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The particle finite element method (PFEM) is a powerful and robust numerical tool for the simulation of multi-physics problems in evolving domains. The PFEM exploits the Lagrangian framework to automatically identify and follow interfaces between different materials (e.g. fluid–fluid, fluid–solid or free surfaces). The method solves the governing equations with the standard finite element method and overcomes mesh distortion issues using a fast and efficient remeshing procedure. The flexibility and robustness of the method together with its capability for dealing with large topological variations of the computational domains, explain its success for solving a wide range of industrial and engineering problems. This paper provides an extended overview of the theory and applications of the method, giving the tools required to understand the PFEM from its basic ideas to the more advanced applications. Moreover, this work aims to confirm the flexibility and robustness of the PFEM for a broad range of engineering applications. Furthermore, presenting the advantages and disadvantages of the method, this overview can be the starting point for improvements of PFEM technology and for widening its application fields.

SUMMARYA Lagrangian finite element method for the analysis of incompressible Newtonian fluid flows, based on a continuous re-triangulation of the domain in the spirit of the so-called Particle Finite Element Method, is here revisited and applied to the analysis of the fluid phase in fluid-structure interaction problems. A new approach for the tracking of the interfaces between fluids and structures is proposed. Special attention is devoted to the mass conservation problem. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation fluid-structure interaction problems with evolving free surfaces and breaking waves. The method is validated against the available analytical and numerical benchmarks.

In this paper, we analyze possible sources of dissipation in aluminium nitride (AlN) contour mode resonators for three different resonance frequency devices (f r ) (220 MHz, 370 MHz, and 1.05 GHz). For this purpose, anchors of different widths (W a ) and lengths (L a ) proportional to the acoustic wavelength (λ) are designed as supports for resonators in which the dimensions of the vibrating body are kept fixed. The Q extracted experimentally confirms that anchor losses are the dominant source of damping for most anchor designs when f r is equal to 220 and 370 MHz. For specific anchor dimensions (W a /λ is in the range of 1/4-1/2) that mitigate energy leakage through the supports, a temperature-dependent dissipation mechanism dominates as seen in higher f r resonators operating close to 1.05 GHz. To describe the Q due to anchor losses, we use a finite-element method with absorbing boundary conditions. We also propose a simple analytical formulation for describing the dependence of the temperature-dependent damping mechanism on frequency. In this way, we are able to quantitatively predict Q due to anchor losses and qualitatively describe the trends observed experimentally.[ 2014-0232]Index Terms-AlN contour mode resonators, quality factor, anchor losses, temperature dependent dissipation, finite element analysis, perfectly matched layer. 1057-7157

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