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The inclusion of domain (point) sources into a three dimensional boundary element method while solving the Helmholtz equation is described. The method is fully desingularized which allows for the use of higher order quadratic elements on the surfaces of the problem with ease. The effect of the monopole sources ends up on the right hand side of the resulting matrix system. Several carefully chosen examples are shown, such as sources near and within a concentric spherical core-shell scatterer as a verification case, a curved focusing surface and a multi-scale acoustic lens.
This paper presents a steady-state and transient heat conduction analysis framework using the polygonal scaled boundary finite element method (PSBFEM) with polygon/quadtree meshes. The PSBFEM is implemented with commercial finite element code Abaqus
This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions which hold fo
In this work we present an adaptive boundary element method for computing the electromagnetic response of wave interactions in hyperbolic metamaterials. One unique feature of hyperbolic metamaterial is the strongly directional wave in its propagating
This paper constructs and analyzes a boundary correction finite element method for the Stokes problem based on the Scott-Vogelius pair on Clough-Tocher splits. The velocity space consists of continuous piecewise quadratic polynomials, and the pressur
In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivariational inequality boundary problems. Constructing so-called boundary