BEGIN:VCALENDAR VERSION:2.0 PRODID:IEEE vTools.Events//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:America/Toronto BEGIN:DAYLIGHT DTSTART:20220313T030000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 RRULE:FREQ=YEARLY;BYDAY=2SU;BYMONTH=3 TZNAME:EDT END:DAYLIGHT BEGIN:STANDARD DTSTART:20221106T010000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 RRULE:FREQ=YEARLY;BYDAY=1SU;BYMONTH=11 TZNAME:EST END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTAMP:20220506T134751Z UID:9746360B-D510-4C3C-B436-0E653EE26DD2 DTSTART;TZID=America/Toronto:20220503T110000 DTEND;TZID=America/Toronto:20220503T120000 DESCRIPTION:The numerical solution of Maxwell’s time-dependent equations plays a very useful role in electrical engineering\, physical chemistry an d photonics at the nanoscale. Maxwell’s equations constitute an involuti on-constrained PDE system. The equations can be cast as a regular hyperbol ic system of conservation laws and many innovations that have been develop ed in that area of study can be used to advantage even for computational e lectrodynamics (CED). However\, the structure of Maxwell’s equations is inherently very different from that of other conservation laws\, with Fara day’s and Ampere’s laws having a curl-type update. This curl-type upda te also ensures that Gauss’ laws for charge and magnetic charge are natu rally satisfied. The highly popular and successful Finite Difference Time Domain (FDTD) scheme can mimetically fulfil the goals of global constraint preservation\, treatment of perfectly matched layer (PML) boundary condit ions and inclusion of auxiliary differential equations (ADEs) for dispersi ve media. However\, FDTD does not extend seamlessly to higher orders. Fini te Volume Time Domain (FVTD) and Discontinuous Galerkin Time Domain (DGTD) schemes have been designed for CED and they do extend to higher orders. H owever\, versions of these methods that are in the literature do not simul taneously satisfy the global constraints\, and present a seamless path for the inclusion of PML and ADEs. Clearly\, a synthesis is needed where the best aspects and versatility of FDTD are retained\, while rethinking from the ground-up the best aspects of FVTD and DGTD schemes for CED.\n\nThe go al of this talk is to present recently innovated FVTD and DGTD schemes tha t are indeed the closest analogues of FDTD. In fact\, these novel methods are built on the same foundation provided by the Yee-type mesh\; thereby r etaining many of the advantages of FDTD. However\, they also incorporate r ecent innovations. They represent a confluence of three leading-edge innov ations that have been pioneered by the author:- 1) The new methods use WEN O and DG reconstruction methods\, but only with a highly innovative recast ing of the reconstruction\, so as to satisfy Gauss’ laws (Balsara 2001\, 2004\, 2009\, Balsara et al. 2017\, 2018). 2) The methods also utilize mu ltidimensional Riemann solvers so that the global constraints are satisfie d on the same control volume (Balsara 2010\, 2012\, 2014\, Balsara & Dumbs er 2015\, Balsara et al. 2017\, 2018). 3) To treat stiff source terms\, PM L and ADEs we also recast the ADER methods (Dumbser et al. 2008\, 2013\, B alsara et al. 2009\, 2013\, Balsara et al. 2017\, 2018a\,b). A full von Ne umann stability analysis of multidimensional\, globally constraint-preserv ing DGTD schemes for CED is also presented (Balsara and Käppeli 2018) and it is shown that DGTD and PNPM schemes that result from our analysis have superior wave propagation properties as well as preservation of electroma gnetic energy at higher orders of accuracy. The PNPM schemes also offer th e advantage of large CFL number relative to DGTD schemes.\n\nAs the focus in engineering and the sciences moves to uncertainty quantification\, mach ine learning and verification and validation of simulated data\, a new gen eration of high accuracy schemes is crucial to those broader goals. The pr oposed new techniques lay a firm foundation for the entire discipline of 2 1st century CED\, leading to advances across multiple disciplines.\n\nCo-s ponsored by: Center for Computational Science and Engineering (CCSE)\, Uni versity of Toronto\n\nSpeaker(s): Prof. Dinshaw Balsara\, \n\nVirtual: htt ps://events.vtools.ieee.org/m/312555 LOCATION:Virtual: https://events.vtools.ieee.org/m/312555 ORGANIZER:costas.sarris@utoronto.ca SEQUENCE:10 SUMMARY:Higher Order Globally Constraint-Preserving FVTD and DGTD Schemes f or Time-Dependent Computational Electrodynamics (Prof. Dinshaw Balsara\, U . of Notre-Dame) URL;VALUE=URI:https://events.vtools.ieee.org/m/312555 X-ALT-DESC:Description: <br /><p>The numerical solution of Maxwell&rsquo\;s time-dependent equations plays a very useful role in electrical engineeri ng\, physical chemistry and photonics at the nanoscale. Maxwell&rsquo\;s e quations constitute an involution-constrained PDE system. The equations ca n be cast as a regular hyperbolic system of conservation laws and many inn ovations that have been developed in that area of study can be used to adv antage even for computational electrodynamics (CED). However\, the structu re of Maxwell&rsquo\;s equations is inherently very different from that of other conservation laws\, with Faraday&rsquo\;s and Ampere&rsquo\;s laws having a curl-type update. This curl-type update also ensures that Gauss&r squo\; laws for charge and magnetic charge are naturally satisfied. The hi ghly popular and successful Finite Difference Time Domain (FDTD) scheme ca n mimetically fulfil the goals of global constraint preservation\, treatme nt of perfectly matched layer (PML) boundary conditions and inclusion of a uxiliary differential equations (ADEs) for dispersive media. However\, FDT D does not extend seamlessly to higher orders. Finite Volume Time Domain ( FVTD) and Discontinuous Galerkin Time Domain (DGTD) schemes have been desi gned for CED and they do extend to higher orders. However\, versions of th ese methods that are in the literature do not simultaneously satisfy the g lobal constraints\, and present a seamless path for the inclusion of PML a nd ADEs. Clearly\, a synthesis is needed where the best aspects and versat ility of FDTD are retained\, while rethinking from the ground-up the best aspects of FVTD and DGTD schemes for CED.</p>\n<p>&nbsp\;&nbsp\;&nbsp\;&nb sp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\; The goal of this tal k is to present recently innovated FVTD and DGTD schemes that are indeed t he closest analogues of FDTD. In fact\, these novel methods are built on t he same foundation provided by the Yee-type mesh\; thereby retaining many of the advantages of FDTD. However\, they also incorporate recent innovati ons. They represent a confluence of three leading-edge innovations that ha ve been pioneered by the author:- <strong>1)</strong> The new methods use WENO and DG reconstruction methods\, but only with a highly innovative rec asting of the reconstruction\, so as to satisfy Gauss&rsquo\; laws (Balsar a 2001\, 2004\, 2009\, Balsara <em>et al</em>. 2017\, 2018). <strong>2)</s trong> The methods also utilize multidimensional Riemann solvers so that t he global constraints are satisfied on the same control volume (Balsara 20 10\, 2012\, 2014\, Balsara &amp\; Dumbser 2015\, Balsara <em>et al</em>. 2 017\, 2018). <strong>3)</strong> To treat stiff source terms\, PML and ADE s we also recast the ADER methods (Dumbser <em>et al</em>. 2008\, 2013\, B alsara <em>et al</em>. 2009\, 2013\, Balsara <em>et al</em>. 2017\, 2018a\ ,b). A full von Neumann stability analysis of multidimensional\, globally constraint-preserving DGTD schemes for CED is also presented (Balsara and K&auml\;ppeli 2018) and it is shown that DGTD and PNPM schemes that result from our analysis have superior wave propagation properties as well as pr eservation of electromagnetic energy at higher orders of accuracy. The PNP M schemes also offer the advantage of large CFL number relative to DGTD sc hemes.</p>\n<p>&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nb sp\;&nbsp\;&nbsp\; As the focus in engineering and the sciences moves to u ncertainty quantification\, machine learning and verification and validati on of simulated data\, a new generation of high accuracy schemes is crucia l to those broader goals. The proposed new techniques lay a firm foundatio n for the entire discipline of 21st century CED\, leading to advances acro ss multiple disciplines.</p> END:VEVENT END:VCALENDAR