We discuss the matrix-free implementation of Discontinuous Galerkin methods for compressible flow problems, i.e. the compressible Navier-Stokes equations. For the spatial discretization the CDG2 method and for temporal discretization an explicit Runge-Kutta method is used. For the presented matrix-free approach we discuss asynchronous communication, shared memory parallelization, and automated ...

|Although numerically very e cient the nite element method exhibits di culties whenever the remeshing of the analysis domain must be performed. For such problems utilizing meshless computation methods is very promising. In this paper, a kind of meshless method called the element-free Galerkin method is introduced for electromagnetic eld computation. The mathematical background for the moving le...

The diffuse element method developed by Nayroles et al. is a new way for solving partial differential equations. In this method, only a mesh of nodes and a boundary description is needed to develop the Galerkin equations. The approximating functions are polynomials fitted to the nodal values of each local domain by a weighted least squares approximation. Belytschko et al. developed an alternati...

• Weak formulation: – Involves a typical primal DG formulation for the Laplace equation (see Arnold et al. (2002)). – Adopt the numerical flux proposed by Brezzi et al. (1999). – Second order accurate time discretization is used for the time derivative in the free surface boundary condition (Van der Vegt and Tomar (2005)). • Finite element discretization results in a symmetric and positive defi...

A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into “finite elements”. The satisfaction of the C1 continuity requirements are easily met by EFG since it requires...

We present a discontinuous Galerkin method on a fully unstructured grid for the modeling of unsteady incompressible fluid flows with free surfaces. The surface is modeled by embedding and represented by a levelset. We discuss the discretization of the flow equations and the level set equation as well a various ways of advancing the equations in time using velocity projection techniques. The eff...

The application of a coupled ®nite element± element-free Galerkin (EFG) method to problems in threedimensional fracture is presented. The EFG method is based on moving least square (MLS) approximations and uses only a set of nodal points and a CAD-like description of the body to formulate the discrete model. The EFG method is coupled with the ®nite element method which allows for the use of the...

We consider numerical solutions of second-order elliptic partial di erential equations, such as Laplace's equation, or linear elasticity, in two-dimensional, non-convex domains by the element-free Galerkin method (EFG). This is a meshless method, in which the shape functions are constructed by using weight functions of compact support. For non-convex domains, two approaches to the determination...

Consideration is given to the free drainage of an Oldroyd four-constant liquid from a vertical porous surface. The governing systems of quasilinear partial differential equations are solved by the Fourier-Galerkin spectral method. It is shown that Fourier-Galerkin approximations are convergent with spectral accuracy. An efficient and accurate algorithm based on the Fourier-Galerkin approximatio...