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Title: A Novel Meshfree Smoothed Least-squares(SLS) Method with Applications to Dielectrophoresis Simulations
Keywords: Meshfree method, Smoothed least-squares method, DEP, Dielectrophoresis
Issue Date: 24-Sep-2008
Citation: SONG CHENGXIANG (2008-09-24). A Novel Meshfree Smoothed Least-squares(SLS) Method with Applications to Dielectrophoresis Simulations. ScholarBank@NUS Repository.
Abstract: This thesis focuses on the development and application of a unified meshfree method applicable for all types of differential equations that govern practical engineering problems. The first part of this thesis is the development of the meshfree smoothed least-squares (SLS) method based on first-order least-squares formulation. The meshfree SLS method uses a unified formulation for all types of partial differential equations: elliptic, parabolic, hyperbolic or mixed. The SLS method is found particularly effective for solving non-self-adjoint system such as the convection dominated problem, which is difficult to solve by conventional Galerkin methods. In the second part, the SLS method is devoted to numerical analysis of various engineering problems, including linear elastic problems, incompressible steady flow problem, and dielectrophoresis problem, etc. It is found that the SLS method achieves better accuracy and convergence rate, comparing with other methods based on Galerkin formulation. The last part of the thesis deals with simulations of DEP based systems using meshfree techniques.
Appears in Collections:Ph.D Theses (Open)

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