BEGIN:VCALENDAR VERSION:2.0 PRODID:-//linuxsoftware.nz//NONSGML Joyous v1.4//EN BEGIN:VEVENT SUMMARY:Adaptive Pseudospectral Evolutions of Wave Models on Hyperboloidal Slices DTSTART:20260625T090000Z DTEND:20260625T110000Z DTSTAMP:20260729T130409Z UID:f3058bb2-e94b-4075-88a9-2de35f4123de SEQUENCE:1 CREATED:20260623T105302Z DESCRIPTION: This thesis extends the bamps framework to solve the wave equ ation on both hyperboloidal slices and hyperboloidal layers. We demonstrat e that the implemented methods achieve promising convergence results in bo th settings. We further investigate how our code handles the inclusion of perturbations in our initial conditions for the hyperboloidal layers setup \, again obtaining encouraging numerical results.Building on this framewor k\, we study the cubic wave equation\, exploring both decaying and blowup solutions through numerical simulations. By tuning initial data toward the threshold of blowup\, we obtain solutions approaching critical behavior w ithin the limitations of our numerical implementation. In addition\, we pr ovide numerical support for several results from modern partial differenti al equations theory by computing the blowup rate of numerically generated blowup solutions and evaluating the associated power indices across the co mputational domain for decaying solutions.As part of this work\, we also d eveloped the foundation of an analysis software suite intended to become a central component of the future bamps development workflow. LAST-MODIFIED:20260623T105302Z LOCATION:Sala V1.25 (Piso 1 do Pavilhão de Civil) do IST/Online URL:http://df.vps.tecnico.ulisboa.pt/en/events/adaptive-pseudospectral-evo lutions-of-wave-models-on-hyperboloidal-slices/ X-ALT-DESC;FMTTYPE=text/html:

This thesis extend s the bamps framework to solve the wave equation on both hyperboloidal sli ces and hyperboloidal layers. We demonstrate that the implemented methods achieve promising convergence results in both settings. We further investi gate how our code handles the inclusion of perturbations in our initial co nditions for the hyperboloidal layers setup\, again obtaining encouraging numerical results.

Building on this framework\, we study the cubi c wave equation\, exploring both decaying and blowup solutions through num erical simulations. By tuning initial data toward the threshold of blowup\ , we obtain solutions approaching critical behavior within the limitations of our numerical implementation. In addition\, we provide numerical suppo rt for several results from modern partial differential equations theory b y computing the blowup rate of numerically generated blowup solutions and evaluating the associated power indices across the computational domain fo r decaying solutions.

As part of this work\, we also developed th e foundation of an analysis software suite intended to become a central co mponent of the future bamps development workflow.

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