SIAM Journal on Numerical Analysis
Coupling of fast multipole method and microlocal discretization for the 3-D Helmholtz equation
Journal of Computational Physics
Computational aspects of the ultra-weak variational formulation
Journal of Computational Physics
Journal of Computational and Applied Mathematics
An ultra-weak method for acoustic fluid-solid interaction
Journal of Computational and Applied Mathematics
An integration scheme for electromagnetic scattering using plane wave edge elements
Advances in Engineering Software
Advances in Engineering Software
Hybrid quadrilateral finite element models for axial symmetric Helmholtz problem
Finite Elements in Analysis and Design
Journal of Computational Physics
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The Partition of Unity Finite Element Method is used to solve wave scattering problems governed by the Helmholtz equation, involving one or more scatterers, in two dimensions. The method allows us to relax the traditional requirement of around ten nodal points per wavelength used in the Finite Element Method. Therefore the elements are multi-wavelength sized and the mesh of the computational domain may be kept unchanged for increasing wave numbers. As a result, the total number of degrees of freedom is drastically reduced. In this work, various numerical aspects affecting the efficiency of the method are investigated by considering an interior Helmhlotz problem. Those include the plane wave enrichment, the h-refinement, the geometry description, and the conjugated or unconjugated type of formulation. The method is then used to solve problems involving multiple scatterers. Last, an exterior scattering problem by a non-smooth rigid body is presented.