Mesh free parallel implementations using multi-core processors are discussed. Particularly, parallelization of the MLPG and SPEM are shown. The appropriate strategies to correctly parallelize the mesh free methods are discussed. Parallel versions run up to 1.96 times faster on dual-core processor and 3.78 on quad-core processor when compared to the sequential one.

Keywords: Meshless method Coupled radiative–conductive transfer Discrete ordinates Even parity Complex geometries a b s t r a c t A meshless method DAM is employed to solve the coupled radiative and conductive heat transfer problem in a semi-transparent medium enclosed in complex 2D and 3D geome-tries. The meshless method for radiative transfer is based on the even parity formulation of the dis...

A graph G = (V, E) is called a pairwise compatibility graph (PCG) if there exists a tree T , a positive edge-weight function w on T , and two non-negative real numbers dmin and dmax, dmin ≤ dmax, such that V coincides with the set of leaves of T , and there is an edge (u, v) ∈ E if and only if dmin ≤ dT,w(u, v) ≤ dmax where dT,w(u, v) is the sum of the weights of the edges on the unique path fr...

This paper presents new developments in meshless local Petrov–Galerkin with Rankine source (MLPG_R) particle based method for studying interaction of waves fixed structures a numerical wave-tank. A 3D formulation the Lagrangian flow problem incompressible fluid optimised solution strategy is presented. The pressure Poisson equation solved weak-form integration done semi-analytically using symme...

A general theory is given for discretized versions of the Galerkin method for solving Fredholm integral equations of the second kind. The discretized Galerkin method is obtained from using numerical integration to evaluate the integrals occurring in the Galerkin method. The theoretical framework that is given parallels that of the regular Galerkin method, including the error analysis of the sup...

The most recent update of financial option models is American options under stochastic volatility models with jumps in returns (SVJ) and stochastic volatility models with jumps in returns and volatility (SVCJ). To evaluate these options, mesh-based methods are applied in a number of papers but it is well-known that these methods depend strongly on the mesh properties which is the major disadvan...