Sequentially optimized meshfree approximation method for the solution of differential equations

Simple item page
dc.contributor.advisorMeade, Andrew J., Jr.en_US
dc.creatorWilkinson, Matthew Clarken_US
dc.date.accessioned2011-07-25T02:05:49Zen_US
dc.date.available2011-07-25T02:05:49Zen_US
dc.date.issued2010en_US
dc.description.abstractThis thesis presents a greedy method for the solution of differential equations that accelerates convergence versus standard Finite Element Methods. The Sequentially Optimized Meshfree Approximation method unites meshfree methods, sequential optimization processes, and radial basis functions to solve the strong form of governing equations. The ability to solve the strong form eliminates the need to develop expensive and time consuming variational and/or weak forms of the governing equations currently employed in many numerical methods. The first section introduces and explains the procedures for using this method and then uses increasingly complex examples to detail the finer points of the method across a range of algebraic and differential equations. The second section explains why this method fails for equations and systems that involve discontinuities and explores future avenues through which these shortcomings might be remedied.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS M.E. 2010 WILKINSONen_US
dc.identifier.citationWilkinson, Matthew Clark. "Sequentially optimized meshfree approximation method for the solution of differential equations." (2010) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/62059">https://hdl.handle.net/1911/62059</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/62059en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectComputer scienceen_US
dc.subjectAerospace engineeringen_US
dc.titleSequentially optimized meshfree approximation method for the solution of differential equationsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMechanical Engineeringen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Scienceen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
1486054.PDF
Size:
3.26 MB
Format:
Adobe Portable Document Format
Download
Collections
Rice University Theses and Dissertations