BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexandre Ern (Université Paris-Est\, CERMICS \, ENPC) DTSTART:20210209T060000Z DTEND:20210209T070000Z DTSTAMP:20260422T225753Z UID:CMWebinar/1 DESCRIPTION:Title: Hybrid high-order methods for the wave equation on unfitted meshes\n by Alexandre Ern (Université Paris-Est\, CERMICS \, ENPC) as part of Aust ralian Seminar on Computational Mathematics\n\n\nAbstract\nWe design and a nalyze an unfitted hybrid high-order (HHO) method for the acoustic wave eq uation. The wave propagates in a domain where a curved interface separates subdomains with different material properties. The key feature of the spa ce discretization method is that the interface can cut more or less arbitr arily through the mesh cells. We address both the second-order formulation in time of the wave equation and its reformulation as a first-order syste m. For explicit time-stepping schemes\, we study the CFL condition and obs erve that the unfitted approach combined with local cell agglomeration lea ds to a comparable condition as when using fitted meshes.\n LOCATION:https://researchseminars.org/talk/CMWebinar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Kris van der Zee (University of Nottingham) DTSTART:20210223T070000Z DTEND:20210223T080000Z DTSTAMP:20260422T225753Z UID:CMWebinar/2 DESCRIPTION:Title: Minimal Residual Finite Element Methods in Banach Spaces\nby Kris va n der Zee (University of Nottingham) as part of Australian Seminar on Comp utational Mathematics\n\n\nAbstract\nMinimal-residual (MinRes) finite elem ent methods have attracted significant attention in the recent numerical a nalysis literature\, owing to their conceptual simplicity and striking sta bility properties. While these methods include classical least-squares and optimal Petrov-Galerkin methods\, recent advances centre around the minim isation of residuals measured in a (discrete) dual norm\, such as the disc ontinuous Petrov--Galerkin (DPG) methodology. \n\nIn this talk\, I will fi rst discuss how MinRes methods can be extended to Banach-space settings. T his general setting allows for a direct discretization of PDEs in nonstand ard non-Hilbert settings that are required when facing rough data and low- regular solutions. This development gives rise to a class of nonlinear Pet rov--Galerkin methods\, or\, equivalently\, abstract mixed methods with mo notone nonlinearity. Discrete stability and quasi-optimal convergence foll ow under a Fortin condition. I will consider applications to PDEs (linear transport\, advection-diffusion)\, as well as the regularization of rough linear functionals. \n\nSecondly\, I will show how the MinRes framework ca n be utilised for model reduction. In particular\, I will present a machin e-learning framework to train a provably stable parametric Petrov-Galerkin method on a fixed underlying mesh\, whose aim is to ensure highly accurat e quantities of interest regardless of the mesh size. Some recent numerics will illustrate these ideas.\n LOCATION:https://researchseminars.org/talk/CMWebinar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Johnny Guzman (Brown University) DTSTART:20210323T000000Z DTEND:20210323T010000Z DTSTAMP:20260422T225753Z UID:CMWebinar/3 DESCRIPTION:Title: A discrete elasticity complex on Alfeld splits\nby Johnny Guzman (Br own University) as part of Australian Seminar on Computational Mathematics \n\n\nAbstract\nWe discuss what appears to be the first finite element ela sticity sequence in 3d on tetrahedral meshes. We build this sequence usin g two discrete de Rham sequences that have more smoothness than the Whitne y forms. To do this we use Alfeld splits that take a tetrahedral decomposi tion and split each tetrahedron into four tetrahedra by adding the barycen ter. We provide degrees of freedom for the spaces as well as commuting pr ojections. This is joint work with Snorre Christiansen\, Kaibo Hu and Jay Gopalakrishnan.\n LOCATION:https://researchseminars.org/talk/CMWebinar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Antti Niemi (University of Oulu) DTSTART:20210504T070000Z DTEND:20210504T080000Z DTSTAMP:20260422T225753Z UID:CMWebinar/4 DESCRIPTION:Title: Computational mathematics for structural engineering with some arctic tw ist\nby Antti Niemi (University of Oulu) as part of Australian Seminar on Computational Mathematics\n\n\nAbstract\nTechnical requirements for st ructural design are based on economic\, environmental\, and social pillars . Assessment of the various kind of criteria requires mathematical models and computational tools suitable for conceptual design at the early design stage as well as for high-fidelity simulation at the component level. Per formance of lightweight thin-walled structures is known to be very sensiti ve to uncertainties in geometry\, material properties\, support conditions and external loading. Therefore\, reliable mathematical models and numeri cal methods are of utmost importance in their modeling. \n\nThis talk shal l address some open problems related to the stability analysis of curved s hell structures and structural reliability of lightweight structures in ge neral. The ideas are based on variational principles of mechanics and appl ied probability theory.\n LOCATION:https://researchseminars.org/talk/CMWebinar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Giancarlo Sangalli (University of Pavia) DTSTART:20210309T060000Z DTEND:20210309T070000Z DTSTAMP:20260422T225753Z UID:CMWebinar/5 DESCRIPTION:Title: Isogeometric Analysis: a high-order method for PDEs\nby Giancarlo Sa ngalli (University of Pavia) as part of Australian Seminar on Computationa l Mathematics\n\n\nAbstract\nIsogeometric Analysis was proposed in the sem inal work of Hughes\, Cottrell\, and Bazilevs in 2005\, and be seen as a g eneralisation of the finite element\nmethod that replaces classical $C^0$ finite elements with smooth\nsplines. Doing so\, IGA aims to be easily co mpatible with\ncomputer-aided geometric design systems\, where smooth spl ines are used\nto create computational geometric models. In this framework \, \nthere has been a successful creation of novel\, robust\, high-order\n accurate numerical methods for solving PDEs.\n\nThe concept of k-refinemen t (or K-method) was proposed as one of\nthe key features of isogeometric analysis\, "a new\, more efficient\,\nhigher-order concept"\, in the origi nal isogeometric article by Hughes and co-workers. The idea of using high- degree\nand continuity splines (or NURBS\, etc.) as a basis for a new\nhig h-order method appeared very promising from the beginning. The\nk-refineme nt leads to several advantages: higher accuracy per\ndegree-of-freedom\, i mproved spectral accuracy\, the possibility of\nstructure-preserving smoot h discretizations are the most interesting\nfeatures that have been studie d actively in the community. At the same\ntime\, the k-refinement brings s ignificant challenges at the\ncomputational level: using standard finite e lement routines\, its\ncomputational cost grows with respect to the degree \, making degree\nraising computationally expensive. After a brief introdu ction of\nIsogeometric Analysis\, I will discuss ideas from\n[Sangalli a nd Tani\, CMAME\, 2018\, arXiv:1712.08565] and following works\, that allo w a computationally\nefficient k-refinement.\n LOCATION:https://researchseminars.org/talk/CMWebinar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura De Lorenzis (ETH Zurich) DTSTART:20210608T070000Z DTEND:20210608T080000Z DTSTAMP:20260422T225753Z UID:CMWebinar/6 DESCRIPTION:Title: Unsupervised discovery of constitutive laws\nby Laura De Lorenzis (E TH Zurich) as part of Australian Seminar on Computational Mathematics\n\n\ nAbstract\nThe speaker and her group recently proposed a new approach for data-driven automated discovery of constitutive laws. The approach is unsu pervised\, i.e.\, it requires no stress data but only displacement and glo bal force data\, which are realistically available through mechanical test ing and digital image correlation techniques\; it delivers interpretable m odels\, i.e.\, models that are embodied by parsimonious mathematical expre ssions discovered through sparse regression of a large catalogue of candid ate functions\; it is one-shot\, i.e.\, discovery only needs one experimen t — but can use more if available. The problem of unsupervised discovery is solved by enforcing equilibrium constraints in the bulk and at the loa ded boundary of the domain. Sparsity of the solution is achieved by Lp reg ularization combined with thresholding\, which calls for a non-linear opti mization scheme. The ensuing fully automated algorithm leverages physics-b ased constraints for the automatic determination of the penalty parameter in the regularization term. We focus on isotropic hyperelasticity and\, us ing numerically generated data including artificial noise\, we demonstrate the ability of the approach to accurately discover five hyperelastic mode ls of different complexity. We also show that\, if a “true” feature is missing in the function library\, the proposed approach is able to surrog ate it in such a way that the actual response is still accurately predicte d. We finally outline the first steps in the direction of extending the ap proach to more complex types of constitutive laws.\n LOCATION:https://researchseminars.org/talk/CMWebinar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Carla Manni (University of Rome Tor Vergata) DTSTART:20210420T070000Z DTEND:20210420T080000Z DTSTAMP:20260422T225753Z UID:CMWebinar/7 DESCRIPTION:Title: Spectral analysis of matrices from isogeometric methods\nby Carla Ma nni (University of Rome Tor Vergata) as part of Australian Seminar on Comp utational Mathematics\n\n\nAbstract\nWhen discretizing a linear PDE by a l inear numerical method\, the computation of the numerical solution reduces \nto solving a linear system. The size of this system grows when we refine the discretization mesh.\nWe are then in the presence of a sequence of li near systems with increasing size.\nIt is usually observed in practice tha t the corresponding sequence of discretization matrices enjoys\n an asympt otic spectral distribution. Roughly speaking this means that there exists a function\, say f\,\nsuch that the eigenvalues of the considered sequence of matrices behave like a sampling of f over an\nequispaced grid on the d omain of f\, up to some outliers.\n\nIsogeometric analysis is a well-estab lished paradigm for the analysis of problems governed by PDEs.\nIt provide s a design-through-analysis connection by exploiting a common representati on model. This connection is achieved\nby using the functions adopted in CAD systems not only to describe the domain geometry\, but also to represe nt the numerical solution of\nthe differential problem.\nIn its original f ormulation IgA is based on (tensor-product) B-splines and their rational e xtension\, the so-called NURBS [2].\n\nIn this talk we review the main spe ctral properties of discretization matrices arising from isogeometric meth ods\, based on \nd-variate NURBS of given degrees and applied to general s econd-order\nelliptic differential problems defined on a d-dimensional dom ain [4\,5]\, \ndiscussing the differences and the similarities with the FE M case [6]. \nWe also discuss the relation between outliers and convergenc e to eigenfunctions of classical differential operators under k-refinement . \n\nThe provided spectral information can be exploited for designing i terative solvers [3] \nwith convergence speed independent of the fineness parameters and also substantially independent of the degrees of the used N URBS\, [1].\n\nThe talk is based on joint works with C. Garoni\, F. Pelosi \, E. Sande\, H. Speleers\, S. Serra-Capizzano.\n\nReferences\n\n[1] N. Co llier\, L. Dalcin\, D. Pardo\, V.M. Calo\nThe cost of continuity: Performa nce of iterative solvers on isogeometric finite elements\, \nSIAM Journal on Scientific Computing\, 35 A767-A784\, 2013\n \n[2] J.A. Cottrell\, T.J. R. Hughes\, Y. Bazilevs\,\nIsogeometric Analysis: Toward Integration of CA D and FEA\,\nJohn Wiley & Sons\, 2009.\n\n[3] M. Donatelli\, C. Garoni\, C. Manni\, S. Serra-Capizzano\, H. Speleers\, \nSymbol-based multigrid met hods for Galerkin B-spline isogeometric analysis\, SIAM Journal on Numeric al Analysis\, 55\, 31-62\, 2017.\n\n[4] C. Garoni\, C. Manni\, F. Pelosi\, S. Serra-Capizzano\, H. Speleers\, \nOn the spectrum of stiffness matrice s arising from isogeometric analysis\, Numerische Mathematik\, 127\, 751-7 99\, 2014.\n\n[5] C. Garoni\, C. Manni\, S. Serra-Capizzano\, H. Speleers\ , NURBS in isogeometric discretization methods: A spectral analysis\, \nN umerical Linear Algebra with Application}\, 2020\;27:e2318.\n\n[6] C. Garo ni\, H. Speleers\, S-E. Ekstrom\, A. Reali\, S. Serra-Capizzano\, T.J.R. Hughes\, \nSymbol-based analysis of finite element and isogeometric B-spli ne discretizations of eigenvalue problems: \nExposition and review\, Archi ves of Computational Methods in Engineering\, 26\, 1639-1690\, 2019.\n\n[ 7] E. Sande\, C. Manni\, H. Speleers:\nSharp error estimates for spline approximation: explicit constants\, n-widths\, and eigenfunction convergen ce\,\nMathematical Models and Methods in Applied Sciences}\, 29\, 1175--1 205\, 2019\n LOCATION:https://researchseminars.org/talk/CMWebinar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Colin Cotter (Imperial College) DTSTART:20210720T070000Z DTEND:20210720T080000Z DTSTAMP:20260422T225753Z UID:CMWebinar/8 DESCRIPTION:Title: Hybridised implicit solvers for the Gung Ho dynamical core\nby Colin Cotter (Imperial College) as part of Australian Seminar on Computational Mathematics\n\n\nAbstract\nGung Ho is the name of the Met Office project t o build a new dynamical core (fluid dynamics component) for their weather/ climate prediction system. Gung Ho is built around compatible finite eleme nt methods as the apparently unique solution to the question of how to fin d a consistent gridpoint (i.e. non-spectral) discretisation that supports various essential wave propagation properties at the discrete level on gri ds with near-equal edge lengths "pseudo-uniform" on the sphere. One downsi de of this approach versus their current finite difference approach is the non-diagonal mass matrix for the velocity component\, which means that th e usual strategy of eliminating velocity to get an elliptic problem for pr essure results in a non-sparse matrix. The solution to this\, known for de cades\, is to "hybridise" the mixed system by breaking continuity constrai nts to get a discontinuous velocity space\, and to introduce Lagrange mult ipliers as trace variables supported on cell facets to enforce continuity of the solution. The system can then be eliminated down to a sparse reduce d system for the trace variables only. The question then arises of how to efficiently iteratively solve this system when the domain is very thin (li ke the Earth's atmosphere). This question can be answered by combining var ious results from (a) the analysis of hybridised mixed finite element meth ods and (b) the analysis of additive Schwarz methods. I will briefly intro duce these\, describe a solver algorithm and sketch a proof that it gives iteration counts that are independent of depth in the thin layer limit\, b efore illustrating with some numerical results produced using Firedrake an d PETSc.\n LOCATION:https://researchseminars.org/talk/CMWebinar/8/ END:VEVENT END:VCALENDAR