Meade, Andrew J., Jr.2012-09-062012-09-062012-09-062012-09-062012-052012-09-05May 2012Wilkinson, Matthew. "Sequentially Optimized Meshfree Approximation as a New Computation Fluid Dynamics Method." (2012) Diss., Rice University. <a href="https://hdl.handle.net/1911/64673">https://hdl.handle.net/1911/64673</a>.https://hdl.handle.net/1911/64673This thesis presents the Sequentially Optimized Meshfree Approximation (SOMA) method, a new and powerful Computational Fluid Dynamics (CFD) solver. While standard computational methods can be faster and cheaper that physical experimentation, both in cost and work time, these methods do have some time and user interaction overhead which SOMA eliminates. As a meshfree method which could use adaptive domain refinement methods, SOMA avoids the need for user generated and/or analyzed grids, volumes, and meshes. Incremental building of a feed-forward artificial neural network through machine learning to solve the flow problem significantly reduces user interaction and reduces computational cost. This is done by avoiding the creation and inversion of possibly dense block diagonal matrices and by focusing computational work on regions where the flow changes and ignoring regions where no changes occur.application/pdfengCopyright 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.Aerospace engineeringComputational fluid dynamicsMechanical engineeringMeshfree methodsSequential optimizationNeural networksThesis2012-09-06123456789/ETD-2012-05-138