Zurich Colloquium in Applied and Computational Mathematics

   

×

Modal title

Modal content

Date / Time Speaker Title Location
10 April 2024
16:30-17:30
Dr. Kaibo Hu
University of Edinburgh, UK
Event Details
Speaker invited by Prof. Dr. Ralf Hiptmair
Abstract Finite Element Exterior Calculus (FEEC) provides a cohomology framework for structure-preserving discretisation of a large class of PDEs. Differential complexes are important tools in FEEC. The de Rham complex is a basic example, with applications in curl-div related problems such as the Maxwell equations. There is a canonical finite element discretisation of the de Rham complex, which in the lowest order case coincides with discrete differential forms (Whitney forms). Different problems involve different complexes. In this talk, we provide an overview of some efforts towards Finite Element Tensor Calculus, inspired by tensor-valued problems from continuum mechanics and general relativity. On the continuous level, we systematically derive new complexes from the de Rham complexes. On the discrete level, We review the idea of distributional finite elements, and use them to obtain analogies of the Whitney forms for these new complexes. A special case is Christiansen’s finite element interpretation of Regge calculus, a discrete geometric scheme for metric and curvature.
Towards Finite Element Tensor Calculus
HG E 1.2
17 April 2024
16:00-17:00
Prof. Dr. Vincent Perrier
Inria, France
Event Details
Speaker invited by Prof. Dr. Rémi Abgrall
Abstract Some hyperbolic systems are known to include implicit preservation of differential constraints: these are for example the time conservation of the vorticity for the first order wave system or divergence preservation for the Maxwell system or the induction equation. In this talk, I will address this problem with the classical discontinuous Galerkin method. Based on discrete de-Rham ideas, I will show that by considering an adapted approximation space (but still discontinuous) for vectors , divergence or curl can be easily preserved under mild assumption on the numerical flux
How to preserve a divergence or a curl constraint in a hyperbolic system with the discontinuous Galerkin method
HG E 1.2
24 April 2024
16:30-18:00
Prof. Dr. Guglielmo Scovazzi
Department of Civil and Environmental Engineering, Duke University
Event Details
Speaker invited by Prof. Dr. Rémi Abgrall
Abstract Scientific computing is routinely assisting in the design of systems or components, which have potentially very complex shapes. In these situations, it is often underestimated that the mesh generation process takes the overwhelming portion of the overall analysis and design cycle. If high order discretizations are sought, the situation is even more critical. Methods that could ease these limitations are of great importance, since they could more effectively interface with meta-algorithms from Optimization, Uncertainty Quantification, Reduced Order Modeling, Machine Learning, and Artificial Neural Networks, in large-scale applications. Recently, immersed/embedded/unfitted boundary finite element methods (cutFEM, Finite Cell Method, Immerso-Geometric Analysis, etc.) have been proposed for this purpose, since they obviate the burden of body-fitted meshing. Unfortunately, most unfitted finite element methods are also difficult to implement due to: (a) the need to perform complex cell cutting operations at boundaries, (b) the necessity of specialized quadrature formulas on cut elements, and (c) the consequences that these operations may have on the overall conditioning/stability of the ensuing algebraic problems. This talk introduces a simple, stable, and accurate unfitted boundary method, named “Shifted Boundary Method” (SBM), which eliminates the need to perform cell cutting operations. Boundary conditions are imposed on the boundary of a “surrogate” discrete computational domain, specifically constructed to avoid cut elements. Appropriate field extension operators are then constructed by way of Taylor expansions (or similar operators), with the purpose of preserving accuracy when imposing boundary conditions. An extension of the SBM to higher order discretizations will also be presented, together with a summary of the numerical analysis results. The SBM belongs to the broader class of Approximate Boundary Methods, a less explored or somewhat forgotten class of algorithms, which however might have an important role in the future of scientific computing. The performance of the SBM is tested on large-scale problems selected from linear and nonlinear elasticity, fluid mechanics, shallow water flows, thermos-mechanics, porous media flow, and fracture mechanics.
The Shifted Boundary Method: How Approximate Boundaries Can Help in Complex-Geometry Computations
HG E 1.2
8 May 2024
16:30-17:30
Prof. Dr. Maarten de Hoop
Rice University
Event Details
Speaker invited by Prof. Dr. Habib Ammari
Title T.B.A.
HG E 1.2
15 May 2024
16:30-17:30
Dr. Leonardo Zepeda-Nunez
Google Research, USA
Event Details
Speaker invited by Prof. Dr. Siddhartha Mishra
Title T.B.A.
HG E 1.2
22 May 2024
16:30-17:30
Prof. Dr. Dirk Pauly
TU Dresden
Event Details
Speaker invited by Prof. Dr. Ralf Hiptmair
Title T.B.A.
HG E 1.2
29 May 2024
16:30-17:30
Prof. Dr. Ivan Trapasso
Politecnico di Torino
Event Details
Speaker invited by Prof. Dr. Rima Alaifari
Title T.B.A.
HG E 1.2
25 September 2024
16:30-17:30
Dr. Martin Averseng
Université d’Angers
Event Details
Speaker invited by Prof. Dr. Ralf Hiptmair
Title T.B.A.
HG ? ?
JavaScript has been disabled in your browser