A new method called Boundary Integral-based Domain Decomposition is proposed for the fast solution of the Laplace equation on regular and irregular regions. The idea of the method is to adopt the domain decomposition approach by partitioning into subdomains and use an integral equation formulation to compute the interface values. The method provides a particularly eecient algorithm for parallel...

In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...

In this paper, a hybrid approach for solving the Laplace equation in general threedimensional (3-D) domains is presented. The approach is based on a local method for the Dirichletto-Neumann (DtN) mapping of a Laplace equation by combining a deterministic (local) boundary integral equation (BIE) method and the probabilistic Feynman–Kac formula for solutions of elliptic partial differential equat...

We consider the numerical solution for the Helmholtz equation in R with mixed boundary conditions. The solvability of this mixed boundary value problem is established by the boundary integral equation method. Based on the Green formula, we express the solution in terms of the boundary data. The key to the numerical realization of this method is the computation of weakly singular integrals. Nume...

Abstrac-Based on a variational principle, a new approach to derive the exact boundary equation for the analysis of nonlinear Reissner plates and a related existing criterion for the solution of the boundary integral equation is presented in this paper. In this procedure, the boundary and the domain of the plate are discredited to solve the nonlinear problems. All unknown variables are at the bo...

In this paper we consider the (2D and 3D) exterior problem for the non homogeneous wave equation, with a Dirichlet boundary condition and non homogeneous initial conditions. First we derive two alternative boundary integral equation formulations to solve the problem. Then we propose a numerical approach for the computation of the extra “volume” integrals generated by the initial data. Finally, ...

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

Boundary integral methods for the solution of boundary value PDEs are an alternative to ‘interior’ methods, such as finite difference and finite element methods. They are attractive on domains with corners, particularly when the solution has singularities at these corners. In these cases, interior methods can become excessively expensive, as they require a finely discretised 2D mesh in the vici...