• ICERM's home (121 South Main Street) day

    Welcome to ICERM

    The Institute for Computational and Experimental Research in Mathematics

  • A poster session at ICERM

    Welcome to ICERM

    The Institute for Computational and Experimental Research in Mathematics

  • ICERM's lecture hall

    Welcome to ICERM

    The Institute for Computational and Experimental Research in Mathematics

  • Board work at ICERM

    Welcome to ICERM

    The Institute for Computational and Experimental Research in Mathematics

This Week at ICERM

February 25, 2024

There are no events currently scheduled for February 25th.

February 26, 2024
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
February 27, 2024
  • 12:00 - 1:00 pm EST
    Convection-dominated equations
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Casey Cavanaugh, Louisiana State University
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
February 28, 2024
  • 12:00 - 1:00 pm EST
    Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations
    11th Floor Lecture Hall
    • Yingda Cheng, Virginia Tech
    Abstract
    In this talk, we present a new class of implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using a base implicit solve for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. We prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
February 29, 2024
  • 12:00 - 1:00 pm EST
    Fundamentals of (simplicial) Mesh Generation
    11th Floor Lecture Hall
    • Noel Walkington, Carnegie Mellon University
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
March 1, 2024
  • 9:30 - 10:30 am EST
    Ethics II
    Professional Development - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
March 2, 2024

There are no events currently scheduled for March 2nd.

All event times are listed in ICERM local time in Providence, RI (Eastern Standard Time / UTC-5).

All event times are listed in .

Upcoming Programs

PDEs and Geometry: Numerical Aspects
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The Industrialization of SciML
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The Ceresa Cycle in Arithmetic and Geometry
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Connect with ICERM

ICERM Fall 2023 Newsletter
ICERM Summer 2023 Newsletter
ICERM Spring 2023 Newsletter