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  • Feb
    7

    Keaton Burns: Solving Partial Differential Equations Exactly Over Polynomials

    McCormick-Engineering Sciences and Applied Mathematics (ESAM)

    11:15 AM M416, Technological Institute

    EVENT DETAILS

    Title: Solving Partial Differential Equations Exactly Over Polynomials

    Speaker: Keaton Burns, Instructor of Applied Mathematics, MIT

    Abstract: Numerical simulations of partial differential equations (PDEs) have become an indispensable tool across science and engineering. For problems in simple geometries, spectral methods are a powerful class of techniques that produce extremely accurate solutions for broad ranges of equations. But many flavors of spectral methods exist with different properties and performance, and choosing the best method for a complex nonlinear problem is often challenging.

    Here we will present a framework that unifies different polynomial spectral methods, from classical "collocation" to modern "ultraspherical" schemes, by examining the exact equations satisfied by the discrete solutions they produce. By understanding how these equations are perturbed from the original PDE (called the "tau correction"), we can precisely categorize existing methods and derive new solvers that robustly implement new boundary conditions, eliminate spurious numerical modes, and satisfy exact conservation laws.

    This approach conceptually separates *what* discrete model a spectral scheme solves from *how* it solves it, allowing for much more freedom when building and optimizing numerical solvers. Along the way, we will illustrate these advantages with examples from the Dedalus Project, an open-source package for solving PDEs with modern spectral methods.

    **Please note, this event will be held in-person, as well as online via Zoom at the following link: https://northwestern.zoom.us/j/92082212753

    Special Note: This colloquium is on Tuesday at 11:15am, the new regular time for the applied math colloquium.

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    TIME Tuesday, February 7, 2023 at 11:15 AM - 12:15 PM

    LOCATION M416, Technological Institute    map it

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    CONTACT Ted Shaeffer    ted.shaeffer@northwestern.edu EMAIL

    CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)

  • Jun
    15

    2024-2025 Commencement Ceremony

    University Academic Calendar

    All Day

    EVENT DETAILSmore info

    TIME Sunday, June 15, 2025

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    CONTACT Office of the Registrar    nu-registrar@northwestern.edu EMAIL

    CALENDAR University Academic Calendar

  • Jun
    16

    Northwestern Engineering PhD Hooding and Master's Degree Recognition Ceremony

    McCormick School of Engineering and Applied Science

    9:00 AM 2705 Ashland Ave

    EVENT DETAILS

    TIME Monday, June 16, 2025 at 9:00 AM - 11:00 AM

    LOCATION 2705 Ashland Ave   

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    CONTACT Northwestern Engineering Events    northwestern-engineering-events@northwestern.edu EMAIL

    CALENDAR McCormick School of Engineering and Applied Science

  • Jun
    16

    Northwestern Engineering Undergraduate Convocation

    McCormick School of Engineering and Applied Science

    2:00 PM 2705 Ashland Ave

    EVENT DETAILSmore info

    TIME Monday, June 16, 2025 at 2:00 PM - 4:00 PM

    LOCATION 2705 Ashland Ave   

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    CONTACT Northwestern Engineering Events    northwestern-engineering-events@northwestern.edu EMAIL

    CALENDAR McCormick School of Engineering and Applied Science

  • Jun
    23

    Summer classes begin

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Monday, June 23, 2025

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    CONTACT Office of the Registrar    nu-registrar@northwestern.edu EMAIL

    CALENDAR University Academic Calendar

  • Sep
    16

    Fall 2025 Classes Begin

    University Academic Calendar

    All Day

    EVENT DETAILS

    TIME Tuesday, September 16, 2025

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    CONTACT Office of the Registrar    nu-registrar@northwestern.edu EMAIL

    CALENDAR University Academic Calendar