Centre for Computational Science and Engineering
Upcoming Events
CCSE Student Seminar
Date & Time: February 3rd 2023, 12:10pm-1:30pm
Location: UTIAS Lecture Hall and Zoom
Zoom registration: https://utoronto.zoom.us/meeting/register/tZ0rdOquqTgtHNNodhK3VoMkdNxzWnoQNSBv
Talk 1:
Title: Intro to Gradient-Enhanced Gaussian Processes and Overcoming their Ill-Conditioning Problem
Speaker: André Marchildon
Abstract: This talk will introduce Gaussian processes as a method of constructing probabilistic surrogates that can be used for various applications including classification, uncertainty quantification, and optimization. Having a probabilistic surrogate is beneficial since it quantifies the uncertainty of the surrogate’s approximation to a function of interest. Furthermore, a Gaussian process can be used to construct a surrogate even when the evaluations of the function of interest and of its gradients are noisy.
Gradient-enhanced Gaussian processes utilize the gradient of a function of interest to construct a more accurate surrogate. Unfortunately, a major challenge in their use is the ill-conditioning of the gradient-enhanced covariance matrix. Existing approaches to address this challenge include drawbacks such as having to reduce the number of data points used to construct the surrogate and also limiting how close the data points can be to each other in the parameter space. A new method has been developed that allows all of the data points to be kept and it provides a provable upper bound on the condition number of the gradient-enhanced covariance matrix. Optimization results will be presented that demonstrate how this method overcomes the ill-conditioning problem and thus allows for deep convergence to be achieved.
Talk 2:
Title: An overview of Summation By Parts Methods for CFD: how to make your CFD discretizations more attractive to both engineers and mathematicians
Speaker: Alex Bercik
Abstract: The three main mesh-based discretization techniques for Computational Fluid Dynamics (CFD), Finite Difference, Finite Volume, and Finite Element, are traditionally thought to be distinct from one another. However, some may be aware that the overlaps between them can be significant. This is especially apparent with the use of Summation By Parts (SBP) methods, in which by constructing these numerical schemes carefully, we can ensure they possess certain mathematical properties that not only give us several computational advantages, but also provide certain analytical tools that allow us to analyze and interpret the schemes in a new light. In this talk, an SBP scheme for the linear advection equation will be presented that can be equivalently interpreted using any of the main three discretization techniques. We will use this test problem to demonstrate the powerful analytical framework allowed by the SBP property, allowing us to prove desirable mathematical properties of the scheme, such as arbitrary design-order, conservation, and notably, stability. Several numerical advantages provided by these schemes will then be discussed, such as straightforward parallelization, flexible element-type blocking for complex geometries, and facilitated treatment of special points through discontinuous or multi-valued solutions. Finally, extensions to the Euler and Navier-Stokes equations will briefly be explored, accompanied by a high-level presentation of non-linearly “entropy-stable” schemes, as well as a general overview of current research being done in Prof. Zingg’s lab on SBP methods.
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Past Events
Events | Speakers | Date & Time | Location |
---|---|---|---|
Seminar: Registration-based model reduction of parameterized PDEs with spatio-parameter adaptivity | Dr. Tommaso Taddei | Nov 3, 2022, 11:00 AM - 12:00 PM | Zoom |
Seminars: Fluid-Structure-Interaction Modelling of Brain Aneurysm Wall Vibrations; A Comparative Study of Regular- and High-Fidelity Solvers for the Prediction of Aortic Hemodynamics; Accelerating Finite-Difference Time-Domain Simulations through Scientific Machine Learning | David Bruneau Yiyang Fu Shutong Qi | Oct. 24, 2022, 11:00 AM - 1:00 PM | MC 331 |
Seminars: Variational Data Assimilation for 1D Magnetohydrodynamics; Efficient Data Assimilation with a Multi-Fidelity Ensemble Kalman Filter and Hyperreduced ROMs | Jose Arnal Geoff Donoghue | Sep. 29, 2022, 12:00 PM - 1:30 PM | UTIAS Lecture Hall |
Seminar: Summation-by-parts schemes and strong imposition of homogeneous Dirichlet boundary conditions | Anita Gjesteland | May 26, 2022, 1:30 PM - 2:30PM | Zoom |
Seminar: High Order Adaptive Mesh Refinement (AMR) for Divergence Constraint-Preserving Schemes – Focus on MHD and CED | Prof. Dinshaw Balsara | May 10, 2022, 11:00 AM - 12:00 PM | Zoom |
Seminar: Higher Order Globally Constraint-Preserving FVTD and DGTD Schemes for Time-Dependent Computational Electrodynamics | Prof. Dinshaw Balsara | May 3, 2022, 11:00 AM - 12:00 PM | Zoom |
Seminar: Fast solvers for electromagnetics-based analysis and design of integrated circuits and systems | Prof. Dan Jiao | Feb. 25, 2022 04:00 PM - 05:00 PM | Zoom |
Seminar: High-order and reduced-order numerical methods based on implicit tracking for shock-dominated flows | Prof. Matthew Zahr | Aug. 23, 2021 02:00 PM - 03:00 PM | Zoom |
Seminar: Uncertainty Quantification and Management: From Computational Design to Robust AI | Prof. Zheng Zhang | March 19, 2021 02:00 PM - 03:00 PM | Zoom |
Seminar: Entropy stable schemes for nonlinear conservation laws: high order methods and reduced order modeling | Prof. Jesse Chan | Dec. 3, 2019 01:00 PM - 02:00 PM | UTIAS Lecture Hall |
Computational Science and Engineering Symposium 2019 | Prof. Jan Hesthaven Prof. Stephen Wright Prof. Alan Aspuru-Guzik Prof. Eleuterio Toro Dr. Ann Almgren Prof. Alessandro Veneziani Prof. Remi Abgrall Dr. Fariba Fahroo Prof. Steven Johnson Prof. Anthony Patera Dr. Nobuyuki Umetani | May 21 - May 22, 2019 | UTIAS Lecture Hall |
Seminar: Entropy Stability and Finite Element Methods for Compressible Flows. | Prof. David Williams | April 29, 2019 02:00 PM - 03:00 PM | UTIAS Lecture Hall |
Seminar: Higher-order space-time discontinuous Galerkin methods for compressible flows | Dr. Laslo Diosady | March 20, 2019 03:30 PM - 04:30 PM | UTIAS Lecture Hall |
Seminar: Transforming Computation and Communication Patterns for High-Performance | Prof. Maryam Dehnavi | March 14, 2019 11:00 AM - 12:00 PM | GB 220 |
Seminar: CCSE Seminar with Prof. R.O. Fox | Prof. Rodney Fox | Feb. 21, 2019 11:00 AM - 12:00 PM | UTIAS Lecture Hall |
Seminar: Spline collocation methods for a PDE with discontinuous diffusion coefficient | Prof. Christina Christara | Nov. 30, 2018 11:00 AM - 12:00 PM | SS 2118 |
Seminar: A numerical method for modeling interfacial flows with variable surface tension | Prof. Shahriar Afkhami | June 15, 2018 10:00 AM - 12:00 PM | SF 1105 |
Seminar: Improving Robustness of CFD Applications through Output-Based Adaptive Methods | Prof. Krzysztof Fidkowski | April 5, 2018 10:00 AM - 12:00 PM | SF 1105 |
Seminar: Reduced-Order Modelling | Prof. Aimy Bazylak Prof. Piero Triverio Prof. Masayuki Yano | Feb. 2, 2018 11:00 AM - 02:00 PM | GB 202 |
Seminar: Multiscale and Multiphysics Modelling | Prof. Clinton Groth Prof. Costas Sarris Dr. Lucie Freret | Nov. 1, 2017 10:00 AM - 12:00 PM | CB 114 |
Seminar: Broadband Electromagnetic Modelling and Stochastic Signal Analysis of Multiconductor Interconnections | Prof. Daniel De Zutter | Oct. 5, 2017 04:00 PM - 05:00 PM | SF 1105 |
Seminar: Discontinuous Galerkin Method for Convection Dominated Partial Differential Equations | Prof. Chi-Wang Shu | Sept. 14, 2017 03:00 PM - 05:00 PM | UTIAS Lecture Hall |
Seminar: Computational Research at the University of Toronto | Dr. Pieter Boom Rafid Mahmood | July 12, 2017 01:00 PM - 03:00 PM | BA 1220 |
Seminar: Numerical Optimization | Prof. David Zingg Prof. Prasanth Nair Prof. Timoth Chan | March 30, 2017 12:00 PM - 02:00 PM | UTIAS Lecture Hall |
Seminar: CFD, order reduction and cardiovascular simulations II | Dr. Francesco Ballarin | Feb. 9, 2017 03:00 PM - 05:00 PM | GB 202 |
Seminar: CFD, order reduction and cardiovascular simulations I | Prof. Gianluigi Rozza | Feb. 8, 2017 11:00 AM - 01:00 PM | GB 202 |
Seminar: Student Seminar #2 | Xingqi Zhang, Nan Ge Xinyue Zhang, Gurjot Dhaliwal, Keyi Ni | Jan. 26, 2017 03:00 PM - 05:00 PM | MC 331 |
Seminar: Student Seminar #1 | Trefor Evans, Jacques Xing Gregg Streuber, Dan Macdonald, Aaron Babier Adam O'Brien | Dec. 16, 2016 11:00 AM - 01:00 PM | WB 130 |