creator Gundaboina Harish, Aditya Kiran advisor Li, Xiaofan In this paper, we consider the boundary integral equation (BIE) corresponding to the Brinkmans equation. We compute the velocities of the interacting particles when the point-wise forces acting on them are known. We assume a ctitious ow point inside the bead and eliminate the double-layer in the BIE. This BIE is now numerically solved by covering the surface of the bead by two overlapping patches and de ning their partition of unity. We then discuss the e ect of the overlapping of the patches on the results. We develop a second-order accurate numerical method for the BIE. ix Submitted by Erma Thomas (thomase@iit.edu) on 2015-07-13T22:01:16Z No. of bitstreams: 2 Final thesis Aditya_unsigned.pdf: 1398652 bytes, checksum: d07d263e16fbc2b199a330f9c6dd443c (MD5) 1st Page_signed by advisor.pdf: 79236 bytes, checksum: da93c0e8ef21973b7cfda219ba87eaa7 (MD5) Made available in DSpace on 2015-07-13T22:01:16Z (GMT). No. of bitstreams: 2 Final thesis Aditya_unsigned.pdf: 1398652 bytes, checksum: d07d263e16fbc2b199a330f9c6dd443c (MD5) 1st Page_signed by advisor.pdf: 79236 bytes, checksum: da93c0e8ef21973b7cfda219ba87eaa7 (MD5) Previous issue date: 2014-12 M.S. in Applied Mathematics, December 2014 2014 2014-12 http://hdl.handle.net/10560/3453 en Thesis born digital application/pdf In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access MATH / Applied Mathematics Illinois Institute of Technology Affiliated department