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- W88641905 abstract "For approximating the solution of partial dierential equations (PDE), meshless methods have been introduced to alleviate the diculties arising in mesh generation using the conventional Finite Element Method (FEM). Many meshless methods introduced lack the Kronecker delta property making them inecient in handling essential boundary conditions. Oh et al. developed several meshfree shape functions that have the Kronecker delta property. Boundary Element Methods (BEM) solve a boundary integral equation (BIE) which is equivalent to the PDE, thus reducing the dimensionality of the problem by one and the amount of computation when compared to FEM. In this dissertation, three meshless collocation based boundary element methods are introduced: meshfree reproducing polynomial boundary particle method (RPBPM), patch-wise RPBPM, and patch-wise reproducing singularity particle method (RSBPM). They are applied to the Laplace equation for convex and non-convex domains in two and three dimensions for problems with and without domain singularities. Electromagnetic wave propagation through photonic crystals is governed by Maxwell’s equations in the frequency domain. Under certain conditions, it can be shown that the wave propagation is also governed by Helmholtz equation. Patch-wise RPBPM is applied to the two dimensional Helmholtz equation and used to model electromagnetic wave propagation though lattices of photonic crystals. For thin plate problems, using the Kircho hypothesis, the three dimensional elasticity" @default.
- W88641905 created "2016-06-24" @default.
- W88641905 creator A5076812038 @default.
- W88641905 date "2011-01-01" @default.
- W88641905 modified "2023-09-24" @default.
- W88641905 title "Meshless boundary particle methods for boundary integral equations and meshfree particle methods for plates" @default.
- W88641905 hasPublicationYear "2011" @default.
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