Overview of current research projects at IMCS

 

Multi-scale algorithms and simulation for the patient-specific optimization of endovascular interventions in cerebral aneurysms

Funding/Agency DFG Priority Program 2311
Funding Period 2021-2024
Partner Chair for Numerical Mathematics, TU Munich, Department of Neuroradiology, University Hospital rechts der Isar, TU Munich
Project Abstract
Within this project embedded into the DFG Priority Program 2311, a continuum mechanics approach is being developed for the simulation of the endovascular intervention in cerebral aneurysms with devices such as coils, Woven EndoBridges (Web) or flow diverters. It targets the patient-specific improvement of cerebral aneurysm treatment through predictive simulation and optimization.
 
IMCS is actively involved in the numerical modeling of the different devices and the involved biochemical processes of blood coagulation in the aneurysm cavity. In collaboration with the project partners, the device and coagulation models will be coupled to a Lattice-Boltzman-based arterial model of the blood flow to predict the long-term treatment outcome and quantify treatment success.
Contact at IMCS

Prof. Dr.-Ing. Alexander Popp, Dr.-Ing. Matthias Mayr, Martin Frank M.Sc.

 

Multi-scale modelling of thermomechanical frictional contact for complex problems in engineering

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Funding/Agency Deutscher Akademischer Austauschdienst (DAAD)
Ministero dell'Istruzione dell'Università e della Ricera (MIUR)
Funding Period 2018-2020, 2021-2024
Partners MUSAM Lab, IMT School for Advanced Studies Lucca, Italien (Prof. Paggi)
Project Abstract This project aims to develop an efficient two-scale numerical scheme integrating implicit finite element (FEM) computations at the macro-scale and the boundary element method (BEM) at the micro-scale for the accurate solution of frictional and thermomechanical contact problems with microscopic interface roughness. The whole range of frictional regimes, from full stick over stick-slip transitions to full sliding, will be handled as well as any complex loading path. The two-scale model will be compared with a fully resolved 3D FEM model using high-performance computing (HPC) techniques. Frictional contact problems are relevant in many engineering and physics research areas. In mechanical engineering, they arise in configurations such as wheel-rail contact, bearings, brakes or wheel-asphalt contact. Applications of thermomechanical contact include screw connections under temperature loading and shrink fitting. Friction is also of interest for the interaction between soil and pile foundations in civil and geotechnical engineering applications, and in biomechanics the relative motion in hip-joint prostheses leads to abrasive wear. In all these scenarios, the interface between bodies in contact is not microscopically flat, but its roughness presents multi-scale features that influence the deformation and the stress states in the material.
Contact at IMCS Prof. Dr.-Ing. Alexander Popp, Rishav Shaw M.Sc., Jacopo Bonari M.Sc.

 

Algebraic multigrid methods for preconditioning of block systems

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Funding/Agency Zentrum für Digitalisierungs- und Technologieforschung der Bundeswehr (dtec.bw)
Funding Period 2021-2024
Partners Institutes of dtec.bw project HPC.bw
Project Abstract The goal of this project is the development of algebraic multigrid methods for the preconditioning of multi-physics block system. Approaches for the treatment of the problem-specific block structure of the underlying matrix as well as novel algebraic multigrid approaches will be developed. The software environment will be the multigrid framework Muelu, which is embedded in the open-source library Trilinos. The newly developed methods will be applied in parallel simulations of beam-solid interactions on supercomputers.
Contact at IMCS

Dr.-Ing. Matthias Mayr, Max Firmbach M.Sc.

 

Highly efficient and parallel scalable mortar methods for contact and multi-field problems

Funding Period 2021 -
Partners 4C-project partners at TU Munich and Helmholtz center Hereon
Project Abstract

In this PhD project, we will advance the coupling of multi-physics problems using mortar finite element methods with a particular focus on the application in nonlinear contact mechanics. Due to the intrinsically nonlinear nature of the introduced constraints at the contact boundary, significantly increased requirements arise for, among other things, contact search algorithms, nonlinear solvers, optimal preconditioning of linear systems of equations, a fully consistent linearization of the problem for implicit time integration, and Mortar-specific operations such as the computation of the mesh intersection at the contact surface within each Newton iteration.

High-fidelity finite element simulations of contact problems potentially require several million degrees of freedom, but demand more computational effort than comparable problems from pure solid mechanics due to the issues mentioned above. Thus, the implementation in a parallel software framework is inevitable. The first step of the PhD project is the development of a highly parallel scalable framework in a MPI-based distributed memory environment, an independently distributed volume and mortar discretization, and an optimal load balancing on the physical processor cores. The implementation is carried out in the multi-physics framework 4C, which is jointly developed in cooperation with the TU Munich and the Helmholtz Zentrum Hereon.

Contact at IMCS Prof. Dr.-Ing. Alexander Popp, Dr.-Ing. Matthias Mayr, Christopher Steimer M.Sc.

 

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Period 2021-
Project Abstract

The project focuses on the approximate calculation of eigenvalues of various differential operators on areas with cracks using isogeometric analysis. Methods are to be developed that allow the simulated eigenvalues to represent as accurately as possible the eigenfrequencies of test objects with cracks that can be measured in practice, and also to show corresponding convergence results. Subsequently, these natural frequencies shall be used to identify the crack, i.e., to determine the shape of the crack. This inverse problem is to be solved with a neural network, for the training of which we need simulation data of as high quality as possible in order to be able to guarantee a meaningful application in practice.

Contact at IMCS

Prof. Dr. Thomas Apel, Philipp Zilk M.Sc.

 

Combination of Isogeometric Analysis, Finite Element Methods, and Embedded Mesh Coupling Methods for contact problems​

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Funding/Agency Deutsche Forschungsgemeinschaft (DFG)
Funding Period 2021-2024
Project Abstract

In the last years, contact formulations have mostly been developed using the classical Finite Element Method (FEM). However, a typical finite element mesh cannot provide a continuous normal vector field due to the C0 continuity at element intersections. A common solution is to refine the mesh at the contact boundary, which leads to an unnecessary extension of the refined elements into the domain volume. To achieve a higher-order continuity on the contact boundary, contract formulations using Isogeometric Analysis (IGA) have been proposed more recently. These typically use NURBS shape functions for the geometry description as well as the approximation of the solution field. However, the NURBS elements again reach into the domain volume, where their higher-order continuity do not necessarily offer more advantages (due to the reduced regularity of contact problems) but rather cause computational costs. 


In this project, we propose a separation of the meshing process for the contact boundary region and for the internal volume of the involved bodies, since the two regions pose different requirements on continuity, element type, mesh orientation and mesh refinement. For the discretization of the contact boundary region, a boundary layer of NURBS elements is defined, which can be refined locally at desired areas without influencing the mesh size within the internal volume. On the other hand, the volume domain is discretized using classical hexahedral finite elements on Cartesian grids in the reference configuration. This results in two independent, yet overlapping meshes, which are consistently coupled to each other using an Embedded Mesh (EM) approach. For doing this, appropriate mortar / Lagrange multiplier formulations as well as Nitsche's method will be investigated.

Contact at IMCS Prof. Dr.-Ing. Alexander Popp, Eugenia Gabriela Loera Villeda M.Sc.

 

Combination of data- and physics-based methods for hybrid digital twins

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Funding/Agency Zentrum für Digitalisierungs- und Technologieforschung der Bundeswehr (dtec.bw)
Funding Period 2021-2024
Partners Institutes of dtec.bw project RISK.twin within research center RISK
Project Abstract

In this project, methods for hybrid digital twins of critical infrastructure are investigated and developed. The main focus is the combination of physic-based modeling using Finite Element Methods (FEM) and data-based modeling with machine learning techniques.

The first application case are steel-reinforced concrete bridges. On the physics-based modeling side, a mixed-dimensional FEM model for steel-reinforced concrete components is developed. Complementary, variants of neural networks are investigated. Both are combined to improve the material model with measurement data and obtain a reduced order model of the physical system. 

Still, attention is paid to generality and application independence of the methods, so that the developed techniques can also be used by the project partners. New algorithms are implemented in the form of an in-house software solution. An associated hardware platform for high performance computing is provided at the Data Science & Computing Lab.

Contact at IMCS Prof. Dr.-Ing. Alexander Popp, Dr.-Ing. Max von Danwitz, Thank Thank Kochmann M.Sc., Tarik Sahin M.Sc.

 

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Period 2018-
Project Abstract This project aims at developing highly efficient mixed-dimensional Mortar finite element methods specifically tailored to model the interaction of very slender rods with the 3-dimensional incompressible Navier-Stokes equations. The interaction of such beam-like structures with fluid flow plays an important role in a broad spectrum of applications varying from biomechanical to industrial processes. Such applications include the interaction of endovascular devices with blood flow and the use of fibrous coverings in flow control for example.
 
At IMCS, we focus on developing specialized 1D-3D coupling approaches that allow for relatively coarse background meshes in order to conserve the benefits — e.g. in terms of the system size, solver time as well as the evaluation of the coupling terms itself — of using a reduced-dimensional structure formulation. Special attention is paid to the application of efficient and scalable parallel algorithms capable of tackling large and complex engineering applications.
Contact at IMCS Prof. Dr.-Ing. Alexander Popp, Dr.-Ing. Matthias Mayr, Nora Hagmeyer M.Sc.

 

Anisotropic pressure-robust discretizations for the Navier-Stokes equations

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Funding Period 2018-
Partners Weierstrass Institute for Applied Analysis and Stochastics (Priv.-Doz. Dr. Alexander Linke, Dr. Christian Merdon)
Project Abstract The focus of the project is to develop error estimates for discretizations of the Navier-Stokes equations on anisotropically refined meshes, where the velocity error is independent of the pressure approximability. Further information can be found here.
Contact at IMCS

Prof. Dr. Thomas Apel, Volker Kempf M.Sc.

 

 

Mixed-dimensional coupling in solid mechanics

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Period 2018-
Partners Institute for Computational Mechanics, TU Munich
Project Abstract In a variety of engineering and biomechanical applications, coupling between slender fibers and general three-dimensional bodies (volumes) improves the mechanical properties of the overall coupled structure. In this project, novel coupling methods are developed for such problems, where the fibers are explicitly modelled using one-dimensional (1D) beam theories, resulting in a very accurate and efficient numerical formulation. State-of-the-art finite element methods (FEM) are used for the 3D solids. For this reason, such approaches are also referred to as mixed-dimensional coupling. These mixed-dimensional coupling methods allow for a very simple model generation, since the 1D fibers and the 3D body can be discretized completely independently of each other. Over the course of this project, coupling methods for embedded fibers in volumes (1D-3D) and fibers connected to surfaces (1D-2D) based on Mortar/Lagrange multiplier methods have already been successfully developed. One of the next challenging steps is the design and implementation of contact algorithms between 1D fibers and 2D surfaces.
Contact at IMCS Prof. Dr.-Ing. Alexander Popp, Dipl.-Ing. Ivo Steinbrecher

 

Optimal control problems governed by elliptic variational inequalities

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Funding/Agency Deutsche Forschungsgemeinschaft (DFG)
within the international research training group IGDK 1754 with the title
Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures
Funding Period 2017-2022
Partners Technische Universität München (Prof. Vexler)
Technische Universität Graz (Prof. Steinbach)
Project Abstract

The project deals with optimal control of variational inequalities. A priori error estimates for finite element discretizations of optimal control problems for elliptic variational inequalities and different regularization strategies are considered. Further information can be found here.

Contact at IMCS

Prof. Dr. Thomas Apel, Christof Haubner M.Sc.