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:20220513T133056Z UID:2516B0BA-B405-429F-BECC-62CDE9EF0BA5 DTSTART;TZID=America/Toronto:20220510T110000 DTEND;TZID=America/Toronto:20220510T120000 DESCRIPTION:Adaptive mesh refinement (AMR) is the art of solving PDEs on a mesh hierarchy with increasing mesh refinement at each level of the hierar chy. Accurate treatment on AMR hierarchies requires accurate prolongation of the solution from a coarse mesh to a newly-defined finer mesh. For scal ar variables\, suitably high order finite volume WENO methods can carry ou t such a prolongation. However\, classes of PDEs\, like computational elec trodynamics (CED) and magnetohydrodynamics (MHD)\, require that vector fie lds preserve a divergence constraint. The primal variables in such schemes consist of normal components of the vector field that are collocated at t he faces of the mesh. As a result\, the reconstruction and prolongation st rategies for divergence constraint-preserving vector fields are necessaril y more intricate.\n\nIn this talk\, we present a fourth order divergence c onstraint-preserving prolongation strategy that is analytically exact. Ext ension to higher orders using analytically exact methods is very challengi ng. To overcome that challenge\, a novel WENO-like reconstruction strategy is invented that matches the moments of the vector field in the faces whe re the vector field components are collocated. This approach is almost div ergence constraint-preserving\; so we call it WENO-ADP. To make it exactly divergence constraint-preserving\, a touch-up procedure is developed that is based on a constrained least squares (CLSQ) based method for restoring the divergence constraint up to machine accuracy. With the touch-up\, it is called WENO-ADPT. It is shown that refinement ratios of two and higher can be accommodated. An item of broader interest in this work is that we h ave also been able to invent very efficient finite volume WENO methods whe re the coefficients are very easily obtained and the multidimensional smoo thness indicators can be expressed as perfect squares. We demonstrate that the divergence constraint-preserving strategy works at several high order s for divergence-free vector fields as well as vector fields where the div ergence of the vector field has to match a charge density and its higher m oments. We also show that our methods overcome the late time instability t hat has been known to plague adaptive computations in Computational Electr odynamics.\n\nCo-sponsored by: Center for Computational Science and Engine ering\, University of Toronto\n\nSpeaker(s): Prof. D. S. Balsara\, \n\nTor onto\, Ontario\, Canada\, Virtual: https://events.vtools.ieee.org/m/312557 LOCATION:Toronto\, Ontario\, Canada\, Virtual: https://events.vtools.ieee.o rg/m/312557 ORGANIZER:costas.sarris@utoronto.ca SEQUENCE:5 SUMMARY:High Order Adaptive Mesh Refinement (AMR) for Divergence Constraint -Preserving Schemes (Prof. Dinshaw Balsara\, U. of Notre Dame) URL;VALUE=URI:https://events.vtools.ieee.org/m/312557 X-ALT-DESC:Description: <br /><p>Adaptive mesh refinement (AMR) is the art of solving PDEs on a mesh hierarchy with increasing mesh refinement at eac h level of the hierarchy. Accurate treatment on AMR hierarchies requires a ccurate prolongation of the solution from a coarse mesh to a newly-defined finer mesh. For scalar variables\, suitably high order finite volume WENO methods can carry out such a prolongation. However\, classes of PDEs\, li ke computational electrodynamics (CED) and magnetohydrodynamics (MHD)\, re quire that vector fields preserve a divergence constraint. The primal vari ables in such schemes consist of normal components of the vector field tha t are collocated at the faces of the mesh. As a result\, the reconstructio n and prolongation strategies for divergence constraint-preserving vector fields are necessarily more intricate.</p>\n<p>In this talk\, we present a fourth order divergence constraint-preserving prolongation strategy that is analytically exact. Extension to higher orders using analytically exact methods is very challenging. To overcome that challenge\, a novel WENO-li ke reconstruction strategy is invented that matches the moments of the vec tor field in the faces where the vector field components are collocated. T his approach is almost divergence constraint-preserving\; so we call it WE NO-ADP. To make it exactly divergence constraint-preserving\, a touch-up p rocedure is developed that is based on a constrained least squares (CLSQ) based method for restoring the divergence constraint up to machine accurac y. With the touch-up\, it is called WENO-ADPT. It is shown that refinement ratios of two and higher can be accommodated. An item of broader interest in this work is that we have also been able to invent very efficient <em> finite volume</em> WENO methods where the coefficients are very easily obt ained and the multidimensional smoothness indicators can be expressed as p erfect squares. We demonstrate that the divergence constraint-preserving s trategy works at several high orders for divergence-free vector fields as well as vector fields where the divergence of the vector field has to matc h a charge density and its higher moments. We also show that our methods o vercome the late time instability that has been known to plague adaptive c omputations in Computational Electrodynamics.</p> END:VEVENT END:VCALENDAR