# CE Seminar

Together with the Computational Engineering Research Center of the TU Darmstadt a joint seminar with interesting talks in the field of CE is organized in every semester. If you are interested in these seminars and would like to receive invitations please subscribe for the corresponding mailing list.

# Previous Talks

## 2018

## Model Predictive Control for DAEs from an ODE perspective

### Jun.-Prof. Dr. Karl Worthmann, TU Ilmenau

**26 Nov 2018, 16:15–17:45; Location: S2|17-103**

Differential Algebraic Equations (DAEs) combine Ordinary Differential Equations (ODEs) with algebraic constraints. Hence, even for linear systems both the initial condition and the control input cannot be arbitrarily chosen. We present a framework for linear regular systems, which allows to characterise the space of consistent initial conditions and the set of admissible controls from an ODE point of view. Then, based on an augmented system, we design a Model Predictive Control (MPC) scheme such that asymptotic stability of the origin w.r.t. the MPC closed loop is guaranteed.

## Exploring Emerging Memory Technologies in Extreme Scale High Performance Computing

### Jeffrey S. Vetter, Ph.D., Oak Ridge National Laboratory, USA

**6 Nov 2018, 17:00–18:30; Location: S2|02-C205**

Abstract:

Concerns about energy-efficiency and cost are forcing our community to reexamine system architectures, and, specifically, the memory and storage hierarchy. While memory and storage technologies have remained relatively stable for nearly two decades, new architectural features, such as deep memory hierarchies, non-volatile memory (NVM), and near-memory processing, have emerged as possible solutions. However, these architectural changes will have a major impact on HPC software systems and applications. To be effective, software and applications will need to be redesigned to exploit these new capabilities. In this talk, I will sample these emerging memory technologies, discuss their architectural and software implications, and describe several new approaches to programming these systems. One system is Papyrus (Parallel Aggregate Persistent -yru- Storage); it is a programming system that aggregates NVM from across the system for use as application data structures, such as vectors and key-value stores, while providing performance portability across emerging NVM hierarchies.

Short Bio:

Jeffrey Vetter, Ph.D., is a Distinguished R&D Staff Member at Oak Ridge National Laboratory (ORNL). At ORNL, Vetter is the founding group leader of the Future Technologies Group in the Computer Science and Mathematics Division, and the founding director of the Experimental Computing Laboratory (ExCL). Vetter also holds joint appointment at the University of Tennessee-Knoxville. Vetter earned his Ph.D. in Computer Science from the Georgia Institute of Technology. Vetter is a Fellow of the IEEE, and a Distinguished Scientist Member of the ACM. In 2010, Vetter, as part of an interdisciplinary team from Georgia Tech, NYU, and ORNL, was awarded the ACM Gordon Bell Prize. In 2015, Vetter served as the SC15 Technical Program Chair. His recent books, entitled “Contemporary High Performance Computing: From Petascale toward Exascale (Vols. 1 and 2),” survey the international landscape of HPC. See his website for more information: ft.ornl.gov/~vetter/.

## Eigenvalue problems for the curl operator, 3D geometric inverse problems and 7D analogies

### Dr. Robert Kotiuga, Boston University, USA

**29 Oct 2018, 16:15–17:45; Location: S2|17-103**

Decades ago, the author obsessed with articulating why topological aspects of 3D finite element (FE) meshes could be deceptively unintuitive, while 2D was so obvious. For EEs, this dichotomy didn’t originate with FE meshes, but is implicit in how nonplanar electronic circuits are communicated. In FE for electromagnetics, the ease with which homology calculations can be reduced to sparse matrix linear algebra, enables certain complexities of 3D geometries to be automated, taking the user out of the loop. Although linking numbers, the problem of making cuts for magnetic scalar potentials, and the “helicity” of a vector field, all helped to articulate how 3D was so much richer than 2D, knotted geometries were largely dismissed in the decades of milling machines and lathes.

The quadratic constraint imposed by the Lorentz force is a game changer which forced the embrace of 3D topological complexities. From magnets made of superconducting tapes for particle accelerators, or compact MRI and fusion devices, to astrophysical object like magnetaurs, this nonlinear constraint unleashed topological considerations far more subtle than the comfortable linear algebra and graph theory associated with homology calculations. Taming this increased complexity, the eigenvalue problem (EVP) for the curl operator has emerged as a very important bridge between topological characterizations of optimal designs involving the Lorentz force, and tools associated with computational linear algebra.

This talk will focus on how the curl EVP differs from the more familiar curlcurl EVP, its unique features for tackling inverse problems, and how a 7D analogy helps formalize unintuitive aspects.

## On the role of entropy in mathematical modeling, computation and uncertainty quantification

### Prof. Dr. Martin Frank, K.I.T. Karlsruhe

**25 Oct 2018, 17:00–18:30; Location: S4|10-314**

This talk discusses entropy structures for partial differential equations, and how they can be used for efficient HPC computations, and uncertainty quantification. Especially, we recall the entropy-entropy flux structure of hyperbolic conservation laws describing macroscopic flows, and how this structure is inherited from underlying mesoscopic models for particle transport. We investigate the numerical solution of generalized entropy closures, and discuss their suitability for modern computer architectures. Lastly, we show that entropy-based methods are suitable for uncertainty quantification, as they overcome the loss of hyperbolicity in standard generalized polynomial chaos stochastic Galerkin methods.

## Asymptotic stability of autonomous (P)DAEs with network structure

### Prof. Dr. Caren Tischendorf, Humboldt-Universität zu Berlin

**24 Oct 2018, 13:00–14:30; Location: S4|10-314**

We analyze autonomous differential algebraic equations (DAEs) with the following particular structure:

\[\begin{aligned} x'_1 & = \frac{\text{d}}{\text{d}t} f_1 (y_1) + g_1 (y_1) + r_1,\\ y'_2 & = \frac{\text{d}}{\text{d}t} f_2 (x_2) + g_2 (x_2) + r_2,\\ x_1 & = A_1^\top z,\\ x_2 & = A_2^\top z,\\ 0 & = A_1 y_1 + A_2 y_2, \end{aligned}\]

where (\(A_1\), \(A_2\)) is an incidence matrix of full row rank. First we show that a transient modeling of the flow of different kind of networks (circuits, water network, gas network, blood circuits) leads to DAEs with this structure. The functions \(f_i\) and \(g_i\) represent the element models and their spatial discretizations (in case of PDE models). The matrices Ai describe the network topology.

We present sufficient criteria on the element model functions \(f_i\) and \(g_i\) for the asymptotic stability of DAEs with this structure. It includes a characterization of the eigenvalue structure for the related generalized eigenvalue problem. Furthermore, we discuss the correlation to port Hamiltonian modeling of networks.

## Galerkin boundary element methods for electromagnetic resonance problems

### Dr. Gerhard Unger, Graz University of Technology

**5 Sep 2018, 10:00–11:30; Location: S4|10-314**

We consider Galerkin boundary element methods for the approximation of different kinds of electromagnetic resonance problems. Examples are the cavity resonance problem, the scattering resonance problem and the plasmonic resonance problem. An analysis of the used boundary integral formulations and their numerical approximations ispresented in the framework of eigenvalue problems for holomorphic Fredholmoperator-valued functions. We use recent abstract results to show that theGalerkin approximations with Raviart-Thomas elements provide a so-called regular approximation of the underlying operators of the eigenvalue problems. This enables us to applyclassical results of the numerical analysis of eigenvalue problems for holomorphic Fredholm operator-valued functions which implies convergence of the approximations and quasi-optimal error estimates.

We also address practical issues of the numerical computations of resonances and modes as the application of the contour integral method and of Newton-type methods for eigenvalue tracking.

## Solving Maxwell's equations in time: from Yee splitting to Krylov exponential methods

### Mike Botchev, PhD, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow

**2 Aug 2018, 10:00–11:30; Location: S2|17-103**

Solving Maxwell's equations in time domain efficiently is a nontrivial task and represents a fascinating research area. This talk will consist of two parts. In the first part a brief introduction to time integration methods for Maxwell's equations will be given. In particular, we will discuss

(1) why the celebrated Yee scheme (often used in Finite Difference Time Domain (FDTD) computations) is successful and how it can be generalized to higher order methods, to finite element discretizations in space and to treat damping terms;

(2) why fully implicit methods are often not efficient for Maxwell's equations;

(3) why exponential time integration methods (unlike implicit methods) can be made competitive for these problems.

In the second part of the talk speaker's recent work on solving a particular photonics problem with multiple source terms by Krylov exponential methods will be discussed. For this application Krylov exponential methods allowed a significant speed up in computing times. This part is speaker's joint work with Abel Hanse and Ravitej Uppu.

## Modeling the impact of stenting of aortic coarctations upon left ventricular load

### Dr. Elias Karabelas, University of Graz

**28 Jun 2018, 17:00–18:30; Location: S4|10-314**

Hemodynamic models of blood flow in the left ventricle (LV) and aorta are important tools for analyzing the mechanistic links between myocardial deformation and flow patterns in human hearts. Typically, computational fluid dynamics (CFD) models driven by image-based kinematic models are employed aiming to predict the acute response to an intervention. While such models have proven to be suitable for analyzing the hemodynamic status quo of a patient, they are of limited predictive power as they rely upon the tacit assumption that the kinematics of the heartbeat remains unaffected by the intervention. Electro-mechano-fluidic (EMF) models that capture the entire physics of ventricular electromechanics (EM) promise high potential to overcome this limitation. Such models render feasible the prediction of changes in essential parameters such as myocardial wall stresses and work rates, which are known to be key factors driving ventricular remodeling and disease progression and their potential reversal post-treatment.

In a recent study we built a cohort of twenty in silico electro-mechanical LV and aorta models of patients suffering from aortic valve disease (AVD) and/or aortic Coarctations (CoA). All models comprising electrophysiological, mechanical and circulatory components were parameterized for individual patients using comprehensive clinical datasets. These validated EM models were fed into our recently developed in-house CFD solver.

In this talk we will present our general workflow together with first results on hemodynamics in the LV for some personalized EM models.

## Quasi-Newton – A Universal Approach for Coupled Problems and Optimization

### Prof. Dr. Miriam Mehl, University of Stuttgart

**20 Jun 2018, 17:00–18:30; Location: S4|10-314**

Quasi-Newton methods are used in many fields to solve non-linear equations without explicitly known derivatives. This is the case, e.g., in coupled multi-physics applications such as fluid-structure interactions where we combine several independent solvers in a partitioned approach coupled simulation environment. To do so, we have to solve a (in general non-linear) interface equation that contains operator contributions from all involved single-physics solvers. If we assume that these solvers are black-box, quasi-Newton methods are the best known method to accelerate pure interface fixed point iterations. In PDE-constrained optimization, i.e., inverse solvers that are based on gradient descent, we have to find the root of the (reduced) gradient of the objective function. Though the Hessian can usually be calculated and used in an inner Krylov method, these calculations are typically costly as they involve the solution of forward and adjoint problems. Thus, quasi-Newton methods are an efficient alternative. In both cases, coupled problems and optimization, an additional advantage of quasi-Newton over Newton methods is the fact that we can directly approximate the inverse Jacobian or Hessian such that no inner linear solver is required. We present a comparison of known quasi-Newton methods for multi-physics such as interface quasi-Newton with methods usually used in optimization, in particular the BFGS method that is, e.g., used in PETCs’s TAO package. Results for two applications – fluid-structure interaction and inverse tumor simulation – demonstrate their potential in terms of robustness, generality, and efficiency.

## Spatially dispersive metals for nanophotonics-about DGTD, model calibration and experimental evidence

### M.Sc. Nikolai Schmitt, INRIA Sophia Antipolis, France

**18 Jun 2018, 16:15–17:45; Location: S2|17-103**

In nanoplasmonics, most metal devices are sub wavelength. This leads to geometrical sizes comparable to the skin-depth of electromagnetic waves at optical frequencies. Appropriate material models of the metallic bulk are hence indispensable.

Additionally, if the effective wavelength of the plasmon (a wave that relies on oscillations of the free electrons in the metal) becomes comparable to the mean free path length, spatial dispersion has to be considered.

This talk addresses the modeling and discretization of Maxwell's equations coupled to a spatial (nonlocal) dispersion law. Further, a model calibration strategy is proposed for future experiments. A comparison of simulation results with experimental data is also carried out.

## Massively Parallel Mixed Integer Programs (MIP) Solving: Towards Harnessing over a Million CPU Cores to Solve a Single MIP on Supercomputers

### Dr. Yuji Shinano, Zuse-Institute Berlin

**14 Jun 2018, 17:00–18:30; Location: S4|10-314**

Mixed integer programming (MIP) problem is a general form to model combinatorial optimization problems and has many industrial applications. The performance of MIP solvers, software packages to solve MIPs, has improved tremendously in the last two decades and these solvers have been used to solve many real-word problems. However, against the backdrop of modern computer technology, parallelization is of pivotal importance. In this way, ParaSCIP, which uses an academic code SCIP as base MIP solver, and ParaXpress, which uses the commercial MIP solver Xpress, are the most successful parallel MIP solver in terms of solving previously unsolvable instances from the well-known benchmark instance set MIPLIB by using supercomputers. ParaSCIP has solved two instances from MIPLIB2003 and 12 from MIPLIB2010 for the first time to optimality by using up to 80,000 cores of supercomputers and ParaXpress has solved two open instances from MIPLIB2010. ParaSCIP and ParaXpress have been developed by using the Ubiquity Generator (UG) framework, which is a general software package to parallelize any state-of-the-art branch-and-bound based solver. Moreover, UG is being used to parallelize PIPS-SBB, a solver for stochastic MIPs. In this talk, we will introduce and show the ground design of UG framework and UG Synthesizer (UGS), which is a new framework to flexibly realize any combinations of algorithm portfolios and racing to solve MIPs on a distributed computing environment. They can instantiate a massively parallel MIP solver with the potential to harness over a million CPU cores to solve a single MIP on supercomputers.

## An introduction to energy-based modeling of lumped- and distributed-parameter coupled problems

### M.Sc. Michal Maciejewski, CERN, Switzerland

**11 Jun 2018, 16:15–17:45; Location: S2|17-103**

Power-conservation is a fundamental property of mathematical models describing physical phenomena. The modeling consistency can be ensured if each subsystem fulfills this requirement. Next step in modeling is to ensure, that the combination of these subsystems still maintains this property. To this end, we employ bond graph and port-Hamiltonian modeling. These are complementary, domain-agnostic techniques allowing for a consistent modeling of energy flow in physical systems. They are particularly useful to represent multi-physical systems for which a generic representation is relevant. The presented material will be illustrated with recent developments in the modelling of superconducting magnets and circuits.

## Nonsmooth Optimization via Successive Abs-Linearization

### Prof. Andreas Griewank, Yachaytech University, Ecuador

**4 Jun 2018, 17:00–18:30; Location: S4|10-314**

In finite dimensions abs-linearization of a function defined by smooth elementals and abs, min, and max yields a piecewise linear continuous approximation function at a given development point. The error between this local model and the underlying piecewise smooth function is uniformly of second order in the distance to the development point. Since the local model can be evaluated in its abs-normal form by a minor extension ADOL-C, Tapenade and other algorithmic differentiation tools, this suggests the iterative solution of nonsmooth computational problems by successive abs-linearization. That applies in particular to equation solving and unconstrained or constrained optimization including complementarity constraints. We describe regularity, optimality and convexity conditions, the corresponding rates of convergence, and various algorithms for solving the inner, abs-linear problem. Finitely, we briefly discuss the extension of the approach to function spaces, where the notion “piecewise smooth” does not appear natural.

## Network of elastic rods in relation to elastic plate and shell models

### MSc Matko Ljulj, University of Zagreb, Kroatia

**17 May 2018, 17:00–18:30; Location: S4|10-314**

In this talk the linear elastic rod (1D) model and linear elastic shell (2D) model will be shown. Since numerical solving of 3D linear elasticity PDE on thin domains is challenging and gives incorrect results due to using dense meshes, low-dimensional models show great advantage. After that, we will show applications of those concepts in modelling interaction between vascular walls and coronary stents, and secondly in homogenization of network of rods.

## Multiscale simulation of slow-fast high-dimensional stochastic processes: methods and applications

### Prof. Dr. Giovanni Samaey, KU Leuven, Belgium

**14 May 2018, 16:15–17:45; Location: S2|17-103**

We present a framework for the design, analysis and application of computational multiscale methods for slow-fast high-dimensional stochastic processes. We call these processes “microscopic'', and assume existence of an approximate ”macroscopic'' model that captures the slow behaviour of a selected set of macroscopic state variables. The methodology combines short bursts of microscopic simulation with extrapolation at the macroscopic level. The methodology requires the careful study of a few key algorithmic ingredients. First, we need to properly initialise the microscopic system, based on a given macroscopic state and (possibly) a prior microscopic state that contains additional information about the system. Second, we need to control the variance of the noise that originates from the microscopic Monte Carlo simulation. Third, we need to analyse stability of the extrapolation step. We will discuss these aspects on two types of model problems -- scale-separated SDEs and kinetic equations -- and show the efficacity of the resulting methods in diverse applications, ranging from tumor growth to fusion energy.

## Application of the ACA to problems in electromagnetic scattering

### Dr. Lucy Weggler, Biotronik SE & Co KG, Berlin

**7 May 2018, 16:15–17:45; Location: S2|17-103**

Because of quadratic memory requirements classical boundary element realisations are applicable only for a rather moderate number N of boundary elements. A possible solution to this problem is to take advantage of the good approximation properties of the boundary element matrices. One established approximation scheme is called the adaptive cross approximation (ACA) [1, 2].

In this talk the author’s ideas of how to apply the ACA to boundary element formulations of the harmonic Maxwell equations are explained and illustrated by numerical experiments. The principal topics are

•ACA in the context of high order boundary element methods [3, 4, 5].

•ACA in the context of multi-frequency problems.

References

[1] Bebendorf, M., Approximation of boundary element matrices., Numerische Mathematik, 2000.

[2] Kurz, S., Rain, O.,Rjasanow, S., The adaptive cross approximation technique for the 3D boundary element method., IEEE Transaction on Magnetics, Vol. 38(2):421-424, 2002.

[3] L. Weggler, High Order Boundary Element Methods, Dissertation, Saarland University, 2011.

[4] Rjasanow, S., Weggler, L., ACA accelerated high order BEM for Maxwell problems, Comput. Mech, Vol. 51:431-441, 2013.

[5] Rjasanow, S., Weggler, L., Matrix valued adaptive cross approximation, Math. Meth. Appl. Sci., Vol. 40:2522-2531, 2017.

## Asymptotic modeling of the wave-propagation over acoustic liners

### Dr. Adrien Semin, TU Berlin/ BTU Cottbus

**3 May 2018, 17:00–18:30; Location: S4|10-314**

We will consider the acoustic wave propagation in a channel separated from a chamber by a thin periodic layer. This model stand for microperforated absorbers which are used to supress reflections from walls. Due to the smallness of the periodicity a direct numerical simulation, e.g. with the finite element method (FEM), is only possible for very large costs. In this talk we aim do describe equivalent transmission conditions for the viscous acoustic equations, which integrated into numerical methods like the FEM or the boundary element method leads to much lower computational costs.

## HPC Programming Models and Tools: Programmer’s Expectations

### Dr. Christian Terboven, RWTH Aachen University

**18 Apr 2018, 16:30–18:00; Location: S1|22-403**

Parallel programming for HPC systems is a challenging task, and will remain so. Although we have found that certain programming models and development approaches are more productive than others, there is no single best tool for the job. In this talk, I will present our performance analysis and engineering workflow and and our findings on the programming model’s influence on productivity. Case studies will illustrate how the use of patterns and recent advancements in the programming models can foster programmer’s productivity and may provide the basis for portable performance across architectures.

## A High Order Method for the Approximation of Integrals over Implicitly Defined Hypersurfaces

### Dr. Holger Heumann, CASTOR, INRIA, Sophia Antipolis, France

**15 Mar 2018, 17:00–18:30; Location: S4|10-1**

We present a novel method to compute approximations of integrals over implicitly defined hypersurfaces. Control applications for thermonuclear fusion reactors, such as the upcoming ITER tokamak, are the initial motivation of this research work. The new method is based on a weak formulation that uses the coarea formula to circumvent an explicit integration over the hypersurfaces. As such it is possible to use standard quadrature rules in the spirit of hp/spectral finite element methods, and the expensive computation of explicit hypersurface parametrizations is avoided. We derive error estimates showing that high order convergence can be achieved provided the integrand and the hypersurface defining function are sufficiently smooth. The theoretical results are supplemented by numerical experiments including an application for magnetohydrodynamic equilibrium problems in nuclear fusion.

## Quasistatic Field Models and Recent Developments in their Numerical Simulation Methods

### Prof. Dr. Markus Clemens, Bergische Universität Wuppertal

**5 Feb 2018, 16:15–17:45; Location: S2|17-103**

Quasistatic electromagnetic field models are considered for situations, where the shortest wave length of a problem exceeds the spatial dimensions of the problem by at least one order of magnitude. A taxonomy of such quasistatic field models distinguishes between the electro-quasistatic, the magneto-quasistic and the so-called Darwin field models. These models have in common, that the additional assumptions made within the Maxwell equations changes the describing set of partial differential equations from hyperbolic to parabolic, or even to elliptic in the static limit case.

In electro-quasistatic fields problems the electric energy density exceeds the magnetic field energy of the problem. These fields are modelled commonly using a scalar electric potential formulation within the continuity equation. This field formulation allows to describe capacitive and resistive field effects and is used to simulate electric fields mostly in electric power distribution systems and high voltage technology, but also has applications in microelectronics or in the simulation of biological cells. After spatial discretization of the governing equations with schemes e.g. as the Finite Integration Technique (FIT) or the Finite Element Method (FEM), the resulting electro-quasistatic system of ordinary differential equations (ODE) is discretized in time with either implicit or (semi-)explicit time integration schemes. Implementations using advanced multiple right hand side, GPU acceleration and both linear/nonlinear model order reduction techniques, respectively, allow e.g. to efficiently simulate components of electric power supply with nonlinear electric field stress grading materials. Alternative variants of the electro-quasistatic field model are used for simulations of the quasistatic evolution of electric fields and space charges within high-voltage direct current cables.

Many of these numerical techniques are directly applicable also to magneto-quasistatic field problems. Such field are considered when the magnetic field energy of a quasistatic problem exceeds the electric energy density. Often also dubbed as eddy current problems, magneto-quasistatic field models are used to describe electromechanical energy conversion systems, nondestructive testing and inductive energy transport systems. Based on a variety of applicable vector and combined vector and scalar potential formulations the spatially discretized resulting systems of differential-algebraic equations (DAE) are commonly time integrated using implicit schemes. Recent research efforts concentrate on the applicability of (semi-)explicit time integration schemes. These become applicable after reformulating the magneto-quasistatic DAE systems into ODE systems using generalized Schur complements, and also on multigrid-type space-and-time parallel time integration schemes using the Parareal framework.

For the electromagnetic environmental analysis of magneto-quasistatic fields of inductive power transport systems involving high-resolution body phantoms of biological organisms recently several two-step and flexible co-simulation schemes have been developed using either frequency-scaled full wave solution schemes or a modified scalar potential finite difference scheme.

Finally, the so-called Darwin field models include both the electro- and the magneto-quasistatic field description and describe quasistatic field models for problems, where inductive, resistive and capacitive field effects are considered as e.g. in the electromagnetic compatibility analyses of electric and magnetic fields emanating from electric power inverter systems as e.g. traction inverters in hybrid electric cars. Again, the applicability of implicit as well as semi-explicit time integration schemes for the resulting Darwin DAE systems is of practical interest, but faces additional problems due to the non-symmetry and ill-conditioning of the system matrices.

## Sparse optimal control of PDEs with uncertain coefficients

### Prof. Dr. Georg Stadler, New York University

**16 Jan 2018, 17:00–18:30; Location: S4|10-1**

We study sparse solutions of optimal control problems governed by elliptic PDEs with uncertain coefficients. Sparsity of controls is achieved by incorporating the ** L^{1}**-norm of the mean of the pointwise squared controls in the objective. Two optimal control formulations are proposed, one where the solution is a deterministic control that optimizes the mean objective, and a formulation aiming at stochastic controls that all share the same sparsity structure. For the solution of the stochastic control problem, we propose a norm reweighting algorithm, which iterates over functions defined over the physical space only and thus avoids approximation of the random space. Combined with low-rank operator approximations, this results in an efficient solution method that avoids approximation of the uncertain parameter random space. The qualitative structure of the optimal controls and the performance of the solution algorithm are studied numerically using control problems governed by the Laplace and Helmholtz equations. This is joint work with Chen Li (NYU).