A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. Furthermore, the method proposed also shares several of the advantages of the Finite Element Method such as: (a) the simplicity of the shape functi...

Meshfree analysis methods, on a per degree of freedom basis, are typically more computationally expensive and yet more accurate than finite element methods. For very large models, whether meshfree or finite element, the memory and computational effort associated with direct equation solvers makes them prohibitively expensive. In this work, the performance of different linear equation solvers wi...

This paper is concerned with the treatment of essential boundary conditions in meshfree methods. In particular we focus on the particle–partition of unity method (PPUM). However, the proposed technique is applicable to any partition of unnity based approach. We present an efficient scheme for the automatic construction of a direct splitting of a PPUM function space into the degrees of freedom s...

An element-free Galerkin method (EFGM) is proposed to simulate the propagation of myocardial electrical activation without explicit mesh constraints using a monodomain model. In our framework the geometry of myocardium is first defined by a meshfree particle representation that is, a sufficient number of sample nodes without explicit connectivities are placed in and inside the surface of myocar...

The boundary knot method is a recent truly meshfree boundary-type radial basis function (RBF) collocation scheme, where the nonsingular general solution is used instead of the singular fundamental solution to evaluate the homogeneous solution, while the dual reciprocity method is employed to the approximation of particular solution. Despite the fact that there are not nonsingular RBF general so...

In this paper we describe and compare preconditioners for saddle-point systems obtained from meshfree discretizations, using the concepts of hierarchical (or H )matrices. Previous work by the authors using this approach did not use H -matrix techniques throughout, as is done here. Comparison shows the method described here to be better than the author’s previous method, an AMG method adapted to...

We develop and analyze a meshfree discretization method for Darcy’s problem. Our approximation scheme is based upon optimal recovery which leads to a collocation scheme using divergence-free positive definite kernels. Besides producing analytically incompressible flow fields, our method can be of arbitrary order, works in arbitrary space dimension and for arbitrary geometries. After deriving th...