Enriched Isogeometric Collocation for two-dimensional time-harmonic acoustics

Frequency domain Bernstein-Bézier finite element solver for modelling short waves in elastodynamics

“…They reported superior convergence compared to the partition of unity boundary element method. More recently, Ayala et al [59] studied the performance of the enriched isogeometric collocation method in time-harmonic acoustics. They found improved convergence compared to the isogeometric collocation method.…”

A novel high‐order collocation indirect boundary element method based on the Leis formulation for three‐dimensional high frequency exterior acoustic problems

“…Another increasingly popular approach for acoustic problems is the so‐called “wave‐based method” or “partition‐of‐unity (PU) method” 18–26 . The rationale is to incorporate a priori knowledge regarding the local oscillatory feature of the solution into the numerical method.…”

“…However, the wave‐based FEM or BEM may suffer from ill‐conditioning of the system matrices, especially for the case of large wavenumber, in which a large number of plane wave directions are required to capture the highly oscillatory characteristic of the solutions. In addition, the optimal relation between degree of polynomial shape function, the mesh size and the number of plane‐wave functions is still an open issue 22 …”

“…With the aim to improve accuracy and to alleviate pollution effect, high‐order polynomials based FEMs have been successfully developed in recent years to handle frequency limitation and high‐resolution requirement of low‐order polynomial based methods 22,28–31 . It was reported that high‐order FEM schemes are more effective and accurate in reducing the pollution error than low‐order ones 22,28–31 .…”

“…7 Another increasingly popular approach for acoustic problems is the so-called "wave-based method" or "partition-of-unity (PU) method". [18][19][20][21][22][23][24][25][26] The rationale is to incorporate a priori knowledge regarding the local oscillatory feature of the solution into the numerical method. For acoustic problems, this is generally achieved by injecting plane waves or Bessel functions into the element approximate solutions.…”