Meshfree point collocation method is developed for the stream-vorticity formulation of two-dimensional incompressible Navier– Stokes equations. Particular emphasis is placed on the novel formulation of effective vorticity condition on no-slip boundaries. The moving least square approximation is employed to construct shape functions in conjunction with the framework of point collocation method. ...

This paper is concerned with the adaptive multilevel solution of elliptic partial differential equations using the partition of unity method. While much of the work on meshfree methods is concerned with convergence-studies, the issues of fast solution techniques for the discrete system of equations and the construction of optimal order algorithms are rarely addressed. However, the treatment of ...

A uni9ed design sensitivity analysis method for a meshfree shell structure with respect to size, shape, and con9guration design variables is presented in this paper. A shear deformable shell formulation is characterized by a CAD connection, thickness degeneration, meshfree discretization, and nodal integration. Because of a strong connection to the CAD tool, the design variable is selected from...

Meshfree discretizations construct approximate solutions to partial differential equation based on particles, not on meshes, so that it is well suited to solve the problems on irregular domains. Since the nodal basis property is not satisfied in meshfree discretizations, it is difficult to handle essential boundary conditions. In this paper, we employ the Lagrange multiplier approach to solve t...

A truly meshfree method – the radial basis function collocation method is implemented for some 2-D and 3-D groundwater models. The results showed the superior simplicity, general applicability and accuracy of this method, which is a very promising simulation tool in many application areas.

This paper develops a class of meshless methods that are well-suited to statistical inverse problems involving partial differential equations (PDEs). The methods discussed in this paper view the forcing term in the PDE as a random field that induces a probability distribution over the residual error of a symmetric collocation method. This construction enables the solution of challenging inverse...

The finite element method is the reference technique in the simulation of metal forming and provides excellent results with both Eulerian and Lagrangian implementations. The latter approach is more natural and direct but the large deformations involved in such processes require remeshing-rezoning algorithms that increase the computational times and reduce the quality of the results. Meshfree me...

This paper presents meshfree method for solving systems of linear Volterra integro-differential equations with initial conditions. This approach is based on collocation method using Sinc basis functions. It's well-known that the Sinc approximate solution converges exponentially to the exact solution. Some numerical results are included to show the validity of this method.

This paper will address the problem of time marching function approximated solutions inherent in emerging meshfree Computational Fluid Dynamics (CFD) solution techniques. The numerical solutions of partial differential equations (PDEs) of CFD has been dominated by either finite difference methods (FDM), finite element methods (FEM), and finite volume methods (FVM). These methods can be derived ...