The accuracy of the algorithm is the highest when the support-domain dimensionless size is 1.0 and the distribution of field nodes is consistent with the nodes of background elements. First, the proposed meshfree method and corresponding coupled methods are well-suited for electromagnetic numerical modeling. The results of the numerical modeling suggest the following. The coupling algorithm of EFG-PIM and EFG-RPIM are generated by integrating the PIM or RPIM and EFGM. The accuracy of boundary conditions imposed directly and by a penalty function are discussed in the case of forward modeling of two-dimensional magnetotellurics in a homogeneous medium model. RPIM and EFGM are applied to controlled-source two-dimensional electromagnetic modeling with fixed shape parameters. Taking two dimensional Poisson equation as an example, we discuss the support-domain dimensionless size, the field nodes, and background element settings with respect to their effect on calculation accuracy of the meshfree method. We comparatively analyze the global weak form meshfree methods, such as element-free Galerkin method (EFGM), the point interpolation method (PIM), and the radial point interpolation method (RPIM). Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications.Meshfree method offers high accuracy and computational capability and constructs the shape function without relying on predefined elements. This book also addresses their implementation and provides small MATLAB codes on each sub-topic. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics.
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