BEGIN:VCALENDAR VERSION:2.0 X-WR-CALNAME:EventsCalendar PRODID:-//hacksw/handcal//NONSGML v1.0//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:America/New_York LAST-MODIFIED:20240422T053451Z TZURL:https://www.tzurl.org/zoneinfo-outlook/America/New_York X-LIC-LOCATION:America/New_York BEGIN:DAYLIGHT TZNAME:EDT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 DTSTART:19700308T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU END:DAYLIGHT BEGIN:STANDARD TZNAME:EST TZOFFSETFROM:-0400 TZOFFSETTO:-0500 DTSTART:19701101T020000 RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT CATEGORIES:College of Arts and Sciences,College of Engineering,Thesis/Disse rtations DESCRIPTION:Topic: High-order Conservative Discontinuous Galerkin Methods via Implicit Penalization for the Generalized Korteweg--de Vries Equation and the Hirota--Satsuma KdV SystemAbstract: We develop a new cons ervative discontinuous Galerkin (DG) methods for nonlinear wave problems, focusing on the generalized Korteweg–de Vries (gKdV) equation and the co upled Hirota–Satsuma KdV (HS-KdV) system. The proposed methods preserve mass through the single-valued structure of numerical traces, while energy and Hamiltonian conservation are enforced by implicitly determining penal ty parameters in the numerical traces through auxiliary conservation const raints. In our previous work, we developed a conservative DG method for th e gKdV equation; however, that formulation involves the time derivative of the jump of the approximate solution, which complicates extensions beyond second-order temporal accuracy. Our new formulation overcomes this limita tion by introducing a redesigned trace configuration that eliminates the d erivative-of-jump term. This novel enhancement seamlessly paves the way fo r higher-order time discretizations and requires solving fewer nonlinear s ystems per time step than the previous approach. For the coupled HS-KdV sy stem, we present the first conservative DG method capable of preserving al l three invariants of the exact solution. Numerical results demonstrate th e accuracy and expected convergence behavior of the proposed methods, as w ell as long-time stability and strong conservation properties for both the gKdV equation and HS- KdV system. ADVISOR(s): Dr. Bo Dong, Department of Mathematics (bdong@umassd.edu) Dr. Yanlai Chen, Chief Research Officer (yanlai.chen@umassd.edu) COMMITTE E MEMBERS: Dr. Zheng Chen, Department of Mathematics Dr. Mazdak Tootkabon i, Department of Civil and Environmental Engineering NOTE: All EAS Stud ents are ENCOURAGED to attend.\nEvent page: https://www.umassd.edu/events/ cms/eas-doctoral-proposal-defense--by-muhammad-shan-tariq.php X-ALT-DESC;FMTTYPE=text/html:

Topic:

High-order Con servative Discontinuous Galerkin Methods via Implicit Penalization for the Generalized Korteweg--de Vries Equation and the Hirota--Satsuma KdV Syste mAbstract:

We develop a new conservative discontinuous Gal erkin (DG) methods for nonlinear wave problems\, focusing on the generaliz ed Korteweg–de Vries (gKdV) equation and the coupled Hirota–Satsuma Kd V (HS-KdV) system. The proposed methods preserve mass through the single-v alued structure of numerical traces\, while energy and Hamiltonian conserv ation are enforced by implicitly determining penalty parameters in the num erical traces through auxiliary conservation constraints. In our previous work\, we developed a conservative DG method for the gKdV equation\; howev er\, that formulation involves the time derivative of the jump of the appr oximate solution\, which complicates extensions beyond second-order tempor al accuracy. Our new formulation overcomes this limitation by introducing a redesigned trace configuration that eliminates the derivative-of-jump te rm. This novel enhancement seamlessly paves the way for higher-order time discretizations and requires solving fewer nonlinear systems per time step than the previous approach. For the coupled HS-KdV system\, we present th e first conservative DG method capable of preserving all three invariants of the exact solution. Numerical results demonstrate the accuracy and expe cted convergence behavior of the proposed methods\, as well as long-time s tability and strong conservation properties for both the gKdV equation and HS- KdV system.

ADVISOR(s):

Dr. Bo Dong\, Department of Mathematics (bdong@umassd.e du)
Dr. Yanlai Chen\, Chief Research Officer (yanlai.chen@umassd .edu)

COMMITTEE MEMBERS:

Dr. Zheng Chen\, D epartment of Mathematics
Dr. Mazdak Tootkaboni\, Department of C ivil and Environmental Engineering

NOTE: All EAS Student s are ENCOURAGED to attend.

Event page: https://www.umassd.edu/events/cms/eas-doctoral-proposal-defense--by-muhamm ad-shan-tariq.php

DTSTAMP:20260508T145558 DTSTART;TZID=America/New_York:20260528T093000 DTEND;TZID=America/New_York:20260528T110000 LOCATION:TXT 105 - CSCDR SUMMARY;LANGUAGE=en-us:EAS Doctoral Proposal Defense by Muhammad Shan Tari q UID:550f52c8f6810db31b6026b9247def06@www.umassd.edu END:VEVENT END:VCALENDAR