We present a numerical scheme based on a Galerkin finite element metho...

A recently developed application of computer vision is pathfinding in self-driving cars. Semantic scene understanding and semantic segmentation, as subfields of computer vision, are widely used in autonomous driving. Semantic segmentation for pathfinding uses deep learning methods and various large sample datasets to train a proper model. Due to th...

This work considers a Stokes flow in a deformable fracture interacting with a linear elastic medium. To this end, we employ a phase-field model to approximate the crack dynamics. Phase-field methods belong to interface-capturing approaches in which the interface is only given by a smeared zone. For multi-domain problems, the accuracy of the couplin...

In this work, a space-time scheme for goal-oriented a posteriori error estimation is proposed. The error estimator is evaluated using a partition-of-unity dual-weighted residual method. As application, a low mach number combustion equation is considered. In some numerical tests, different interpolation variants are investigated, while observing con...

We hide grayscale secret images into a grayscale cover image, which is considered to be a challenging steganography problem. Our goal is to develop a steganography scheme with enhanced embedding capacity while preserving the visual quality of the stego-image as well as the extracted secret image, and ensuring that the stego-image is resistant to st...

The time-harmonic Maxwell equations are used to study the effect of electric and magnetic fields on each other. Although the linear systems resulting from solving this system using FEMs are sparse, direct solvers cannot reach the linear complexity. In fact, due to the indefinite system matrix, iterative solvers suffer from slow convergence. In this...

We numerically explore synthetic crystal diamond for realizing novel light sources in ranges which are up to now difficult to achieve with other materials, such as sub-10-fs pulse durations and challenging spectral ranges. We assess the performance of on-chip diamond waveguides for controlling light generation by means of nonlinear soliton dynamics...

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, we develop a posteriori error control for a generalized Boussinesq model in which thermal conductivity and viscosity are temperature-dependent. Therein, the stationary Navier-Stokes equations are coupled with a stationary heat equation. The coupled problem is modeled and solved in a monolithic fashion. The focus is on multigoal-orient...

In this work, a method for automatic hyper-parameter tuning of the stacked asymmetric auto-encoder is proposed. In previous work, the deep learning ability to extract personality perception from speech was shown, but hyper-parameter tuning was attained by trial-and-error, which is time-consuming and requires machine learning knowledge. Therefore, o...

The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. Specifically in the optimal control minimization problem, a tracking-type cost functional is minimized to steer the crack via the phase-field variable into a desired pattern. To achieve such optimal solutions, Neumann type boun...

In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives are the development and analysis of space-time estimators, in which the localization is based on a weak form emp...

In this paper, we consider Mandel's problem in the context of nonlinear single-phase poroelasticity, where it is assumed that the fluid is sightly compressible and porosity and permeability are given functions of the volume strain. In the first part of the paper we prove well-posedness of the time-discrete incremental problem by recasting the equat...

We consider the widely used continuous $\mathcal{Q}_{k}$-$\mathcal{Q}_{k-1}$ quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations,...

In this paper, we study a cancer invasion model both theoretically and numerically. The model is a nonstationary, nonlinear system of three coupled partial differential equations modeling the motion of cancer cells, degradation of the extracellular matrix, and certain enzymes. We first establish existence of global classical solutions in both two-...