**Dr. Moritz Flascel** is the winner of the **SWICCOMAS prize 2024 **

His thesis was selected as the Swiss-based candidate for the 2023 ECCOMAS PhD thesis award on Computational Methods in Applied Sciences and Engineering.

For the thesis dissertation:

« Automated Discovery of Material Models in Continuum Solid Mechanics »

Supervised by Professor Laura de Lorenzis, ETH Zürich

Abstract:

The mathematical description of the mechanical behavior of solid materials at the continuum scale is one of the oldest and most challenging tasks in solid mechanics and material science. The process of finding adequate mathematical formulae to describe the material characteristics is called material modeling and it is traditionally a time-consuming, intuition-driven and error-prone task. The new advances in data-driven and machine-learning-based methods promise an automation of the material model discovery process. In this work, the novel method EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) is discussed, which aims to mitigate the two main weak spots of the state-of-the-art machine-learning-based methods for material modeling; their data inefficiency and their physical uninterpretability. Instead of deploying a supervised training process informed by many labeled stress-strain data pairs, which are difficult to acquire experimentally, at the core of EUCLID stands an unsupervised and physics-driven training process that is informed by full-field displacement and reaction force data. In this way, all data needed for the material characterization can be acquired from a single experiment. Further, instead of describing the material behavior by uninterpretable black-box models, EUCLID discovers a suitable material model from a potentially large set of candidate models using sparse regression. A sparsity promoting regularization term ensures that the discovered model is parsimonious, i.e., it entails a small number of material parameters, function evaluations and internal variables, thus increasing the physical interpretability and efficiency of the model. By posing certain restrictions on the material model candidates, it is ensured that the discovered models fulfill physical requirements that are well-known in the field. In this thesis, EUCLID is studied in the context of hyperelastic materials, elastoplastic materials and generalized standard materials. The method is verified by numerical tests, proving that EUCLID infers from indirect data appropriate material models that are encoded by parsimonious mathematical expressions. Finally, the current challenges and future perspectives of EUCLID are critically discussed.

**Dr. Alice Cortinovis** is one of two winners of the **SWICCOMAS prize 2023**

Her thesis was selected as the Swiss-based candidate for the 2022 ECCOMAS PhD thesis award on Computational Methods in Applied Sciences and Engineering.

For the thesis dissertation:

« Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation »

Supervised by Professor Daniel Kressner, EPFL

Abstract:

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building low-rank approximations of a matrix from some rows or columns of the matrix itself. We prove a priori error bounds for a greedy algorithm for cross approximation and we develop a faster and more efficient variant of an existing algorithm for column subset selection. Moreover, we present a new deterministic polynomial-time algorithm that gives a cross approximation, which is quasi-optimal in the Frobenius norm. The second part of the thesis is concerned with matrix functions. We develop a divide-and-conquer algorithm for computing functions of matrices that are banded, hierarchically semiseparable, or have some other off-diagonal low-rank structure. An important building block of our approach is an existing algorithm for updating the function of a matrix that undergoes a low-rank modification (update), for which we present new convergence results. The convergence analysis of our divide-and-conquer algorithm is related to polynomial or rational approximation of the function. In the third part we consider the problem of approximating the trace of a matrix which is available indirectly, through matrix-vector multiplications. We analyze a stochastic algorithm, the Hutchinson trace estimator, for which we prove tail bounds for symmetric (indefinite) matrices. Then we apply our results to the computation of the (log)determinants of symmetric positive definite matrices.

**Dr. Pier Giuseppe Ledda** is one of two winners of the **SWICCOMAS prize 2023**

For the thesis dissertation:

« From coating flow patterns to porous body wake dynamics via multiscale models »

Supervised by Professor Francois Gallaire, EPFL

Abstract:

This thesis investigates the pattern formation of several coating flows and the wake dynamics past diverse permeable bodies via multiscale models. We initially consider the flow of a thin viscous film underneath an inclined planar substrate. We show the emergence of free- surface structures modulated along the direction transversal to the main flow, called rivulets. These rivulets result from a pure equilibrium between hydrostatic gravity and surface tension effects, and may destabilize with the formation of traveling drops. We determine via a linear stability analysis the critical values of the inclination angle and film thickness beyond which rivulets destabilize. We numerically study the linear and non-linear response with respect to a harmonic forcing in the inlet flow rate, determining the diverse lenses’ patterns emerging on a steady rivulet. Subsequently, we investigate the role of these instabilities in karst draperies formation, by coupling the hydrodynamic model with the deposition of calcium carbonate on the substrate. We implement an algorithm which retrieves the asymptotic properties of the two-dimensional linear impulse response from numerical simulations. The analysis shows the predominance of streamwise structures, reminiscent of draperies, growing on the substrate. The last part of the thesis is devoted to the modifications of wake flows instabilities past bluff bodies when composed of a permeable microstructure, with a focus on the case of a porous sphere and a cylindrical circular membrane. We develop an inverse procedure to optimize and retrieve the microstructure based on flow objectives.

**Dr. Erik Orvehed Hiltunen **is one of the three winners of the **SWICCOMAS prize 2022**

His thesis was selected as the Swiss-based candidate for the 2021 ECCOMAS PhD thesis award on Computational Methods in

Applied Sciences and Engineering.

For the thesis dissertation:

« Asymptotic analysis of high-contract subwavelgenth resonator structures »

Supervised by Professor Habib Ammari, ETH Zürich.

Abstract:

The ability to focus, trap, and guide the propagation of waves is of fundamental importance in physics. One of the most essential questions is how to localize waves to a prescribed position. If the wavelength is very long, the length scale of the localization must be considerably smaller (so-called subwavelength scales) to be physically feasible. In addition, the desired properties must be robust against imperfections that might appear in the manufacturing of such devices.

The aim of this thesis is to address these questions and provide a mathematical understanding of robust wave localization on subwavelength scales. We analyze so-called high-contrast subwavelength metamaterials and prove that these materials may exhibit a range of exotic wave properties on subwavelength scales. We prove the possibility of localizing and guiding waves in such materials, and use the concept of topological insulators to achieve robust localization. These problems are tackled using layer-potential techniques combined with asymptotic analysis, which offer powerful tools for solving wave problems on subwavelength scales. Throughout, the mathematical results are numerically illustrated using the efficient and reliable Multipole method.

**Dr. Mattia Cenedese** is one of the three winners of the **SWICCOMAS prize 2022**

For the thesis dissertation:

« A Geometric Approach to Nonlinear Mechanical Vibrations: from Analytic to Data-driven Methods »

Supervised by Professor George Haller, ETH Zürich.

Abstract:

This thesis devises analytical and data-driven methods for the analysis of nonlinear vibrations in mechanical systems, potentially with a large number of degrees of freedom. Modern challenges in engineering require deeper understanding of nonlinear oscillations in mechanical systems, as well as extracting data-driven predictive models. In the first part of this thesis, the focus is set on analytical models, with forced-damped nonlinear mechanical systems viewed as small perturbations from their energy-preserving counterpart. Indeed, amplitude frequency plots for the conservative limit have frequently been observed, both numerically and experimentally, to serve as backbone curves for the near-resonance peaks of the forced-damped response. A systematic mathematical analysis is then derived, allowing to predict which members of conservative periodic orbit families will survive in the forced-damped response. The second part of this thesis looks at oscillatory dynamics from a data-driven perspective to construct reduced-order models. Based on the theory of spectral submanifolds, a method is developed for simultaneous dimensionality reduction and normal form identification of the dynamics, offering valuable insights and capable of predictions when small perturbations, such as external forcing, are added to systems. The algorithm based on this approach automatically detects the appropriate normal form for a given set of trajectories data, thereby providing an intelligent, unsupervised learning strategy for dynamical systems. The accuracy of the method is demonstrated on different examples, featuring data from simulations and experiments.

**Dr. Adrien Laurent **is one of the three winners of the **SWICCOMAS prize 2022**

For the thesis dissertation:

« Algebraic Tools and Multiscale Methods for the Numerical Integration of Stochastic Evolutionary Problems »

Supervised by: Professor Gilles Vilmart, Université de Genève.

Abstract:

This thesis focuses on the construction and the study of numerical integrators in time to solve stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs). More precisely, we are interested in the convergence of the methods, in the weak sense and for sampling the invariant measure in the case of ergodic dynamics, introducing a new algebraic framework of trees for the computation of order conditions. We focus on the preservation of geometric properties by the numerical integrators, in particular invariants and constraints, as well as on the robustness of the methods in the case of multiscale problems. We introduce new integrators for solving overdamped Langevin dynamics and the non-linear Schrödinger equation with dispersive white noise to confirm our theoretical findings.

**Dr. Lucas Frérot** is one of two winners of the **SWICCOMAS prize 2021**

His thesis was selected as the Swiss-based candidate for the 2020 ECCOMAS PhD thesis award on Computational Methods in Applied Sciences and Engineering.

For the thesis dissertation:

« Bridging scales in wear modeling with volume integral methods for elastic-plastic contact »

Supervised by Professor Jean-François Molinari and Dr Guillaume Anciaux, EPFL

Abstract:

Friction and wear are fundamental tribological phenomena that affect many aspects of our society: from the gears of a Swiss watch to car brakes and earthquakes. Despite being integral parts of everyday life, friction and wear remain elusive to quantitative predictions. Their systematic study, since the seminal experiments of Da Vinci, Amontons and Coulomb, has been quasi-exclusively experimental. This limits our capacity to understand tribological systems to those that can be reproduced experimentally. Perhaps the most challenging factors are the profoundly multi-scale and multi-physics aspect of both friction and wear, as well as the difficulty of observing what occurs at frictional interfaces. Due to natural or artificial roughness, things that appear in contact at the macro-scale actually only interact on an area that is much smaller than their apparent contact area. The processes that give rise to macroscopic friction and wear occur that the micro-contacts that make up this “true” contact area. During my thesis, I have developed simulation methods to accurately compute contact interfaces with multi-scale roughness. Because the true contact area is small, contact pressures can be very large, causing plastic (irreversible) deformation of the bodies in contact. To account for this effect, I developed a new approach to volume integral methods. My contributions allowed large scale simulations of plastic rough contact, which contributed to the understanding of the role of plasticity on the formation of cracks that can lead to wear debris detachment.

**Dr. Tommaso Vanzan **is one of two winners of the **SWICCOMAS prize 2021
**

For the thesis dissertation:

« Domain decomposition methods for multiphysics problems »

Supervised by: Professor Martin J. Gander, UNIGE

Abstract:

This thesis contributes to the development of Domain Decomposition (DD) methods which are numerical algorithms to solve efficiently large linear and nonlinear systems arising from the discretization of Partial Differential Equations (PDE).

The main focus is on Optimized Schwarz Methods (OSMs) as they are the natural DD framework for multiphysics problems due to their property of convergence in the absence of overlap and the possiblity to tune the transmission conditions according to the physical parameters.

We study one-level and multilevel OSMs and derive optimized transmission conditions for several couplings of second order PDEs.

We then introduce a new substructured framework for a two-level and multilevel parallel Schwarz method, and provide a convergence analysis both for geometric and spectral coarse spaces. This framework is further extended to nonliner systems.

Finally, we present some results on the scalability of DD methods for specific geometries and for discrete fracture networks.

As an application, the methods developed have been applied to the Stokes-Darcy coupling, which is an instance of a multiphysics problem describing the filtration of fluids in porous media.

**Dr. Predrag Andric** is one of two winners of the **SWICCOMAS prize 2020**

His thesis was selected as the Swiss-based candidate for the 2019 ECCOMAS PhD thesis award on Computational Methods in Applied Sciences and Engineering.

For the thesis dissertation:

« The mechanics of crack-tip dislocation emission and twinning »

Supervised by Professor Bill Curtin, EPFL

Abstract:

This thesis proposes two new theories for describing the mechanics of crack tip dislocation emission and twinning. Dislocation emission from a crack tip is a necessary mechanism for crack tip blunting and toughening, and at the same time one of the classical problems in mechanics of materials. A material is intrinsically ductile under Mode I loading when the critical stress intensity factor for dislocation emission *K _{Ie}* is lower than the critical stress intensity factor

*K*for cleavage.

_{IC}*K*is usually evaluated using the approximate Rice theory. Atomistic simulations have shown that this theory is reasonable but not highly accurate. The discrepancy arises because Mode I emission is accompanied by the formation of a surface step that is not considered in the Rice theory. In this work we propose a new theory for Mode I emission based on the idea that (i) the stress resisting step formation at the crack tip creates “lattice trapping” against dislocation emission such that (ii) emission is due to a mechanical instability at the crack tip. Furthermore, a theory for crack-tip twinning has been proposed accounting for (i) the absence of the step formation, and (ii) the fact that nucleation does not occur directly at the tip. Both theories are quantitatively validated against atomistic simulations across a wide set of fcc materials.

_{Ie}

**Dr. Maria Han Veiga **is one of two winners of the **SWICCOMAS prize 2020
**

For the thesis dissertation:

« High order structure preserving numerical schemes for astrophysical flows »

Supervised by: Professor Rémi Abgrall and Romain Teyssier, UZH

Abstract:

In the thesis, we develop high order numerical methods which are structure preserving, as well as structure preserving data-driven method that aim to provide better numerical tools for simulations in astrophysics.

Motivated by the early stages of planet formation, we present a method that solves the unsteady compressible Euler system with gravity type source terms which can capture steady states beyond hydrostatic equilibrium on Cartesian coordinates. Then, motivated by the growing interest in high-order magneto-hydrodynamics (MHD) solvers in astrophysics and the difficulty in addressing the divergence free condition of magnetic fields, we present two methods that solve the linear induction equation (a simplification of MHD) while fulfilling the divergence constraint. We also present work towards structure preserving learning algorithms: a data-driven limiter which is symmetry and scale invariant as well as a methodology to transfer the data-driven limiter across different numerical schemes. Finally, we present some work towards high fidelity multi-scale modeling, combining two distinct simulation regimes (that model different space and time scales) with data-driven methods.

**Dr. Max Hodapp **is one of two winners of the **SWICCOMAS prize 2019
**and has been selected as the Swiss-based candidate for the 2018 ECCOMAS PhD thesis award on Computational Methods in Applied Sciences and Engineering.

For the thesis dissertation:

« On flexible Green function methods for atomistic/continuum coupling”

Thesis director – William Curtin, EPFL

Abstract:

Atomistic/continuum (A/C) coupling schemes have been developed during the past twenty years to overcome the vast computational cost of fully atomistic models, but have not yet reached full maturity to address many open problems in metal plasticity. This thesis has therefore been devoted to the development of an extension of the coupled atomistic/discrete dislocations method to three dimensions (CADD-3d). To simulate the motion of hybrid dislocations along A/C interfaces a simplified solution procedure, which updates the boundary conditions on the atomistic problem based on the Green function of the entire dislocation network, has been introduced and validated. In order to solve the complementary elasticity problem a discrete boundary element method (DBEM) has been developed and implemented using an efficient hierarchical representation of the dense system matrices. The coupled atomistic/DBEM problem is solved using a fast stabilized monolithic Newton-Krylov method and an improvement of the overall accuracy by several orders of magnitude has been found in comparison with naive clamped boundary conditions. In addition, a semi-monolithic solution procedure has been conceptually proposed for CADD-3d which iterates between the entire physical and the discrete dislocation problem. Using the atomistic/DBEM coupling the computational complexity of this method becomes highly favorable in comparison with existing schemes in terms of the required degrees of freedom if many dislocations have passed the A/C interface.

**Dr. Paola Bacigaluppi** is one of two winners of the **SWICCOMAS prize 2019**

For the thesis dissertation:

“High Order Fully Explicit Residual Distribution Approximation for Conservative and Non-Conservative Systems in Fluid Dynamics”

Thesis director – Rémi Abgrall, UZH

Abstract:

In this work we collect several studies that embroil diverse techniques to tackle some of the many unsolved challenges linked to the study of strong interacting discontinuities for multidimensional, time-dependent hyperbolic systems of equations in Fluid Dynamics written both in conservative and non-conservative form.

To this end, we propose methodologies based on Residual Distribution schemes, which can be reinterpreted as non-standard Finite Volume and Finite Element approaches (Abgrall, Computational Methods in Applied Mathematics 2018). In particular, we develop fully explicit high-order oscillation-free numerical methods without exceeding dissipation across shocking waves and allow to work directly with non-conservative variables, like pressures and internal energies, without any loss of conservation, and thus of information.

The robustness and accuracy of the novel strategies are assessed on several challenging benchmark problems in the context of the Euler equations for single phase flows and reduced Baer and Nunziato type systems for two-phase flows.

Dr. Joseph B. Nagel won **The SWICCOMAS prize 2018**

For the thesis dissertation:

« Bayesian techniques for inverse uncertainty quantification »

ETH Zürich – Thesis director Prof. Dr. Bruno Sudret

Abstract:

The thesis deals with Bayesian techniques for inverse problems under uncertainty. A probabilistic framework for treating both epistemic (lack of knowledge) and aleatoric uncertainties (natural variability) is established. Hamiltonian Monte Carlo is then proposed in order to tackle the computational challenge of exploring possibly high-dimensional posterior distributions. Beyond that, novel approaches to computational Bayesian inference are developed on the basis of variational methods and polynomial chaos expansions. They try to overcome the shortcomings of traditional sampling-based Markov chain Monte Carlo algorithms. A variety of problems, either simple or realistically complex, from the domain of civil, mechanical and hydrological engineering serve for demonstration purposes.