@article{45969, abstract = {{AbstractAn evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms are proposed, both based on a system coupling the diffusion equation to evolution equations for geometric quantities in the velocity law for the surface. One of the numerical methods is proved to be convergent in the$$H^1$$H1norm with optimal-order for finite elements of degree at least two. We present numerical experiments illustrating the convergence behaviour and demonstrating the qualitative properties of the flow: preservation of mean convexity, loss of convexity, weak maximum principles, and the occurrence of self-intersections.}}, author = {{Elliott, Charles M. and Garcke, Harald and Kovács, Balázs}}, issn = {{0029-599X}}, journal = {{Numerische Mathematik}}, keywords = {{Applied Mathematics, Computational Mathematics}}, number = {{4}}, pages = {{873--925}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces}}}, doi = {{10.1007/s00211-022-01301-3}}, volume = {{151}}, year = {{2022}}, } @article{45963, abstract = {{AbstractThe scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this includes a thin coating around a perfect conductor and the skin effect of a highly conducting material. The approach taken in this work is to derive, analyse and discretize a system of time-dependent boundary integral equations that determines the tangential traces of the scattered electric and magnetic fields. In a familiar second step, the fields are evaluated in the exterior domain by a representation formula, which uses the time-dependent potential operators of Maxwell’s equations. The time-dependent boundary integral equation is discretized with Runge–Kutta based convolution quadrature in time and Raviart–Thomas boundary elements in space. Using the frequency-explicit bounds from the well-posedness analysis given here together with known approximation properties of the numerical methods, the full discretization is proved to be stable and convergent, with explicitly given rates in the case of sufficient regularity. Taking the same Runge–Kutta based convolution quadrature for discretizing the time-dependent representation formulas, the optimal order of convergence is obtained away from the scattering boundary, whereas an order reduction occurs close to the boundary. The theoretical results are illustrated by numerical experiments.}}, author = {{Nick, Jörg and Kovács, Balázs and Lubich, Christian}}, issn = {{0029-599X}}, journal = {{Numerische Mathematik}}, keywords = {{Applied Mathematics, Computational Mathematics}}, number = {{4}}, pages = {{1123--1164}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Time-dependent electromagnetic scattering from thin layers}}}, doi = {{10.1007/s00211-022-01277-0}}, volume = {{150}}, year = {{2022}}, } @article{45964, abstract = {{Abstract Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients in the parabolic equations at a fixed time and utilizing a perturbation argument around the freezed time, it is shown that backward difference time discretizations of linear parabolic equations on an evolving surface along characteristic trajectories can preserve maximal $L^p$-regularity in the discrete setting. The result is applied to prove the stability and convergence of time discretizations of nonlinear parabolic equations on an evolving surface, with linearly implicit backward differentiation formulae characteristic trajectories of the surface, for general locally Lipschitz nonlinearities. The discrete maximal $L^p$-regularity is used to prove the boundedness and stability of numerical solutions in the $L^\infty (0,T;W^{1,\infty })$ norm, which is used to bound the nonlinear terms in the stability analysis. Optimal-order error estimates of time discretizations in the $L^\infty (0,T;W^{1,\infty })$ norm is obtained by combining the stability analysis with the consistency estimates.}}, author = {{Kovács, Balázs and Li, Buyang}}, issn = {{0272-4979}}, journal = {{IMA Journal of Numerical Analysis}}, keywords = {{Applied Mathematics, Computational Mathematics, General Mathematics}}, publisher = {{Oxford University Press (OUP)}}, title = {{{Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems}}}, doi = {{10.1093/imanum/drac033}}, year = {{2022}}, } @article{45966, abstract = {{Abstract This paper studies bulk–surface splitting methods of first order for (semilinear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a coupled partial differential–algebraic equation system, i.e., the boundary conditions are considered as a second dynamic equation that is coupled to the bulk problem. The splitting approach is combined with bulk–surface finite elements and an implicit Euler discretization of the two subsystems. We prove first-order convergence of the resulting fully discrete scheme in the presence of a weak CFL condition of the form $\tau \leqslant c h$ for some constant $c>0$. The convergence is also illustrated numerically using dynamic boundary conditions of Allen–Cahn type.}}, author = {{Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}}, issn = {{0272-4979}}, journal = {{IMA Journal of Numerical Analysis}}, keywords = {{Applied Mathematics, Computational Mathematics, General Mathematics}}, number = {{2}}, pages = {{950--975}}, publisher = {{Oxford University Press (OUP)}}, title = {{{Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions}}}, doi = {{10.1093/imanum/drac002}}, volume = {{43}}, year = {{2022}}, } @article{45968, abstract = {{Abstract We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe the coupling and the dynamics in the abstract bulk- and surface-spaces, and treats the nonlinear terms similarly to an exponential integrator. The convergence proof is based on estimates for a recursive formulation of the error, using the parabolic smoothing property of analytic semigroups, and a careful comparison of the exact and approximate flows. This analysis also requires a deep understanding of the effects of the Dirichlet operator (the abstract version of the harmonic extension operator), which is essential for the stable coupling in our method. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented.}}, author = {{Csomós, Petra and Farkas, Bálint and Kovács, Balázs}}, issn = {{0272-4979}}, journal = {{IMA Journal of Numerical Analysis}}, keywords = {{Applied Mathematics, Computational Mathematics, General Mathematics}}, publisher = {{Oxford University Press (OUP)}}, title = {{{Error estimates for a splitting integrator for abstract semilinear boundary coupled systems}}}, doi = {{10.1093/imanum/drac079}}, year = {{2022}}, } @article{45958, abstract = {{AbstractIn this paper, we consider a non-linear fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix–vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.}}, author = {{Beschle, Cedric Aaron and Kovács, Balázs}}, issn = {{0029-599X}}, journal = {{Numerische Mathematik}}, keywords = {{Applied Mathematics, Computational Mathematics}}, number = {{1}}, pages = {{1--48}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces}}}, doi = {{10.1007/s00211-022-01280-5}}, volume = {{151}}, year = {{2022}}, } @article{45956, abstract = {{Abstract The full Maxwell equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert equation serve as a well-tested model for ferromagnetic materials. We propose a weak formulation of the coupled system based on the boundary integral formulation of the exterior Maxwell equations. We show existence and partial uniqueness of a weak solution and propose a new numerical algorithm based on finite elements and boundary elements as spatial discretization with backward Euler and convolution quadrature for the time domain. This is the first numerical algorithm which is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and full Maxwell’s equations without any simplifications like quasi-static approximations (e.g. eddy current model) and without restrictions on the shape of the domain (e.g. convexity). We show well-posedness and convergence of the numerical algorithm under minimal assumptions on the regularity of the solution. This is particularly important as there are few regularity results available and one generally expects the solution to be non-smooth. Numerical experiments illustrate and expand on the theoretical results.}}, author = {{Bohn, Jan and Feischl, Michael and Kovács, Balázs}}, issn = {{1609-4840}}, journal = {{Computational Methods in Applied Mathematics}}, keywords = {{Applied Mathematics, Computational Mathematics, Numerical Analysis}}, number = {{1}}, pages = {{19--48}}, publisher = {{Walter de Gruyter GmbH}}, title = {{{FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation}}}, doi = {{10.1515/cmam-2022-0145}}, volume = {{23}}, year = {{2022}}, } @article{53321, abstract = {{ The chemotaxis system [Formula: see text] is considered in a ball [Formula: see text], [Formula: see text], where the positive function [Formula: see text] reflects suitably weak diffusion by satisfying [Formula: see text] for some [Formula: see text]. It is shown that whenever [Formula: see text] is positive and satisfies [Formula: see text] as [Formula: see text], one can find a suitably regular nonlinearity [Formula: see text] with the property that at each sufficiently large mass level [Formula: see text] there exists a globally defined radially symmetric classical solution to a Neumann-type boundary value problem for (⋆) which satisfies [Formula: see text] }}, author = {{Winkler, Michael}}, issn = {{0219-1997}}, journal = {{Communications in Contemporary Mathematics}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{10}}, publisher = {{World Scientific Pub Co Pte Ltd}}, title = {{{Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems}}}, doi = {{10.1142/s0219199722500626}}, volume = {{25}}, year = {{2022}}, } @article{53327, author = {{Tao, Youshan and Winkler, Michael}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, keywords = {{Analysis, Applied Mathematics}}, pages = {{390--418}}, publisher = {{Elsevier BV}}, title = {{{Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension}}}, doi = {{10.1016/j.jde.2022.10.022}}, volume = {{343}}, year = {{2022}}, } @article{53325, author = {{Desvillettes, Laurent and Laurençot, Philippe and Trescases, Ariane and Winkler, Michael}}, issn = {{0362-546X}}, journal = {{Nonlinear Analysis}}, keywords = {{Applied Mathematics, Analysis}}, publisher = {{Elsevier BV}}, title = {{{Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing}}}, doi = {{10.1016/j.na.2022.113153}}, volume = {{226}}, year = {{2022}}, } @article{35685, author = {{Liebendörfer, Michael and Göller, Robin and Gildehaus, Lara and Kortemeyer, Jörg and Biehler, Rolf and Hochmuth, Reinhard and Ostsieker, Laura and Rode, Jana and Schaper, Niclas}}, issn = {{0020-739X}}, journal = {{International Journal of Mathematical Education in Science and Technology}}, keywords = {{Applied Mathematics, Education, Mathematics (miscellaneous)}}, number = {{5}}, pages = {{1133--1152}}, publisher = {{Informa UK Limited}}, title = {{{The role of learning strategies for performance in mathematics courses for engineers}}}, doi = {{10.1080/0020739x.2021.2023772}}, volume = {{53}}, year = {{2022}}, } @article{45849, abstract = {{AbstractDependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic(PDL)and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) ofPDLisNP-complete (Ebbing and Lohmann, SOFSEM 2012). The subject of this research is to identify a list of parameterisations (formula-size, formula-depth, treewidth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) which classically is known to beNP-complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT isparaNP-complete whereas under all other mentioned parameters the problem isFPT. Finally, we introduce a variant of the satisfiability problem, asking for a team of a given size, and show for this problem an almost complete picture.}}, author = {{Mahmood, Yasir and Meier, Arne}}, issn = {{1012-2443}}, journal = {{Annals of Mathematics and Artificial Intelligence}}, keywords = {{Applied Mathematics, Artificial Intelligence}}, number = {{2-3}}, pages = {{271--296}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Parameterised complexity of model checking and satisfiability in propositional dependence logic}}}, doi = {{10.1007/s10472-021-09730-w}}, volume = {{90}}, year = {{2022}}, } @article{34264, abstract = {{In industrial x-ray computed tomography (CT), the application of more complex scan paths in comparison to the typical circular trajectory (${360}^{\circ}$ rotation of the measurement object) can extend the potential of CT. One way to enable such 3D scan trajectories is to use a 6-degrees-of-freedom (DOF) object manipulator system. In our case, a hexapod is mounted on top of the rotary table of a commercial CT scanner. This allows for adaptive tilting of the measurement object during the scan. For high accuracy, the geometry calibration of such setups is typically done using the x-ray projections of a calibrated multi-sphere object. Contrary to this, here, we demonstrate a procedure that is based on only a single sphere and can therefore experimentally be implemented with low effort. Using the intrinsic geometry parameters of the CT device as prior information, the hexapod coordinate system with respect to the CT machine coordinate system is determined by means of a one-step optimization approach. The resulting parameters are used to calculate projection matrices that enable the volume reconstruction for 3D scan trajectories. The method is validated using simulated x-ray images and experimental investigations including dimensional measurements. For the used setup, geometric measurement results for 3D scan trajectories that are calibrated with the presented method show in sum increased errors compared to the circular scans. A limited pose accuracy of the manipulator system is discussed as a potential cause. The results nevertheless indicate that the presented method is generally feasible for dimensional CT measurements provided that the pose accuracy is sufficient. The calibration procedure can therefore be a low-cost and easier to implement alternative compared to trajectory calibration methods based on multi-sphere objects, but with a tendency towards lower measurement accuracy. The methodology can in principle be transferred to different setups with 6-DOF manipulator systems, e.g. C-arm CT devices with a robot arm.}}, author = {{Butzhammer, Lorenz and Müller, Andreas Michael and Hausotte, Tino}}, issn = {{0957-0233}}, journal = {{Measurement Science and Technology}}, keywords = {{Applied Mathematics, Instrumentation, Engineering (miscellaneous)}}, number = {{1}}, publisher = {{IOP Publishing}}, title = {{{Calibration of 3D scan trajectories for an industrial computed tomography setup with 6-DOF object manipulator system using a single sphere}}}, doi = {{10.1088/1361-6501/ac9856}}, volume = {{34}}, year = {{2022}}, } @article{35206, author = {{Bonnard, Bernard and Rouot, Jérémy and Wembe Moafo, Boris Edgar}}, issn = {{2156-8472}}, journal = {{Mathematical Control and Related Fields}}, keywords = {{Applied Mathematics, Control and Optimization, General Medicine}}, pages = {{0--0}}, publisher = {{American Institute of Mathematical Sciences (AIMS)}}, title = {{{Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies}}}, doi = {{10.3934/mcrf.2022052}}, year = {{2022}}, } @article{30655, author = {{Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua}}, issn = {{0178-7675}}, journal = {{Computational Mechanics}}, keywords = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}}, number = {{3}}, pages = {{847--863}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua}}}, doi = {{10.1007/s00466-021-02117-y}}, volume = {{69}}, year = {{2022}}, } @article{34839, abstract = {{We describe the relations among the ℓ-torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent in some sense. Altogether, the three conjectures are equivalent for the class of solvable groups. We then prove the ℓ-torsion conjecture for ℓ-groups and the other two conjectures for nilpotent groups.}}, author = {{Klüners, Jürgen and Wang, Jiuya}}, issn = {{0002-9939}}, journal = {{Proceedings of the American Mathematical Society}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{7}}, pages = {{2793--2805}}, publisher = {{American Mathematical Society (AMS)}}, title = {{{ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group}}}, doi = {{10.1090/proc/15882}}, volume = {{150}}, year = {{2022}}, } @article{44236, author = {{Wende, Marc and Staggenborg, Christoph and Kenig, Eugeny Y.}}, issn = {{0009-2509}}, journal = {{Chemical Engineering Science}}, keywords = {{Applied Mathematics, Industrial and Manufacturing Engineering, General Chemical Engineering, General Chemistry}}, publisher = {{Elsevier BV}}, title = {{{Modelling and simulation of zero-gravity distillation units with metal foams}}}, doi = {{10.1016/j.ces.2021.117097}}, volume = {{247}}, year = {{2022}}, } @article{30591, author = {{Bertling, René and Hack, M. and Ausner, I. and Horschitz, B. and Bernemann, Sören Antonius and Kenig, Eugeny}}, issn = {{0009-2509}}, journal = {{Chemical Engineering Science}}, keywords = {{Applied Mathematics, Industrial and Manufacturing Engineering, General Chemical Engineering, General Chemistry}}, publisher = {{Elsevier BV}}, title = {{{Modelling film and rivulet flows on microstructured surfaces using CFD methods}}}, doi = {{10.1016/j.ces.2021.117414}}, volume = {{251}}, year = {{2022}}, } @article{30382, author = {{Bertling, R. and Hack, M. and Ausner, I. and Horschitz, B. and Bernemann, S. and Kenig, E.Y.}}, issn = {{0009-2509}}, journal = {{Chemical Engineering Science}}, keywords = {{Applied Mathematics, Industrial and Manufacturing Engineering, General Chemical Engineering, General Chemistry}}, publisher = {{Elsevier BV}}, title = {{{Modelling film and rivulet flows on microstructured surfaces using CFD methods}}}, doi = {{10.1016/j.ces.2021.117414}}, volume = {{251}}, year = {{2022}}, } @article{44468, author = {{Schmidt, Stephan and Gräßer, Melanie and Schmid, Hans-Joachim}}, issn = {{1064-8275}}, journal = {{SIAM Journal on Scientific Computing}}, keywords = {{Applied Mathematics, Computational Mathematics}}, number = {{4}}, pages = {{B1175--B1194}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges}}}, doi = {{10.1137/20m1389054}}, volume = {{44}}, year = {{2022}}, }