Lagrangian codes with mesh moving with the fluid suffer in many cases by mesh distortion leading to tangled mesh which in principle stops the computation as basic assumptions of the numerical method as e.g. positive volume of cells are not valid any more. Arbitrary LagrangianEulerian (ALE) method overcomes this difficulty by untangling or smoothing the mesh and conservative remapping of conserv...

In this paper, static and free vibrations behaviors of the orthotropic functionally graded material (FGM) plates resting on the two-parameter elastic foundation are analyzed by the a mesh-free method based on the first order shear deformation plate theory (FSDT). The mesh-free method is based on moving least squares (MLS) shape functions and essential boundary conditions are imposed by transfer...

In this paper, the effects of carbon nanotube (CNT) orientation and aggregation on the static behavior of functionally graded nanocomposite cylinders reinforced by CNTs are investigated based on a mesh-free method. The used nanocomposites are made of the straight CNTs that are embedded in an isotropic polymer as matrix. The straight CNTs are oriented, randomly or aligned or local aggregated int...

Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...

It is well accepted that the efficient solution of complex partial differential equations (PDEs) often requires methods which are adaptive in both space and time. In this paper we are interested in a class of spatially adaptive moving mesh (r-refinement) methods introduced in [9, 10, 12]. Our purpose is to introduce and explore a natural coupling of domain decomposition, Schwarz waveform relaxa...

We propose algorithms to incrementally modify a mesh of a planar domain by interactively inserting and removing elements (points, segments, polygonal lines, etc.) into or from the planar domain, keeping the quality of the mesh during the process. Our algorithms, that combine mesh improvement techniques, achieve quality by deleting, moving or inserting Steiner points from or into the mesh. The c...

Numerical solvers using adaptive meshes can focus computational power on important regions of a model domain capturing or unresolved physics. The adaptation be informed by the state, external information, made to depend In this latter case, one think mesh configuration {\it as part state}. If observational data is assimilated into model, question updating with physical values arises. Adaptive p...