One particular strength of the boundary element method is that it allows for a high-order pointwise approximation of the solution of the related partial differential equation via the representation formula. However, the high-order convergence and hence accuracy usually suffers from singularities of the Cauchy data. We propose two adaptive mesh-refining algorithms and prove their quasi-optimal c...

A complex variable boundary element method is proposed for solving numerically the axisymmetric steady-state problem of heat conduction in a nonhomogeneous isotropic solid. To assess the validity and the accuracy of the method, it is applied to solve specific cases of the problem. The numerical solutions obtained agree well with known solutions.

Recently, Mastroianni and Monegato derived error estimates for a numerical approach to evaluate the integral ∫ b a ∫ 1 −1 f(x, y) x− y dxdy, where (a, b) ≡ (−1, 1) or (a, b) ≡ (a,−1) or (a, b) ≡ (1, b) and f(x, y) is a smooth function (see G. Mastroianni and G. Monegato, Error estimates in the numerical evaluation of some BEM singular integrals, Math. Comp. 7

The radiation efficiency of an acoustically thick circular cylindrical shell has been examined by calculations using the boundary element method for three different boundary conditions, and by conducting experiments using point excitation with the boundary conditions being free at both ends. Both the numerical and experimental results indicate that the radiation efficiency attains a value of un...

In traditional thinking, when the elastic problems are solved, we need to repeatedly plot element grids and analyze computing results according to diverse precision requirement. Against the malpractice exists in the above process, a new method of error estimation was suggested on H-R adaptive boundary element method in this paper. Based on the discrete meshes that are generated for the process ...

Numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. This study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. The crack tip element and a higher order boundary displacement collocation techn...

finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural introduction to finite element vibration analys...

analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (be/fd) formulation. a semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each highe...