• Sascha Eisentraeger, University of New South Wales Sydney
  • Hauke Gravenkamp
  • Ean Tat Ooi
  • Sundararajan Natarajan
  • Carolin Birk

Numerical methods are indispensable tools in modern engineering, facilitating the planning and design process of resilient and economical structures. A special class among the wide variety of approaches available in Computational Mechanics are semi-analytical methods. Examples of typical semi-analytical techniques include: Scaled Boundary Finite Element Method (SBFEM), the Thin Layer Method (TLM), Semi-Analytical Finite Elements (SAFE), Wave Finite Elements (WFE), Trefftz Methods, etc. In general, a dimension reduction is achieved by employing an analytical expansion in one spatial direction of the problem. Consequently, such methods are very competitive compared with standard Finite Element Methods (FEM) for several different applications, including, but not limited to, fracture mechanics, dynamic soil-structure interaction, guided wave propagation, and exterior acoustics.

Although being initially developed for niche applications, e.g., the solution of soil-structure interaction problems in unbounded domains, the SBFEM has matured into a general computational tool for solving boundary value problems for different physical phenomena, highlighting the versatility of semi-analytical approaches. A salient feature of SBFEM compared to the standard FEM is its ability to construct polytope elements of an arbitrary number of faces and edges, which reduces human intervention and computing resources during pre-processing. This possibility makes the SBFEM especially attractive for problems requiring adaptive/local mesh-refinement strategies.

The salient features of semi-analytical methods have also motivated the development of coupled approaches with FEM, Mesh-free and Boundary Element Methods, or Isogeometric Analysis (IGA), to name just a few. These hybrid approaches inherit the advantages of both methodologies and exhibit beneficial features of their own.

This mini-symposium aims to provide a forum to facilitate knowledge exchange and transfer among researchers and engineers on new developments and novel applications of semi-analytical methods. We invite contributions on recent research into the theory, development, and application of these methods.

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