In this paper we analyze the interaction of water waves with a permeable barrier which is slightly perturbed from its vertical position within the framework of linearised water wave theory. The barrier is placed in water of finite depth. Two different kinds of barriers are examined, namely, (I) a partially immersed barrier and (II) a submerged bottom standing barrier. The governing boundary value problem involving the velocity potential function is split into two boundary value problems involving the zeroth order as well as the first order velocity potential functions by using a simplified perturbation technique. The zeroth order reflection and transmission coefficients which are due to a vertical permeable barrier are evaluated by solving a Fredholm integral equation of second kind numerically by using a one term GALERKIN APPROXIMATION. Green’ s theorem is applied to evaluate the first order reflection and transmission coefficients. The first order transmission coefficient vanishes irrespective of the shape of the barrier. The numerical values for the first order reflection coefficient are determined by choosing some appropriate shape functions. The numerical results for the zeroth order reflection coefficient which stand for the case of a vertical barrier are validated against the known results for both the permeable and impermeable barriers. The first order reflection curves are also compared by making the porosity constant to be zero with those available in the literature for an impermeable nearly vertical barrier.

In terms of observational data, there are some problems in the standard Big Bang cosmological model. Inflation era, early accelerated phase of the evolution of the universe, can successfully solve these problems. The inflation epoch can be explained by scalar inflaton field. The evolution of this field is presented by a non-linear differential equation. This equation is considered in FLRW model. In FLRW model, we consider the universe as the warped product of real line with a three dimensional homogeneous and isotropic manifold  which could have positive, negative or zero curvature. The main aim of this paper is the numerical solution of the inflation evolution differential equations using of a meshless discrete GALERKIN method. The method reduces the solution of these types of differential equations to the solution of Volterra integral equations of the second kind. Therefore, we solve these integral equations using moving least squares method. Finally, a numerical example is included to show the validity and efficiency of the new technique.

In this paper we will present an adaptive wavelet scheme to solve the generalized Stokes problem. Using divergence free wavelets, the problem is transformed into an equivalent matrix vector system, that leads to a positive definite system of reduced size for the velocity. This system is solved iteratively, where the application of the infinite stiffness matrix, that is sufficiently compressible, is replaced by an adaptive APPROXIMATION. Finally we prove that this adaptive method has optimal computational complexity, that is it recovers an approximate solution with desired accuracy at a computational expense that stays proportional to the number of terms in a corresponding wavelet-best N-term APPROXIMATION.

This paper presents element-free GALERKIN (EFG) method as a computational technique that can effectively avoid the disadvantage of mesh entanglement. The present method is used to analyze the static defelection of beams. The moving least squares (MLS) APPROXIMATION has been used for constructing the shape function based on a set of nodes arbitrarily distributed in the analysis domain.

‎‎‎Given a fuzzy normed space, we will introduce the notion of fuzzy near best APPROXIMATION as a generalization of the notion of fuzzy best APPROXIMATION. Some basic properties are characterized and also many examples for illustration are presented. Also, the hereditary properties of the fuzzy near best APPROXIMATION on direct sum and tensor product of linear spaces are discussed.

This paper introduces a computational strategy to collaboratively develop the GALERKIN Finite Volume Method (GFVM) as one of the most straightforward and efficient explicit numerical methods to solve structural problems encountering material nonlinearity in a small limited area, while the remainder of the domain represents a linear elastic behavior. In this regard, the Element Free GALERKIN method (EFG), which is remarkably robust and accurate, but presumably more expensive, has locally been employed as a nonlinear sub-model to cover the shortcomings of the GFVM in the elastoplastic analysis. Since the formulations of these two methods are fundamentally different, the iterative zonal coupling has been accomplished using overlapping Multi-Grid (MG) patches with a non-matching interface and Iterative Global/Local (IGL) approach. The main property of such an algorithm is its non-intrusiveness, which means the complex nonlinear EFG solver is locally utilized over an elastic global GFVM without any geometric modification. This method is verified and investigated with available analytical and numerical solutions which gave quiet promising results showing the robustness and accuracy of the method. The Moving Least-Square APPROXIMATION (MLS) has widely been applied on transfer level due to the non-conforming interface at the patch edges, and easily allows us to attach complex geometries with different mesh patterns. The new type of Quasi-Newtonian accelerator is adopted on the global material constitutive matrices and its convergence property and accuracy is compared with dynamic Aitken accelerators for two-dimensional problems in MATLAB. Finally, various accelerator types and mapping strategies are also concerned in the examination.