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Abstract This paper considers a numerical solution of a linear elasticity problem, namely the Cauchy–Navier equation, using a strong form method based on a local Weighted Least Squares (WLS) approximation. The main advantage of the employed numerical approach, also referred to as a Meshless Local Strong Form method, is its generality in terms of approximation setup and positions of computational nodes. In this paper, flexibility regarding the nodal position is demonstrated through two numerical examples, i.e. a drilled cantilever beam, where an irregular domain is treated with a relatively simple nodal positioning algorithm, and a Hertzian contact problem, where again, a relatively simple h-refinement algorithm is used to extensively refine discretization under the contact area. The results are presented in terms of accuracy and convergence rates, using different approximations and refinement setups, namely Gaussian and monomial based approximations, and a comparison of execution time for each block of the solution procedure. [ABSTRACT FROM AUTHOR]

A numerical solution of the Drift-Diffusion Model for simulation of semiconductor devices based on the local meshless numerical method is presented. Numerical difficulties inherited from convection-dominated processes and high gradients near junctions typically results in oscillations within the solution. The difficulties can be alleviated by artificial dissipation schemes or by other stabilization approaches that often require a complex computation to improve the solution convergence. We applied a simple numerical approach with a local coupling and without special treatments of nonlinearities. The proposed approach is straightforward to implement and is suitable for parallel execution. We demonstrate the efficiency of the proposed methodology on a simulation of PN junction. The results are compared against previously published data with a good agreement achieved. The applicability of the proposed methodology is confirmed with the simulation of extended tests with more complicated geometries and more intense dynamics. The computational efficiency is demonstrated through the measurement of execution time and speedup on shared memory computer architecture. [ABSTRACT FROM AUTHOR]

Abstract: Simulation of macrosegregation with mesosegregates as a consequence of solidification of a binary Sn–10%Pb alloy in a 2-dimensional rectangular cast is tackled in the present paper. Coupled volume averaged governing equations for mass, energy, momentum and species transfer are considered by incorporating Lever solidification rule and incompressible Newtonian fluid with Darcy limit in the mushy zone. Solid phase is assumed stationary. Double diffusive effects in the melt are modeled by the thermal and solutal Boussinesq hypothesis. The physical model is solved by the meshless Local Radial Basis Function Collocation Method (LRBFCM) by using 5-noded influence domains, multiquadrics radial basis functions and explicit time stepping. Pressure–velocity coupling is based on local pressure correction. Adaptive upwinding has to be used for stabilization of the convective terms. The numerical simulations reveal instabilities during solidification process that introduce anomalies in the final segregation map that scale with the typical cast as well as sub-cast dimensions. The main advantages of choosing the represented meshless approach for solving the problem are in its simplicity and similar coding in 2D and 3D, as well as straightforward applicability in non-uniform node arrangements. The locality of the proposed numerical approach is also convenient for parallel execution. It is demonstrated that LRBFCM can be advantageously used in casting simulations where the chemical segregation exhibits industrially relevant multi-scale patterns. [Copyright &y& Elsevier]

Abstract: A comparison between weak form meshless local Petrov–Galerkin method (MLPG) and strong form meshless diffuse approximate method (DAM) is performed for the diffusion equation in two dimensions. The shape functions are in both methods obtained by moving least squares (MLS) approximation with the polynomial weight function of the fourth order on the local support domain with 13 closest nodes. The weak form test functions are similar to the MLS weight functions but defined over the square quadrature domain. Implicit timestepping is used. The methods are tested in terms of average and maximum error norms on uniform and non-uniform node arrangements on a square without and with a hole for a Dirichlet jump problem and involvement of Dirichlet and Neumann boundary conditions. The results are compared also to the results of the finite difference and finite element method. It has been found that both meshless methods provide a similar accuracy and the same convergence rate. The advantage of DAM is in simpler numerical implementation and lower computational cost. [Copyright &y& Elsevier]