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USE OR DELETE OPTIONAL SUBHEAD --><!-- <h3>College of Domini (optional subhead)</h3> --> <div style='border-top:solid #666666 1.0pt;border-left:none;border-bottom:solid #666666 1.0pt; border-right:none;mso-border-top-alt:solid #666666 .75pt;mso-border-bottom-alt: solid #666666 .75pt;padding:4.0pt 0in 4.0pt 0in' id=titlebar> <p class=MsoNormal style='mso-line-height-alt:13.2pt;mso-outline-level:2; background:white'><b><span lang=EN style='font-size:18.0pt;font-family:"Arial","sans-serif"; mso-fareast-font-family:"Times New Roman";color:#999966;mso-font-kerning:18.0pt; mso-ansi-language:EN'><a href="../../../../Local%20Settings/Temporary%20Internet%20Files/Content.IE5/Application%20Data/Macromedia/Dreamweaver%208/Configuration/ServerConnections/Mathematics/mathhome.html"><span style='color:#999966;text-decoration:none;text-underline:none'>Department of Mathematics </span></a><o:p></o:p></span></b></p> </div> <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 width=750 style='width:562.5pt;mso-cellspacing:0in;background:white;mso-yfti-tbllook: 1184;mso-padding-alt:0in 0in 0in 0in' id=main> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <!-- INSERT LEFT COLUMN LINKS --> <td width=150 valign=top style='width:112.5pt;border:none;border-right:solid #666666 1.0pt; mso-border-right-alt:solid #666666 .75pt;padding:0in 0in 0in 0in' id=a2> <div style='margin-bottom:12.0pt' id=mainlinks> <div> <div style='mso-element:para-border-div;border:none;border-bottom:solid #CCCCCC 1.0pt; mso-border-bottom-alt:solid #CCCCCC .75pt;padding:0in 0in 0in 0in'> <p class=MsoNormal style='mso-outline-level:4;border:none;mso-border-bottom-alt: solid #CCCCCC .75pt;padding:0in;mso-padding-alt:0in 0in 0in 0in'><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: SimSun;mso-bidi-font-family:Arial;color:#666666'><o:p>&nbsp;</o:p></span></b></p> <p class=MsoNormal style='mso-outline-level:4;border:none;mso-border-bottom-alt: solid #CCCCCC .75pt;padding:0in;mso-padding-alt:0in 0in 0in 0in'><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:#666666'>Math 690N<br> </span></b><span class=style11><b><span style='font-size:7.5pt;font-family: "Verdana","sans-serif";mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: Arial;color:#666666'>TR 9:30</span></b></span><span class=style11><b><span style='font-size:7.5pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: SimSun;mso-bidi-font-family:Arial;color:#666666'>A</span></b></span><span class=style11><b><span style='font-size:7.5pt;font-family:"Verdana","sans-serif"; mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Arial; color:#666666'>-10:45 </span></b></span><span class=style11><b><span style='font-size:7.5pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: SimSun;mso-bidi-font-family:Arial;color:#666666'>A</span></b></span><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:#666666'><br> Carver<span style='mso-spacerun:yes'>  </span>0</span></b><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: SimSun;mso-bidi-font-family:Arial;color:#666666'>290</span></b><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:#666666'> <o:p></o:p></span></b></p> </div> </div> </div> <div> <p class=MsoNormal style='line-height:15.6pt;mso-outline-level:4'><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:black'><!-- INSERT COPY -->Instructor<o:p></o:p></span></b></p> <p class=MsoNormal style='line-height:15.6pt'><span class=SpellE><span style='font-size:9.0pt;font-family:"Arial","sans-serif";color:black'>Hailiang</span></span><span style='font-size:9.0pt;font-family:"Arial","sans-serif";color:black'> Liu <br> 434 Carver Hall<br> 515-294-0392<br> <a href="mailto:hliu@iastate.edu">hliu@iastate.edu</a><o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'><!-- 2ND COLUMN. INSERT COPY -->Lecture notes by topics <br> <a href="http://orion.math.iastate.edu/hliu/teaching/690N.1.09f/690N-note01.pdf">Finite difference methods</a><br> <a href="http://orion.math.iastate.edu/hliu/teaching/690N.1.09f/690N-note02.pdf">Shock capturing methods</a><br> <a href="http://orion.math.iastate.edu/hliu/teaching/690N.1.09f/690N-note03.pdf">Kink capturing methods</a><o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>Assignments by topics <o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>#1 <a href="http://orion.math.iastate.edu/hliu/teaching/690N.1.09f/690N-assign1-09f.pdf">Shock capturing</a> <br> <br style='mso-special-character:line-break'> <![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'> <![endif]></span><u><span style='color:#000066'><o:p></o:p></span></u></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'><o:p>&nbsp;</o:p></span></p> </div> </td> <td width=600 valign=top style='width:6.25in;padding:0in 0in 0in 0in'> <div> <p class=MsoNormal style='line-height:15.6pt;mso-outline-level:3'><b><span style='font-size:11.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:black'>Math 690N: Advanced Topics in Numerical Methods <o:p></o:p></span></b></p> <p class=MsoNormal style='line-height:15.6pt;mso-outline-level:4'><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:black'><br> </span></b><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"; mso-fareast-font-family:SimSun;mso-bidi-font-family:Arial;color:black'>Fall</span></b><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:black'> 200</span></b><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: SimSun;mso-bidi-font-family:Arial;color:black'>9<o:p></o:p></span></b></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>Meeting dates: 08/24/09 - 12/18/09 <o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt;mso-outline-level:4'><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:black'>Course Description (3 credits) <o:p></o:p></span></b></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>Moving fronts or interfaces separating different regions are present in many problems in nature. Such interfaces are often <span class=GramE>dynamic,</span> and driven by singular forces; and involved physical quantities frequently develop discontinuities across the interface.&nbsp; These features make the numerical approximation and simulation of such problems a challenging task and a field of extensive ongoing research. <br> <br> In this course we will focus our attention on two classes of numerical methods that involve sharp interfaces: shock capturing methods and level set methods. A course is suitable for graduate students in computational and applied mathematics whose primary interest is in analysis and design of algorithms for computing scientific problems. Lectures will be particularly geared to students using or interested in using these methods in their ongoing/future research.<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt;mso-outline-level:4'><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:black'>Topics to be Covered <o:p></o:p></span></b></p> <p class=MsoNormal style='line-height:15.6pt'><b><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'><br> <strong><span style='font-family:"Arial","sans-serif"'>A. High resolution numerical methods for nonlinear PDEs of hyperbolic type </span></strong></span></b><span style='font-size:9.0pt;font-family:"Arial","sans-serif";color:black'><o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>1. Basic features of nonlinear PDEs (conservation laws and Hamilton-Jacobi equations)<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>2. Principles for derivation of shock capturing methods<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>3. Implementation of the numerical methods<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>4. Examples of application: e.g., gas dynamics, geometric optics.<br> &nbsp; <o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><strong><span style='font-size: 9.0pt;font-family:"Arial","sans-serif";color:black'>B. Interface capturing methods </span></strong><span style='font-size:9.0pt;font-family:"Arial","sans-serif"; color:black'><o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>1. Basic concepts of level set method, e.g. motion law, distance function, initialization;<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>2. Basic techniques: e.g., <span class=SpellE>discretization</span>, projection, re-initialization, data extension;<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>3. Examples of application: e.g. geometric motion, wave propagation, particle dynamics in complex fluids.<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt;mso-outline-level:4'><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:black'>Homework Assignments <o:p></o:p></span></b></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>There will be 6-8 homework assignments for this course. HW assignments consist of both theoretical and computational work.<span style='mso-spacerun:yes'>  </span>For the computational assignments, we will be using <span class=SpellE>Matlab</span>. <o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='line-height:15.6pt;mso-outline-level:4'><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:black'>Exams<o:p></o:p></span></b></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>One midterm presentation and one final take home project. <o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt;mso-outline-level:4'><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:black'>Grading Policy <o:p></o:p></span></b></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>This course will be graded as a seminar course requiring a presentation (homework assignments 60%; midterm presentation 20%; final project 20%. <o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt;mso-outline-level:4'><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:Arial;color:black'>References</span></b><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif";mso-fareast-font-family: SimSun;mso-bidi-font-family:Arial;color:black'>:<br> </span></b><span style='font-size:9.0pt;font-family:"Arial","sans-serif"; color:black'>&nbsp;</span><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"; mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:Arial; color:black'><o:p></o:p></span></b></p> <p class=MsoNormal style='line-height:15.6pt'><strong><span style='font-size: 9.0pt;font-family:"Arial","sans-serif";color:black'>High resolution numerical methods:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></strong><span style='font-size:9.0pt;font-family:"Arial","sans-serif";color:black'><o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span class=SpellE><span style='font-size:9.0pt;font-family:"Arial","sans-serif";color:black'>Bertil</span></span><span style='font-size:9.0pt;font-family:"Arial","sans-serif";color:black'> <span class=SpellE>Gustafsson</span>, Heinz Otto <span class=SpellE>Kreiss</span> and Joseph <span class=SpellE>Oliger</span>; Time dependent problems and difference methods. A Wiley-<span class=SpellE>Interscience</span> Publication, 1995.&nbsp; (classical)<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>Randall J. <span class=SpellE>LeVeque</span>; Numerical methods for conservation laws. Basel ; Boston : <span class=SpellE>Birkhuser</span>&nbsp; <span class=SpellE>Verlag</span>, 1992 (very readable)<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><b><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'><br> <strong><span style='font-family:"Arial","sans-serif"'>Level-set methods &nbsp;</span></strong></span></b><span style='font-size:9.0pt;font-family: "Arial","sans-serif";color:black'><o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>J.A. <span class=SpellE>Sethian</span>. <em><span style='font-family:"Arial","sans-serif"'>Level Set Methods and Fast Marching Methods: Evolving interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials</span></em>&nbsp;<em><span style='font-family:"Arial","sans-serif"'>Science. </span></em>Cambridge University Press,&nbsp;&nbsp;&nbsp; Cambridge, 1999. <o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>S. J. Osher and R. P. <span class=SpellE>Fedkiw</span>. <em><span style='font-family:"Arial","sans-serif"'>Level Set Methods and Dynamic Implicit Surfaces. </span></em>Springer, 2002.<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='line-height:15.6pt'><span style='font-size:9.0pt; font-family:"Arial","sans-serif";color:black'>&nbsp;<o:p></o:p></span></p> </div> </td> </tr> </table> <!-- INSERT CONTACT INFO: UNIT, PHONE, E-MAIL --> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> </div> </body> </html>