We compare the effectiveness of solving Dirichlet–Neumann problems via the Craig–Sulem (CS) expansion, the Ablowitz-Fokas-Musslimani (AFM) implicit formulation, the dual AFM formulation (AFM∗), a boundary integral collocation method (BIM), and the transformed field expansion (TFE) method. The first three methods involve highly ill-conditioned intermediate calculations that we show can be overco...

The boundary initial value problems of elastodynamics are formulated as boundary integral equations. It is shown that these integral equations may be solved by time-stepping numerical methods for the unknown boundary values, A specific numerical scheme is presented for antiplane strain problems and a numerical example is given,

Many boundary integral equations for exterior boundary value problems for the Helmholtz equation suffer from a notorious instability for wave numbers related to interior resonances. The so-called combined field integral equations are not affected. However, if the boundary is not smooth, the traditional combined field integral equations for the exterior Dirichlet problem do not give rise to an L...

This paper deals with a general framework for a posteriori error estimates in boundary element methods which is specified for three examples, namely Symm's integral equation, an integral equation with a hypersingular operator, and a boundary integral equation for a transmission problem. Based on these estimates, an analog of Eriksson and Johnson's adaptive finite element method is proposed for ...

The classical panel method has been extensively used in external aerodynamics to calculate ideal flow fields around moving vehicles or stationary structures in unbounded domains. However, the panel method, as a somewhat simpler implementation of the boundary element method, has rarely been employed to solve problems in closed complex domains. This paper aims at filling this gap and discusses th...

in this paper, shielding effectiveness (se) of a perforated enclosure with imperfectly conducting walls is evaluated. to this end, first, an accurate numerical technique based on method of moments (mom) ispresented. in this method, lossy metallic walls of the enclosure are replaced by equivalent electric surfacecurrent sources. then, the impedance boundary condition on the imperfectly conductin...

Galerkin boundary element methods for the solution of novel first kind Steklov–Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in twoand three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton iterate linear boundary integral equations...

This paper compares the hybrid FEM-BEM and FEM-DBCI methods for the solution of openboundary electrostatic field problems. Both methods couple a differential equation for the interior problem with an integral equation for the exterior one. The comparison shows that FEM-BEM is more accurate than FEM-DBCI but requires more computing time. PACS. 41.20.Cv Electrostatics; Poisson and Laplace equatio...