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Archive : Numerical Analysis and PDE

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Dan Fortunato, Flatiron Institute141Dan Fortunato, Flatiron InstituteZoom<br> Title: The ultraspherical spectral element method <br> Abstract: We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincaré–Steklov scheme for solving second-order linear partial differential equations on polygonal domains with unstructured quadrilateral or triangular meshes. Properties of the ultraspherical spectral method lead to almost banded linear systems, allowing the element method to be competitive in the high-polynomial regime. The hierarchical Poincaré–Steklov scheme enables precomputed solution operators to be reused, allowing for fast elliptic solves in implicit and semi-implicit time-steppers. The resulting spectral element method achieves an overall computational complexity of O(p^4 / h^3) for mesh size h and polynomial order p, enabling hp-adaptivity to be efficiently performed. We develop an open-source software system, ultraSEM, for flexible, user-friendly spectral element computations in MATLAB. Joint work with Alex Townsend (Cornell University) and Nicholas Hale (Stellenbosch University). 5/14/2021 3:00:00 PM5/14/2021 4:00:00 PM
Yulong Xing, Ohio State University 139Yulong Xing, Ohio State University Zoom<br> Title: TBA <br> Abstract: TBA5/7/2021 3:00:00 PM5/7/2021 4:00:00 PM
Miao-Jung Yvonne Ou, University of Delaware140 Miao-Jung Yvonne Ou, University of DelawareZoom<br> Title: Integral representation formula (IRF) for the permeability tensor of poroelastic media <br> Abstract: In this talk, we will discuss about the role played by the permeability tensor in the viscodynamics of poroelastic media. We will start with the IRF for the dynamic permeability and its application on creating a time-domain solver for the wave equation with a memory term, followed by the presentation of the IRF for the effective viscosity of a two-fluid mixture. The relation between this effective viscosity and the static permeability of a porous media will be derived. These seemingly dirrent parts are tied together by the Herglotz-Nevanlinna function theory. This is joint work with my former Ph.D. students Chuan Bi (NIH, USA) and Jiangmiing Xie (Qinghua University China) and colleagues Hugo Woerdeman (Drexel University, USA), Liwei Xu (Chengdu Institute of Technology, China) and Shangyou Zhang (UD).4/30/2021 3:00:00 PM4/30/2021 4:00:00 PM
Professor Annalisa Buffa, EPFL.142Professor Annalisa Buffa, EPFL.Zoom<br> Title: Defeaturing error: what it is and how to control it <br> Abstract: The design and optimisation of a manufactured object require several steps. Some of them are guided by sound mathematical theories, such as, e.g., the approximation, via numerical techniques, of the equations underlying mechanical behaviour to be simulated; while others require decisions of the user and the implication of such decisions on the accuracy of the final solution, or design, is not always clear. This is the case for defeaturing, i.e., the (often semi-automatic) simplification of a geometric design that is performed before meshing. Indeed, very many geometric details are neglected in order to reduce the complexity of the mesh itself. In this talk, I want to start studying the impact of defeaturing on the accuracy of the analysis, and in particular to provide a posteriori measures that may guide the defeaturing process. In this way, the defeaturing becomes analysis-aware and its impact is fully controlled within the simulation. Joint work with Ondine Chanon and Rafael Vazquez.4/23/2021 3:00:00 PM4/23/2021 4:00:00 PM

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