Interview with Dr Stanley Osher
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Robust High-Resolution Cloth Using Parallelism, History-Based Collisions and Accurate Friction Andrew Selle, Jonathan Su, Geoffrey Irving, Ronald Fedkiw
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 1 Robust High-Resolution Cloth Using Parallelism, History-Based Collisions and Accurate Friction Andrew Selle, Jonathan Su, Geoffrey Irving, Ronald Fedkiw Abstract—In this paper we simulate high resolution cloth consisting of up to 2 million triangles which allows us to achieve highly detailed folds and wrinkles. Since the level of detail is also influenced by object collision and self collision, we propose a more accurate model for cloth-object friction. We also propose a robust history-based repulsion/collision framework where repulsions are treated accurately and efficiently on a per time step basis. Distributed memory parallelism is used for both time evolution and collisions and we specifically address Gauss-Seidel ordering of repulsion/collision response. This algorithm is demonstrated by several high-resolution and high-fidelity simulations. Index Terms—Computer Graphics, Geometric algorithms, Physically based modelling, Cloth, Collision response, Friction ! 1 INTRODUCTION LOTH simulation is pervasive in film, e.g. the untan- C gling strategies for Monsters Inc. [1], the collision and stiction methods for Terminator 3 and Harry Potter [2], and the wrinkle system for Shrek 2 [3]. Cloth sim- ulation also promises to have significant future impact on the clothing industry [4] (see also [5]). While, some researchers have focused on real-time simulation for computer games or non-hero characters [6] that have Bridson [10] Method Our Method lower quality requirements, our focus is on hero char- (45,000 triangles) (1,700,000 triangles) acters, online shopping, and related applications that need photorealistic cloth and clothing. Achieving such Fig. -
The Bibliography
Referenced Books [Ach92] N. I. Achieser. Theory of Approximation. Dover Publications Inc., New York, 1992. Reprint of the 1956 English translation of the 1st Rus- sian edition; the 2nd augmented Russian edition is available, Moscow, Nauka, 1965. [AH05] Kendall Atkinson and Weimin Han. Theoretical Numerical Analysis: A Functional Analysis Framework, volume 39 of Texts in Applied Mathe- matics. Springer, New York, second edition, 2005. [Atk89] Kendall E. Atkinson. An Introduction to Numerical Analysis. John Wiley & Sons Inc., New York, second edition, 1989. [Axe94] Owe Axelsson. Iterative Solution Methods. Cambridge University Press, Cambridge, 1994. [Bab86] K. I. Babenko. Foundations of Numerical Analysis [Osnovy chislennogo analiza]. Nauka, Moscow, 1986. [Russian]. [BD92] C. A. Brebbia and J. Dominguez. Boundary Elements: An Introductory Course. Computational Mechanics Publications, Southampton, second edition, 1992. [Ber52] S. N. Bernstein. Collected Works. Vol. I. The Constructive Theory of Functions [1905–1930]. Izdat. Akad. Nauk SSSR, Moscow, 1952. [Russian]. [Ber54] S. N. Bernstein. Collected Works. Vol. II. The Constructive Theory of Functions [1931–1953]. Izdat. Akad. Nauk SSSR, Moscow, 1954. [Russian]. [BH02] K. Binder and D. W. Heermann. Monte Carlo Simulation in Statistical Physics: An Introduction, volume 80 of Springer Series in Solid-State Sciences. Springer-Verlag, Berlin, fourth edition, 2002. [BHM00] William L. Briggs, Van Emden Henson, and Steve F. McCormick. A Multigrid Tutorial. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, second edition, 2000. [Boy01] John P. Boyd. Chebyshev and Fourier Spectral Methods. Dover Publi- cations Inc., Mineola, NY, second edition, 2001. [Bra84] Achi Brandt. Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, volume 85 of GMD-Studien [GMD Studies]. -
Real-Time Fluid Simulation on GPU
An Improved Study of Real-Time Fluid Simulation on GPU Enhua Wu1, 2, Youquan Liu1, Xuehui Liu1 1Laboratory of Computer Science, Institute of Software Chinese Academy of Sciences, Beijing, China 2Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macao, China email: [email protected], [email protected], [email protected] http://lcs.ios.ac.cn/~lyq/demos/gpgpu/gpgpu.htm Abstract Taking advantage of the parallelism and programmability of GPU, we solve the fluid dynamics problem completely on GPU. Different from previous methods, the whole computation is accelerated in our method by packing the scalar and vector variables into four channels of texels. In order to be adaptive to the arbitrary boundary conditions, we group the grid nodes into different types according to their positions relative to obstacles and search the node that determines the value of the current node. Then we compute the texture coordinates offsets according to the type of the boundary condition of each node to determine the corresponding variables and achieve the interaction of flows with obstacles set freely by users. The test results prove the efficiency of our method and exhibit the potential of GPU for general-purpose computations. KEY WORDS: Graphics Hardware, GPU, Programmability, NSEs, Fluid Simulation, Real-Time Introduction Real-time fluid simulation is a hot topic not only in computer graphics research field for the special effects in movies and video games, but also in engineering applications field. However, the computation of Navier-Stokes equations (NSEs) used to describe the motion of fluids is really hard to achieve real-time. -
Vorticity and Incompressible Flow - Andrew J
Cambridge University Press 0521630576 - Vorticity and Incompressible Flow - Andrew J. Majda and Andrea L. Bertozzi Frontmatter More information Vorticity and Incompressible Flow This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. Although the contents center on mathematical theory, many parts of the book showcase the interactions among rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak solution theory for incompressible flow. Andrew J. Majda is the Samuel Morse Professor of Arts and Sciences at the Courant Institute of Mathematical Sciences of New York University. He is a member of the National Academy of Sciences and has received numerous honors and awards includ- ing the National Academy of Science Prize in Applied Mathematics, the John von Neumann Prize of the American Mathematical Society and an honorary Ph.D. degree from Purdue University. Majda is well known for both his theoretical contributions to partial differential equations and his applied contributions to diverse areas besides in- compressible flow such as scattering theory, shock waves, combustion, vortex motion and turbulent diffusion. His current applied research interests are centered around Atmosphere/Ocean science. Andrea L. Bertozzi is Professor of Mathematics and Physics at Duke University. She has received several honors including a Sloan Research Fellowship (1995) and the Presidential Early Career Award for Scientists and Engineers (PECASE). Her research accomplishments in addition to incompressible flow include both theoretical and applied contributions to the understanding of thin liquid films and moving contact lines. -
UCLA Electronic Theses and Dissertations
UCLA UCLA Electronic Theses and Dissertations Title Algorithms for Optimal Paths of One, Many, and an Infinite Number of Agents Permalink https://escholarship.org/uc/item/3qj5d7dj Author Lin, Alex Tong Publication Date 2020 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA Los Angeles Algorithms for Optimal Paths of One, Many, and an Infinite Number of Agents A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Mathematics by Alex Tong Lin 2020 c Copyright by Alex Tong Lin 2020 ABSTRACT OF THE DISSERTATION Algorithms for Optimal Paths of One, Many, and an Infinite Number of Agents by Alex Tong Lin Doctor of Philosophy in Mathematics University of California, Los Angeles, 2020 Professor Stanley J. Osher, Chair In this dissertation, we provide efficient algorithms for modeling the behavior of a single agent, multiple agents, and a continuum of agents. For a single agent, we combine the modeling framework of optimal control with advances in optimization splitting in order to efficiently find optimal paths for problems in very high-dimensions, thus providing allevia- tion from the curse of dimensionality. For a multiple, but finite, number of agents, we take the framework of multi-agent reinforcement learning and utilize imitation learning in order to decentralize a centralized expert, thus obtaining optimal multi-agents that act in a de- centralized fashion. For a continuum of agents, we take the framework of mean-field games and use two neural networks, which we train in an alternating scheme, in order to efficiently find optimal paths for high-dimensional and stochastic problems. -
A Novel Algorithm for Incompressible Flow Using Only a Coarse Grid Projection
A Novel Algorithm for Incompressible Flow Using Only a Coarse Grid Projection Michael Lentine∗ Wen Zheng Ronald Fedkiw Stanford University Stanford University Stanford University Industrial Light + Magic Industrial Light + Magic Figure 1: High resolution smoke and water. (Left) Smoke flowing above a sphere on a 512 1024 512 grid. (Middle) Water pouring into a box on a 512 512 512 grid. (Right) Smoke flowing around a sphere on a 512 1024× 512 grid.× × × × × Abstract noise (see [Stam and Fiume 1993; Lamorlette and Foster 2002; Ras- mussen et al. 2003]) and curl noise (see [Bridson et al. 2007]) can be Large scale fluid simulation can be difficult using existing tech- used to enhance the visual fidelity of fluid simulations by coupling niques due to the high computational cost of using large grids. We the noise to the incompressible Navier-Stokes equations producing present a novel technique for simulating detailed fluids quickly. Our a more detailed flow. Alternatively, [Kim et al. 2008] and [Narain technique coarsens the Eulerian fluid grid during the pressure solve, et al. 2008] determine where to add noise using information from allowing for a fast implicit update but still maintaining the resolu- the existing simulation and then add it as a postprocess which al- tion obtained with a large grid. This allows our simulations to run at lows them to add noise where it is best suited. Other techniques a fraction of the cost of existing techniques while still providing the such as [Schechter and Bridson 2008] both determine where to add fine scale structure and details obtained with a full projection. -
Institute for Pure and Applied Mathematics, UCLA Award/Institution #0439872-013151000 Annual Progress Report for 2009-2010 August 1, 2011
Institute for Pure and Applied Mathematics, UCLA Award/Institution #0439872-013151000 Annual Progress Report for 2009-2010 August 1, 2011 TABLE OF CONTENTS EXECUTIVE SUMMARY 2 A. PARTICIPANT LIST 3 B. FINANCIAL SUPPORT LIST 4 C. INCOME AND EXPENDITURE REPORT 4 D. POSTDOCTORAL PLACEMENT LIST 5 E. INSTITUTE DIRECTORS‘ MEETING REPORT 6 F. PARTICIPANT SUMMARY 12 G. POSTDOCTORAL PROGRAM SUMMARY 13 H. GRADUATE STUDENT PROGRAM SUMMARY 14 I. UNDERGRADUATE STUDENT PROGRAM SUMMARY 15 J. PROGRAM DESCRIPTION 15 K. PROGRAM CONSULTANT LIST 38 L. PUBLICATIONS LIST 50 M. INDUSTRIAL AND GOVERNMENTAL INVOLVEMENT 51 N. EXTERNAL SUPPORT 52 O. COMMITTEE MEMBERSHIP 53 P. CONTINUING IMPACT OF PAST IPAM PROGRAMS 54 APPENDIX 1: PUBLICATIONS (SELF-REPORTED) 2009-2010 58 Institute for Pure and Applied Mathematics, UCLA Award/Institution #0439872-013151000 Annual Progress Report for 2009-2010 August 1, 2011 EXECUTIVE SUMMARY Highlights of IPAM‘s accomplishments and activities of the fiscal year 2009-2010 include: IPAM held two long programs during 2009-2010: o Combinatorics (fall 2009) o Climate Modeling (spring 2010) IPAM‘s 2010 winter workshops continued the tradition of focusing on emerging topics where Mathematics plays an important role: o New Directions in Financial Mathematics o Metamaterials: Applications, Analysis and Modeling o Mathematical Problems, Models and Methods in Biomedical Imaging o Statistical and Learning-Theoretic Challenges in Data Privacy IPAM sponsored reunion conferences for four long programs: Optimal Transport, Random Shapes, Search Engines and Internet MRA IPAM sponsored three public lectures since August. Noga Alon presented ―The Combinatorics of Voting Paradoxes‖ on October 5, 2009. Pierre-Louis Lions presented ―On Mean Field Games‖ on January 5, 2010. -
2015 ICIAM Lagrange Prize Awarded to Andrew Majda
FOR IMMEDIATE RELEASE International Council for Industrial and Applied Mathematics (ICIAM) Contact: Barbara Keyfitz [email protected] 614-292-5583 Monday, September 15, 2014 2015 ICIAM Lagrange Prize awarded to Andrew Majda Philadelphia, PA— The International Council for Industrial and Applied Mathematics (ICIAM) is pleased to announce Andrew J. Majda of the Courant Institute at New York University as the recipient of the 2015 ICIAM Lagrange Prize in recognition of his ground breaking, original, fundamental and pioneering contributions to applied mathematics and, in particular, to wave front propagation and combustion, scattering theory, fluid dynamics and atmosphere climate science. His research, which has merged asymptotic and numerical methods, physical reasoning and modeling, and rigorous mathematical analysis, has had an enormous and long lasting impact on modern applied mathematics, science and engineering (geophysics, seismology, weather prediction, combustion, and more) and remains the state of the art today. Andrew J. Majda is the Morse Professor of Arts and Sciences at the Courant Institute of New York University. The Lagrange Prize was established to provide international recognition to individual mathematicians who have made an exceptional contribution to applied mathematics throughout their careers. It was created on the initiative of SMAI (Société de Mathématiques Appliquées et Industrielles), SEMA (Sociedad Española de Matematica Aplicada) and SIMAI (Società Italiana di Matematica Applicata e Industriale) and first awarded in 1999. Carrying a cash award of USD 5000, the Lagrange Prize is presently funded by the three member societies SMAI, SEMA and SIMAI. Majda was born in East Chicago, Indiana on January 30, 1949. He received a B.S. -
Selected Papers
Selected Papers Volume I Arizona, 1968 Peter D. Lax Selected Papers Volume I Edited by Peter Sarnak and Andrew Majda Peter D. Lax Courant Institute New York, NY 10012 USA Mathematics Subject Classification (2000): 11Dxx, 35-xx, 37Kxx, 58J50, 65-xx, 70Hxx, 81Uxx Library of Congress Cataloging-in-Publication Data Lax, Peter D. [Papers. Selections] Selected papers / Peter Lax ; edited by Peter Sarnak and Andrew Majda. p. cm. Includes bibliographical references and index. ISBN 0-387-22925-6 (v. 1 : alk paper) — ISBN 0-387-22926-4 (v. 2 : alk. paper) 1. Mathematics—United States. 2. Mathematics—Study and teaching—United States. 3. Lax, Peter D. 4. Mathematicians—United States. I. Sarnak, Peter. II. Majda, Andrew, 1949- III. Title. QA3.L2642 2004 510—dc22 2004056450 ISBN 0-387-22925-6 Printed on acid-free paper. © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. -
Boundary Value Problems for Systems That Are Not Strictly
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Applied Mathematics Letters 24 (2011) 757–761 Contents lists available at ScienceDirect Applied Mathematics Letters journal homepage: www.elsevier.com/locate/aml On mixed initial–boundary value problems for systems that are not strictly hyperbolic Corentin Audiard ∗ Institut Camille Jordan, Université Claude Bernard Lyon 1, Villeurbanne, Rhone, France article info a b s t r a c t Article history: The classical theory of strictly hyperbolic boundary value problems has received several Received 25 June 2010 extensions since the 70s. One of the most noticeable is the result of Metivier establishing Received in revised form 23 December 2010 Majda's ``block structure condition'' for constantly hyperbolic operators, which implies Accepted 28 December 2010 well-posedness for the initial–boundary value problem (IBVP) with zero initial data. The well-posedness of the IBVP with non-zero initial data requires that ``L2 is a continuable Keywords: initial condition''. For strictly hyperbolic systems, this result was proven by Rauch. We Boundary value problem prove here, by using classical matrix theory, that his fundamental a priori estimates are Hyperbolicity Multiple characteristics valid for constantly hyperbolic IBVPs. ' 2011 Elsevier Ltd. All rights reserved. 1. Introduction In his seminal paper [1] on hyperbolic initial–boundary value problems, H.O. Kreiss performed the algebraic construction of a tool, now called the Kreiss symmetrizer, that leads to a priori estimates. Namely, if u is a solution of 8 d X C >@ u C A .x; t/@ u D f ;.t; x/ 2 × Ω; <> t j xj R jD1 (1) C >Bu D g;.t; x/ 2 @ × @Ω; :> R ujtD0 D 0; C Pd where the operator @t jD1 Aj@xj is assumed to be strictly hyperbolic and B satisfies the uniform Lopatinski˘ı condition, there is some γ0 > 0 such that u satisfies the a priori estimate p γ kuk 2 C C kuk 2 C ≤ C kf k 2 C C kgk 2 C ; (2) Lγ .R ×Ω/ Lγ .R ×@Ω/ Lγ .R ×Ω/ Lγ .R ×@Ω/ 2 2 −γ t for γ ≥ γ0. -
TAMAR T. SHINAR CURRICULUM VITAE Computer Science And
TAMAR T. SHINAR CURRICULUM VITAE Computer Science and Engineering phone: (951) 827-5015 University of California, Riverside email: [email protected] Winston Chung Hall, Room 351 https://www.cs.ucr.edu/ shinar Riverside, CA 92521 ~ RESEARCH INTERESTS Physics-based animation, fluid-structure interaction, computational biology. EDUCATION Sept 2003 - Jun 2008 Ph.D., Scientific Computing and Computational Mathematics Stanford University Thesis: Simulation of coupled rigid and deformable solids and multiphase fluids Research Advisor: Prof. Ronald Fedkiw Sept 1995 - May 1998 B.S., Mathematics, minor Computer Science University of Illinois at Urbana-Champaign magna cum laude with Highest Distinction in Mathematics Sept 1994 - May 1995 Iowa State University coursework in Physics, Chemistry, and Mathematics concurrent with senior year of high school ACADEMIC APPOINTMENTS Jul 2020 - present Associate Professor Jul 2011 - Jun 2020 Assistant Professor Computer Science and Engineering University of California, Riverside Sept 2008 - Jun 2011 Postdoctoral Fellow Courant Institute of Mathematical Sciences New York University Research Advisor: Prof. Michael Shelley HONORS AND AWARDS 2014 - 2017, 2011 - 2014 Amrik Singh Poonian Term Chair in Computer Science and Engineering Sept 1995 - Jun 1996 University of Illinois Jobst Scholar Spring 1995 Frank Miller Scholarship PROFESSIONAL AFFILIATIONS 2006 - present Association for Computing Machinery (ACM) 2009 - 2012 American Physical Society (APS) 2009 - 2011 Genetics Society of America (GSA) PROFESSIONAL ACTIVITIES -
AN13 and CT13 Abstracts
AN13 and CT13 Abstracts Abstracts are printed as submitted by the authors. Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference web: www.siam.org/meetings/ Membership and Customer Service: 800-447-7426 (US & Canada) or +1-215-382-9800 (worldwide) 2 2013 SIAM Annual Meeting • SIAM Conference on Control & Its Applications Table of Contents Annual Meeting (AN13) Abstracts ...............................................3 Control & Its Applications (CT13) .............................................127 SIAM Presents Since 2008, SIAM has recorded many Invited Lectures, Prize Lectures, and selected Minisymposia from various conferences. These are available by visiting SIAM Presents (http://www.siam.org/meetings/presents.php). 2013 SIAM Annual Meeting • SIAM Conference on Control & Its Applications 3 AN13 Abstracts 4 AN13 Abstracts IC1 system including cars, buses, pedestrians, ants and molecu- Social Networks as Information Filters lar motors, which are considered as ”self-driven particles”. We recently call this interdisciplinary research on jamming Social networks, especially online social networks, are of self-driven particles as ”jamology”. This is based on driven by information sharing. But just how much informa- mathematical physics, and and includes engineering appli- tion sharing is influenced by social networks? A large-scale cations as well. In the talk, starting from the backgroud experiment measured the effect of the social network on the of this research, simple mathematical models, such as the quantity and diversity of information being shared within asymmetric simple exclusion process and the Burgers equa- Facebook. While strong ties were found to be individu- tion, are introduced as basis of all kinds of traffic flow.