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Spring Semester 2016

Date / Time Speaker Title Location
2 March 2016
16:15-17:15 		Prof. Dr. Alexandre Ern
Université Paris-Est, CERMICS
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Zurich Colloquium in Applied and Computational Mathematics

Title Finite element quasi-interpolation and best approximation
Speaker, Affiliation Prof. Dr. Alexandre Ern, Université Paris-Est, CERMICS
Date, Time 2 March 2016, 16:15-17:15
Location HG E 1.2
Abstract We introduce a quasi-interpolation operator for scalar- and vector-valued finite element spaces with some continuity across mesh interfaces. This operator is stable in L1, leaves the corresponding finite element space point-wise invariant, whether homogeneous boundary conditions are imposed or not, and, assuming regularity in the fractional Sobolev spaces W^{s,p} where p\in [1,\infty] and s can be arbitrarily close to zero, gives optimal local approximation estimates in any Lp-norm. The theory is illustrated on H1-, H(curl)- and H(div)-conforming spaces.
Finite element quasi-interpolation and best approximationread_more
HG E 1.2
9 March 2016
16:15-17:15 		Prof. Dr. John Ball
University of Oxford
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Zurich Colloquium in Applied and Computational Mathematics

Title Interfaces and metastability in solid and liquid crystals
Speaker, Affiliation Prof. Dr. John Ball, University of Oxford
Date, Time 9 March 2016, 16:15-17:15
Location HG E 1.2
Abstract When a new phase is nucleated in a martensitic solid phase transformation, it has to fit geometrically onto the parent phase, forming interfaces between the phases accompanied by possibly complex microstructure. The talk will describe some mathematical issues involved in understanding such questions of compatibility and their influence on metastability, as illustrated by recent experimental discoveries. For liquid crystals planar (as opposed to point and line) defects are not usually considered, but there are some situations in which they seem to be relevant, such as for smectic A thin films where compatibility issues not unlike those for martensitic materials arise.
Interfaces and metastability in solid and liquid crystalsread_more
HG E 1.2
16 March 2016
16:15-17:15 		Dr. Holger Heumann
INRIA Sophia-Antipolis
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Zurich Colloquium in Applied and Computational Mathematics

Title Numerical methods for tokamak plasma equilibrium evolution at the resistive diffusion timescale
Speaker, Affiliation Dr. Holger Heumann, INRIA Sophia-Antipolis
Date, Time 16 March 2016, 16:15-17:15
Location HG E 1.2
Abstract The Grad/Hogan model for plasma equilibrium evolution at the resistive diffusion timescale separates into two low-dimensional subproblems: The axisymmetric free-boundary plasma equilibrium problem and the one-dimensional system of transport and diffusion equations. The equilibrium problem, also known as the Grad-Shafranov equation, is a non-linear elliptic problem for the poloidal flux function. The transport and diffusion equations, basically hydrodynamic equations and resistive diffusion formulated in the curvilinear coordinate system induced by the level lines of the poloidal flux function, are non-linear advection-diffusion equations. The unknowns of the system of transport and diffusion equations determine in some non-linear fashion the profile of the toroidal current density, the non-linear righthand side of the Grad-Shafranov equation and the poloidal flux on the other hand determines coefficients in the system of transport and diffusion equations. Devising stable numerical methods for a self-consistent simulation of equilibrium and transport and diffusion is an active area of research with many open problems, but highly important for scenario development and realtime control in experimental tokamak devices such as ITER. We will present the details of the Grad/Hogan model with a focus on numerical solutions methods towards automated scenario development.
Numerical methods for tokamak plasma equilibrium evolution at the resistive diffusion timescaleread_more
HG E 1.2
17 March 2016
15:15-16:15 		Prof. Dr. Philippe Ciarlet
City University of Hong Kong
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Zurich Colloquium in Applied and Computational Mathematics

Title Nonlinear Korn inequalities on a surface
Speaker, Affiliation Prof. Dr. Philippe Ciarlet, City University of Hong Kong
Date, Time 17 March 2016, 15:15-16:15
Location Y27 H 12
Abstract A nonlinear Korn inequality on a surface asserts that the distance, measured by means of an appropriate norm, between a surface and a deformed surface is, up to rigid body motions, "controlled" by the distances between their fundamental forms, likewise measured by means of appropriate norms. In this talk, we review various recently established nonlinear Korn inequalities on a surface, either in spaces of continuously differentiable functions or in Sobolev spaces. We also briefly discuss some of their potential applications beyond differential geometry per se, such as the intrinsic approach in nonlinear shell theory, or the modelling of the Earth surface. References: P.G. Ciarlet: the continuity of a surface as a function of its two fundamental forms, J. Math. Pures Appl. 82 (2003), 253-274. P.G. Ciarlet, C. Mardare: Recovery of a surface with boundary and its continuity as a function of its two fundamental forms, Anal. Appl. 3 (2005), 99-1117. P.G. Ciarlet, L. Gratie, C. Mardare: A nonlinear Korn inequality on a surface, J. Math. Pures Appl. 85 (2006), 2-16. P.G. Ciarlet, M. Malin, C. Mardare: In preparation.
Nonlinear Korn inequalities on a surfaceread_more
Y27 H 12
6 April 2016
16:15-17:15 		Prof. Dr. Frédéric Coquel
CMAP - Ecole polytechnique
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Zurich Colloquium in Applied and Computational Mathematics

Title +++Cancelled+++!
Speaker, Affiliation Prof. Dr. Frédéric Coquel, CMAP - Ecole polytechnique
Date, Time 6 April 2016, 16:15-17:15
Location HG E 1.2
Abstract +++Cancelled+++!
+++Cancelled+++!read_more
HG E 1.2
11 April 2016
16:15-17:15 		Prof. Dr. Ian Sloan
Department of Mathematics, University of New South Wales, Sydney, Australia
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Zurich Colloquium in Applied and Computational Mathematics

Title PDE with random coefficients as a high-dimensional problem
Speaker, Affiliation Prof. Dr. Ian Sloan, Department of Mathematics, University of New South Wales, Sydney, Australia
Date, Time 11 April 2016, 16:15-17:15
Location HG D 1.2
Abstract This talk describes recent computational developments in partial differential equations with random coefficients treated as a high-dimensional problem. The prototype of such problems is the underground flow of water or oil through a porous medium, with the permeability of the material treated as a random field. (The stochastic dimension of the problem is high if the random field needs a large number of random variables for its effective description.). There are many approaches to the problem, ranging from the polynomial chaos method initiated by Norbert Wiener to the Monte Carlo and (of particular interest to the UNSW group) Quasi-Monte Carlo methods. In recent years there have been significant progress in the development and analysis of algorithms in these areas.
PDE with random coefficients as a high-dimensional problemread_more
HG D 1.2
13 April 2016
17:30-18:30 		Prof. Dr. Youssef Marzouk
MIT
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Zurich Colloquium in Applied and Computational Mathematics

Title Bayesian inference and the low-dimensional structure of measure transport
Speaker, Affiliation Prof. Dr. Youssef Marzouk, MIT
Date, Time 13 April 2016, 17:30-18:30
Location KOL G201 UZH
Abstract Bayesian inference provides a natural framework for quantifying uncertainty in model parameters and predictions, and for combining heterogeneous sources of information. But the computational demands of the Bayesian framework constitute a major bottleneck in large-scale applications. We will discuss how transport maps, i.e., deterministic couplings between probability measures, can enable useful new approaches to Bayesian computation. A first use involves a combination of measure transport and Metropolis correction; here, we use continuous transportation to transform typical MCMC proposals into adapted non-Gaussian proposals, both local and global. Second, we discuss a variational approach to Bayesian inference that constructs a deterministic transport from a reference distribution to the posterior, without resorting to MCMC. Independent and unweighted posterior samples can then be obtained by pushing forward reference samples through the map. Making either approach efficient in high dimensions, however, requires identifying and exploiting low-dimensional structure. We present new results relating sparsity of transport maps to the conditional independence structure of the target distribution, and discuss how this structure can be revealed through the analysis of certain average derivative functionals. A connection between transport maps and graphical models yields many useful algorithms for efficient ordering and decomposition---here, generalized to the continuous and non-Gaussian setting. The resulting inference algorithms involve either the direct identification of sparse maps or the composition of low-dimensional maps and rotations. We demonstrate our approaches on Bayesian inference problems arising in spatial statistics and in partial differential equations. This is joint work with Matthew Parno and Alessio Spantini. Please note that this is a Colloquium of the Computational Science Zurich Distinguished Lecture.
Bayesian inference and the low-dimensional structure of measure transportread_more
KOL G201 UZH
20 April 2016
16:15-17:15 		Prof. Dr. Daniele A. Di Pietro
University of Montpellier
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Zurich Colloquium in Applied and Computational Mathematics

Title Hybrid High-Order methods on general meshes
Speaker, Affiliation Prof. Dr. Daniele A. Di Pietro, University of Montpellier
Date, Time 20 April 2016, 16:15-17:15
Location HG E 1.2
Abstract We develop a family of arbitrary-order primal methods for (possibly degenerate) diffusion problems on general polygonal/polyhedral meshes. The degrees of freedom are scalar-valued polynomials of the same order at mesh elements and faces. The cornerstones of the method are local reconstruction operators defined at the element level. The design of the method additionally hinges on a least-squares penalty term on faces weakly enforcing the matching between local element- and face-based degrees of freedom. We first address the pure diffusion case with regular to lie the cornerstones of the method. In the lowest-order case, equivalence with the Hybrid Finite Volume method is shown. A first extension is to variable diffusion problems, where the diffusion coefficient is embedded in the construction of the discrete gradient. A second, more challenging, extension is to possibly degenerate advection-diffusion problems, where the advection term is discretized by means of a discrete reconstruction of the advective derivative and upwind stabilization. Here, the main difficulty is to ensure consistency of the method when the exact solution jumps at the diffusive/advective interface. The theoretical results are confirmed by numerical experiments on both standard and polygonal meshes.
Hybrid High-Order methods on general meshesread_more
HG E 1.2
27 April 2016
16:15-17:15 		Prof. Dr. Barbara Kaltenbacher
University of Klagenfurt
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Zurich Colloquium in Applied and Computational Mathematics

Title Regularization based on all-at-once formulations for inverse problems
Speaker, Affiliation Prof. Dr. Barbara Kaltenbacher, University of Klagenfurt
Date, Time 27 April 2016, 16:15-17:15
Location HG E 1.2
Abstract Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated via the parameter-to-state map. Alternatively, one might consider both sets of equations (model and observations) as one large system, to which some regularization method is applied. The choice of the formulation (reduced or all-at-once) can make a large difference computationally, depending on which regularization method is used: Whereas almost the same optimality system arises for the reduced and the all-at-once Tikhonov method, the situation is different for iterative methods, especially in the context of nonlinear models. In this talk we will exemplarily provide some convergence results for all-at-once versions of variational, Newton type and gradient based regularization methods. Moreover we will compare the implementation requirements for the respective all-at-one and reduced versions, as well as their computational performance by means of some numerical tests.
Regularization based on all-at-once formulations for inverse problemsread_more
HG E 1.2
4 May 2016
16:15-17:15 		Prof. Dr. Gabriel Lord
Heriot-Watt University
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Zurich Colloquium in Applied and Computational Mathematics

Title Efficient numerical simulation of SPDEs
Speaker, Affiliation Prof. Dr. Gabriel Lord, Heriot-Watt University
Date, Time 4 May 2016, 16:15-17:15
Location HG E 1.2
Abstract We examine new numerical methods to approximate SPDEs and discuss both convergence and efficiency. We are particularly interested in the time discretisation of multiplicative noise. Our techniques are primarily based on approximating the mild solution of the SPDE where we can try and exploit exact solutions in the numerics. Proofs of convergence are for globally Lipschitz nonlinearities. In the case where this condition does not hold, rather than tamed methods, we examine instead using an adaptive timestep for the SPDE. We take as applications SPDEs aising from models of neural and also from models of reactive single phase flow in a porous media.
Efficient numerical simulation of SPDEsread_more
HG E 1.2
11 May 2016
16:15-17:15 		Prof. Dr. Bruno Despres
Laboratoire Jacques Louis Lions, Univ. Paris VI
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Zurich Colloquium in Applied and Computational Mathematics

Title New weak formulations for resonant Maxwell's equations
Speaker, Affiliation Prof. Dr. Bruno Despres, Laboratoire Jacques Louis Lions, Univ. Paris VI
Date, Time 11 May 2016, 16:15-17:15
Location HG E 1.2
Abstract Resonant Maxwell's equations are relevant for the heating of a plasma in a Tokamak. An important difficulty is the mathematical theory of these equations, which shows the possibility of a physical solution in the form of a Dirac mass inside the domain. I will draw a parallel between the search of good entropies for hyperbolic systems and the limit absorption principle. In this setting good entropies become manufactured solutions. It yields original weak formulations of the problem, which are well posed (existence and uniqueness of the solution) in convenient functional spaces.
New weak formulations for resonant Maxwell's equationsread_more
HG E 1.2
18 May 2016
16:15-17:15 		Prof. Dr. Ilaria Perugia
Universitaet Wien
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Zurich Colloquium in Applied and Computational Mathematics

Title A plane wave virtual element method for the Helmholtz problem
Speaker, Affiliation Prof. Dr. Ilaria Perugia, Universitaet Wien
Date, Time 18 May 2016, 16:15-17:15
Location HG E 1.2
Abstract The virtual element method (VEM) is a generalisation of the finite element method recently introduced by Beirao da Veiga, Brezzi, Cangiani, Manzini, Marini and Russo in 2013, which takes inspiration from modern mimetic finite difference schemes, and allows one to use very general polygonal/polyhedral meshes. This talk is concerned with a new method based on inserting plane wave basis functions within the VEM framework in order to construct an H1-conforming, high-order method for the discretisation of the Helmholtz problem, in the spirit of the partition of unity method. The main ingredients of this plane wave VEM scheme (PW-VEM) are: i) a low order VEM space whose basis functions, which form a partition of unity and are associated to the mesh vertices, are not explicitly computed in the element interiors; ii) a local projection operator onto the plane wave space; iii) an approximate stabilization term. The PW-VEM will be derived, and an outline of its convergence analysis will be presented, as well as some numerical tests. These results have been obtained in collaboration with Paola Pietra (IMATI-CNR "E. Magenes'', Pavia, Italy) and Alessandro Russo (Università di Milano Bicocca, Milano, Italy).
A plane wave virtual element method for the Helmholtz problemread_more
HG E 1.2
25 May 2016
16:15-17:15 		Dr. Xavier Claeys
LJLL, UPMC, Paris
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Zurich Colloquium in Applied and Computational Mathematics

Title Analysis of Block-Jacobi Preconditioners for Local Multi-Trace Formulations
Speaker, Affiliation Dr. Xavier Claeys, LJLL, UPMC, Paris
Date, Time 25 May 2016, 16:15-17:15
Location HG E 1.2
Abstract Local Multi-Trace Formulations (local MTF) are block-sparse boundary integral equations adapted to elliptic PDEs with piece-wise constant coefficients (typically multi-subdomain scattering problems) only recently introduced in [Hiptmair & Jerez-Hanckes, 2012]. In these formulations, transmission conditions are enforced by means of local operators, so that only adjacent subdomains communicate. Although they provide an appealing framework for domain decomposition, present literature only offers two contributions in this direction. In [Hiptmair, Jerez-Hanckes, Lee, Peng, 2013] a new version of local MTF is proposed that involves a relaxation parameter in the enforcement of transmission conditions. In [Dolean & Gander, 2014] the authors conduct a basic explicit study of this modified local MTF in a 1-D setting with 2 subdomains and determine a critical value for the relaxation parameter that minimises the spectral radius of block-Jacobi iteration operators. In the present talk, we describe new contributions extending these results to arbitrary geometrical settings in 2-D and 3-D, assuming that the subdomain partition does not involve any junction point.
Analysis of Block-Jacobi Preconditioners for Local Multi-Trace Formulationsread_more
HG E 1.2

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