One of the main steps of the design process is simulation/analysis. During this stage the designer analyses the CAD model, assesses its limitations and improves it accordingly. Improvements typically involve adjusting design features or changing the material. This simulation is used to ensure that a design meets its mechanical requirements (e.g. stress or thermal analysis, number of cycles of function, safety factor, etc.)

Nowadays, such analysis involves 3 possible methods: the *Finite Difference, Finite Volume* or *Finite Element* methods. Those methods are a direct application *discretization* (the process of transferring models and equations into manageable chunks). Partial differential equations get converted into polynomial sets that converge according to many parameters. They are what are termed as “mesh” methods. Such methods are popular and most certification organisations around the world invariably require an analysis report by FEA (*Finite Element Analysis*).

However, FEA has a major downside: since it relies on the solving of many thousands of equations (depending on the complexity of the shapes studied), it requires a great deal of computing power and can be incredibly slow.

Recently, scientific and engineering communities have researched a new way to conduct analysis by looking into “meshless” (or “*mesh-free*”) methods. This numerical technique does not require body or surface polygonisation. Therefore, no mesh is required to connect multiple nodes, and in fact, not many nodes are needed as in classical mesh methods. Presently, meshless methods are being used to handle problems with large deformation, moving boundaries, and complicated geometry, such as encountered in heat transfer, plastic materials and fluid dynamics.

**Left**: the domain is meshed according to the Finite Elements Method.

**Right**: The adapted mesh created using the meshfree method is not requiring the widespread coverage nor the same number of nodes. The calculation is more adapted to the heat/fluid problems.

There are several meshless methods, the oldest being *Smoothed Particle Hydrodynamics* (SPH) which is used for fluid dynamics simulation. In this method, every node is considered as a dynamic particle with a set of properties and relying on a kernel function to smooth it and compute its properties.

Recently, the use of meshless methods has been extended to the heat conduction field. Dr. Darrell W. Pepper, professor of mechanical engineering (and director of the Nevada Center for Advanced Computational Methods) at the University of Nevada-Las Vegas recounts a project where he and several colleagues spent nearly six months creating an acceptable mesh to solve thermal-hydraulic flow within a nuclear reactor. This contained 600 assemblies, and over 150 million nodes were required to complete the project. Such large problems generally result in extremely demanding computational resources, typically requiring supercomputers:

*“Alternatively, a meshless method is not restricted to dimensional limitations: An infinite domain can be modeled (depending on the number of nodes) and run on a PC. The accuracy achieved, with even a limited number of nodes in a meshless method, compares closely to solutions obtained using massively refined grids. Having the versatility of the ubiquitous finite element method and its use of unstructured meshes (elements), the meshless method is becoming a quick, accurate, and viable alternative to these more popular, conventional numerical approaches.”*

Meshless methods display an array of advantages compared to the classic FEM (Finite Elements Method) methods:

- Significantly reduced costs compared to current, expensive commercial codes for doing complex analysis.
- Computer platform independence—apps will eventually be written that will enable simulations to be run on a table or even smartphone.
- Problem class flexibility—almost any problem that can be described with a set of PDEs (Partial Differential Equations) can be solved using the method.
- Familiarity of the method and use within undergraduate curriculums, and advanced extrapolation to graduate level work. Simple models have been written using MATLAB, MAPLE, MATHEMATICA, and FORTRAN, including C++ and JAVA.

Meshless methods are currently still an experimental phase. At present many algorithms actually end up requiring more computing time than traditional FEM ones.

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