Abstract
The boundary integral methods form one group of methods for solving differential equations. The boundary element method (BEM) is the basic method of this group. However, it requires the boundary mesh of elements and the evaluation of improper singular integrals, that arise due to fundamental solution singularity. Therefore, boundary meshless methods have recently have come into focus to remove these shortcomings. One of the most promising boundary collocation numerical schemes is the singular boundary method (SBM). To tackle the singularity of the fundamental solution, this method adopts the concept of original intensity factors (OIFs). The application of the proposed SBM scheme to groundwater flow in the cofferdam structure is presented and compared to the finite element method (FEM) solution.
Highlights
The boundary element method (BEM) is one of those modern numerical methods whose applications can be found in all the technical disciplines as well as in the natural sciences
In the singular boundary method (SBM) the main diagonal members of the characteristic matrix are evaluated using the concept of origin intensity factors (OIF) [5]
The OIF for the Neumann boundary condition is usually solved using the subtracting and adding-back regularization [7] but the OIF for Dirichlet boundary conditions is the weak point of the SBM
Summary
The boundary element method (BEM) is one of those modern numerical methods whose applications can be found in all the technical disciplines as well as in the natural sciences. BEM represents the family of the methods based on the boundary integral theory [1]. The BEM is an imposing method from the mathematical point of view and time-consuming for numerical integration. The method of fundamental solutions (MFS) [2,3,4] overcomes singularities of BEM using a fictitious boundary but the optimum location of this boundary remains the open problem especially for the complex-shaped domains. To avoid the fictitious boundary of MFS, Chen [5, 6] proposed a new numerical method called a singular boundary method (SBM). Have been developed to determine these OIFs, namely, inverse interpolation technique (IIT), empirical approaches [7] based mainly on the fundamental solution integrals mean value [4]. The accuracy and efficiency of this method are verified in the numerical experiment of steady-state groundwater flow in cofferdam
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