BEGIN:VCALENDAR VERSION:2.0 PRODID:-//jEvents 2.0 for Joomla//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:America/New_York BEGIN:STANDARD DTSTART:20221106T010000 RDATE:20230312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20231105T010000 RDATE:20240310T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20241103T010000 RDATE:20250309T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20251102T010000 RDATE:20260308T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20261101T010000 RDATE:20270314T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20271107T010000 RDATE:20280312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:DAYLIGHT DTSTART:20220410T120000 RDATE:20221106T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20230312T030000 RDATE:20231105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20240310T030000 RDATE:20241103T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20250309T030000 RDATE:20251102T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20260308T030000 RDATE:20261101T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20270314T030000 RDATE:20271107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:5ab7dc31b4cfb925e6bfbd771dd5a44c CATEGORIES:PhD Defense CREATED:20230405T151711 SUMMARY:Towards Generalized Modeling for Physics-based Simulation in Computer Graphics LOCATION:CoRE 301 DESCRIPTION:Abstract\nIn the field of science, a unified theory that describes every ph ysical phenomenon and interaction in the universe has always been a hot top ic: it represents the beauty of simplicity. In Computer Graphics, a unified numerical model for physics-based simulation is an equivalent, which extra cts all the core parameters and eliminates the need to adjust algorithms ba sed on different material behaviors. In this dissertation, we show our prog ress in developing unified models in the following aspects:\nFirst, we intr oduce non-Fourier diffusion to accurately deal with the unrealistic infinit e wave speed produced by the traditional diffusion solver and fundamentally explain diffusion from the perspective of the non-equilibrium statistical mechanical Boltzmann Transport Equation. It can capture some of the most ch aracteristic visual aspects of diffusion-driven physics, such as hydrogel s welling, limited diffusive domain for smoke flow, snowflake, and dendrite f ormation, that span from Fourier-type to non-Fourier-type diffusive phenome na. We propose a unified convection-diffusion formulation using this model that treats both the diffusive quantity and its associated flux as the prim ary unknowns, and that recovers the traditional Fourier-type diffusion as a limiting case. We design a novel semi-implicit discretization for this for mulation on staggered MAC grids and a geometric Multigrid-preconditioned Co njugate Gradients solver for fast convergence.\nSecond, we couple the exten ded Pom-Pom model with the Material Point Method (MPM) and develop a unifie d constitutive model for Newtonian and non-Newtonian viscous liquids, which recovers the variational Stokes solver for Newtonian viscosity and a varie ty of non-Newtonian models, such as Oldroyd-B and the Upper Convective Maxw ell (UCM) model. In addition, we show how to two-way couple our viscoelasti c liquid simulator with the non-Fourier heat diffusion solver for simulatin g problems with phase change, such as melting chocolate and digital fabrica tion with 3D printing. \nThird, we exhibit an adaptively updated Lagrangian Material Point Method (A-ULMPM), which extends the current MPM framework t o alleviate non-physical artifacts, such as the cell-crossing instability a nd numerical fracture, that plague state-of-the-art Eulerian formulations o f MPM while still allowing for large deformations that arise in fluid simul ations. For better efficiency and conservation of angular momentum, we furt her integrate the APIC and MLS-MPM formulations in A-ULMPM by augmenting th e accuracy of velocity rasterization using both the local velocity and its first-order derivatives. Our approach does not require significant changes to traditional Eulerian formulations of MPM, and is computationally more ef ficient since it only updates interpolation kernels and their derivatives d uring large topology changes.\nFinally, we present a unified constitutive m odel for versatile physics simulation of inviscid fluids, Newtonian viscosi ty, hyperelasticity, viscoplasticity, elastoplasticity, and other physical effects that arise due to a mixture of these behaviors. The key ideas behin d our formulation are the design of a generalized Kirchhoff stress tensor t hat can describe hyperelasticity, Newtonian viscosity and inviscid fluids, and the use of pre-projection and post-correction rules for simulating mate rial behaviors that involve plasticity, including elastoplasticity and visc oplasticity. We show how our generalized Kirchhoff stress tensor can be cou pled together into a unified constitutive model that allows the simulation of diverse material behaviors by only changing parameter values. More notab ly, our formulation allows for inverse learning of unknown material propert ies directly from data using differentiable physics simulations.\n \n X-ALT-DESC;FMTTYPE=text/html:

Abstract

In the field of science, a unified theory that describes every physical ph enomenon and interaction in the universe has always been a hot topic: it re presents the beauty of simplicity. In Computer Graphics, a unified numerica l model for physics-based simulation is an equivalent, which extracts all t he core parameters and eliminates the need to adjust algorithms based on di fferent material behaviors. In this dissertation, we show our progress in d eveloping unified models in the following aspects:

First, we introduce non-Fourier diffusion to accurately deal wit h the unrealistic infinite wave speed produced by the traditional diffusion solver and fundamentally explain diffusion from the perspective of the non -equilibrium statistical mechanical Boltzmann Transport Equation. It can ca pture some of the most characteristic visual aspects of diffusion-driven ph ysics, such as hydrogel swelling, limited diffusive domain for smoke flow, snowflake, and dendrite formation, that span from Fourier-type to non-Fouri er-type diffusive phenomena. We propose a unified convection-diffusion form ulation using this model that treats both the diffusive quantity and its as sociated flux as the primary unknowns, and that recovers the traditional Fo urier-type diffusion as a limiting case. We design a novel semi-implicit di scretization for this formulation on staggered MAC grids and a geometric Mu ltigrid-preconditioned Conjugate Gradients solver for fast convergence.

Second, we couple the extended Pom-Pom mode l with the Material Point Method (MPM) and develop a unified constitutive m odel for Newtonian and non-Newtonian viscous liquids, which recovers the va riational Stokes solver for Newtonian viscosity and a variety of non-Newton ian models, such as Oldroyd-B and the Upper Convective Maxwell (UCM) model. In addition, we show how to two-way couple our viscoelastic liquid simulat or with the non-Fourier heat diffusion solver for simulating problems with phase change, such as melting chocolate and digital fabrication with 3D pri nting. 

Third, we exhibit an adapti vely updated Lagrangian Material Point Method (A-ULMPM), which extends the current MPM framework to alleviate non-physical artifacts, such as the cell -crossing instability and numerical fracture, that plague state-of-the-art Eulerian formulations of MPM while still allowing for large deformations th at arise in fluid simulations. For better efficiency and conservation of an gular momentum, we further integrate the APIC and MLS-MPM formulations in A -ULMPM by augmenting the accuracy of velocity rasterization using both the local velocity and its first-order derivatives. Our approach does not requi re significant changes to traditional Eulerian formulations of MPM, and is computationally more efficient since it only updates interpolation kernels and their derivatives during large topology changes.

Finally, we present a unified constitutive model for versatile physics simulation of inviscid fluids, Newtonian viscosity, hyperelasticit y, viscoplasticity, elastoplasticity, and other physical effects that arise due to a mixture of these behaviors. The key ideas behind our formulation are the design of a generalized Kirchhoff stress tensor that can describe h yperelasticity, Newtonian viscosity and inviscid fluids, and the use of pre -projection and post-correction rules for simulating material behaviors tha t involve plasticity, including elastoplasticity and viscoplasticity. We sh ow how our generalized Kirchhoff stress tensor can be coupled together into a unified constitutive model that allows the simulation of diverse materia l behaviors by only changing parameter values. More notably, our formulatio n allows for inverse learning of unknown material properties directly from data using differentiable physics simulations.

 

CONTACT:Professor Mridul Aanjaneya DTSTAMP:20260823T112031 DTSTART;TZID=America/New_York:20230411T120000 DTEND;TZID=America/New_York:20230411T140000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR