AI SearchAn adaptive mesh generation for Kriging Element Free Galerkin Method based on delaunay triangulation
Call Number: AIT Thesis no.ST-06-10 Material type:
SeriesSeries: Asian Institute of Technology. Thesis ; no. ST-06-10Publication details: Pathum Thani, Thailand : Asian Institute of Technology, 2006Description: 107 leaves : illSubject(s): Online resources: Dissertation note: Thesis (M.Eng.) - Asian Institute of Technology, 2006 Summary: This study attempts to propose an adaptive mesh generation for Element Free Galerkin Method (EFGM) using Kriging Interpolation function. Since the Kriging interpolation maintains the Kronecker delta property, the imposition of essential boundary conditions is simple. Using 2D problems, the entire problem domain is subdivided into a network of triangular cells, exploiting nodes as vertices. Through Delaunay Triangulation, a unique pattern of triangular cells can be generated based on any given distribution of nodes. Thus, the size of integration cells in a region can be adapted based on the nodal density in that region. The numbers of integration points in all integration cells are fixed. Based on the requirement to maintain adequate numerical conditioning of the system, the size of Domain of Influence (DOI) and integration cells used in the adaptive EFGM scheme vary according to density of nodes in the domain, the DOI is defined by layers of cells which are in the form of polygons. The advantage of using polygon layered DOI is that the integration points in the same cell are influenced by the same nodes for approximation of the field variable and also prevent the occurrence of the singular matrix which occurs when the number of nodes are less than the number of terms in polynomial basis. For an adaptive procedure, a residual based error estimator, based on Galerkin weighted residual method is proposed in this study. With this local error estimator, new nodes are added to specific locations where errors are excessive than the user specified value. Then, the triangulation process is updated and the newly discretized domain is reanalyzed. The sequence is automatically repeated until a situation is reached where local residual errors in all triangles are controlled to within a specified limit. A number of benchmark examples are presented to verify the efficiency and accuracy of the present method
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A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineering and Technology
Thesis (M.Eng.) - Asian Institute of Technology, 2006
This study attempts to propose an adaptive mesh generation for Element Free Galerkin Method (EFGM) using Kriging Interpolation function. Since the Kriging interpolation maintains the Kronecker delta property, the imposition of essential boundary conditions is simple. Using 2D problems, the entire problem domain is subdivided into a network of triangular cells, exploiting nodes as vertices. Through Delaunay Triangulation, a unique pattern of triangular cells can be generated based on any given distribution of nodes. Thus, the size of integration cells in a region can be adapted based on the nodal density in that region. The numbers of integration points in all integration cells are fixed. Based on the requirement to maintain adequate numerical conditioning of the system, the size of Domain of Influence (DOI) and integration cells used in the adaptive EFGM scheme vary according to density of nodes in the domain, the DOI is defined by layers of cells which are in the form of polygons. The advantage of using polygon layered DOI is that the integration points in the same cell are influenced by the same nodes for approximation of the field variable and also prevent the occurrence of the singular matrix which occurs when the number of nodes are less than the number of terms in polynomial basis. For an adaptive procedure, a residual based error estimator, based on Galerkin weighted residual method is proposed in this study. With this local error estimator, new nodes are added to specific locations where errors are excessive than the user specified value. Then, the triangulation process is updated and the newly discretized domain is reanalyzed. The sequence is automatically repeated until a situation is reached where local residual errors in all triangles are controlled to within a specified limit. A number of benchmark examples are presented to verify the efficiency and accuracy of the present method
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