The Wavefront Topology System And Finite Element Method Applied To Engineering Visualization
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Type of WorkText
DepartmentElectrical and Computer Engineering
ProgramDoctor of Engineering
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Finite element method
The Wavefront Topology System (WTS) is a novel algorithm for numerical analysis in computational geometry and electromagnetics. WTS is capable of generating continuous finite elements for discrete subdivision of arbitrary geometrical domains. Structured grids are achievable by a topological algorithm which is invariant to the coordinate system associated with the physical region. The generated grid topology corresponds to an orthogonal coordinate system. The assembly of nodes and edges within this topology form elements. These elements exist in a functional space; and all continuous functions in the functional space are represented as a linear combination of basis functions. The WTS algorithm generates basis functions in cartesian, spherical, cylindrical, and toroidal coordinate systems. The preprocessing phase provides a robust methodology for solving the partial differential equation associated with the physical geometry; post process rendering is also enhanced by this technique. The WTS advancing systematic node insertion process propagates through the interior of the domain. The front travels until boundary conditions are satisfied; constraints are geometrical. Volumes and surfaces are candidates for automatic polygon generation. Global and local coordinates are furnished as the topology advances in an outward propagation. Insertion of coordinates are subjected to a 1st, 2nd, and 3rd order adjacency matrix. The WTS method intrinsically supports numerical quadrature and finite difference analysis for solving integral and partial differential equations. The algorithm begins with a stencil initialization process then proceeds with a node insertion technique. The insertion process results in the creation of a discrete computational lattice. Hybridization with the Finite Element Method (FEM) will demonstrate its functionality as an efficient FEM code. Its integration with current engineering FEM methodologies provides a numerical technique for solving linear systems of equations of the form Ax=b. An exposition of the research will explore a Laplace analysis of voltage distribution. The research will also involve electromagnetic (EM) scattering from a dielectric cylinder. The previous work will include WTS applications to image processing and molecular modeling. The challenge will include a comparison of computation complexity and time for different solutions within complex geometrical domains. The solutions will be displayed in a custom developed scientific visualization system. This research demonstrates the significance of the WTS analysis to copious fields of computational engineering. The WTS technique optimizes preprocessing, solving, and postprocessing.