A Numerical Implementation of Fokas Boundary Integral Approach: Laplace’s Equation on a Polygonal Domain
نویسندگان
چکیده
A recently discovered transform approach allows a large class of initial and initialboundary value problems to be solved in terms of contour integrals. We introduce here a spectrally accurate numerical discretization of this approach for the case of Laplace’s equation on a polygonal domain, and compare it against an also spectrally accurate implementation of the traditional boundary integral formulation.
منابع مشابه
A Boundary Meshless Method for Neumann Problem
Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...
متن کاملAn analytical method for linear elliptic PDEs and its numerical implementation
A new numerical method for solving linear elliptic boundary value problems with constant coe4cients in a polygonal domain is introduced. This method produces a generalized Dirichlet–Neumann map: given the derivative of the solution along a direction of an arbitrary angle to the boundary, the derivative of the solution perpendicular to this direction is computed without solving on the interior o...
متن کاملEfficient discretization of Laplace boundary integral equations on polygonal domains
We describe a numerical procedure for the construction of quadrature formulae suitable for the efficient discretization of boundary integral equations over very general curve segments. While the procedure has applications to the solution of boundary value problems on a wide class of complicated domains, we concentrate in this paper on a particularly simple case: the rapid solution of boundary v...
متن کاملNumerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets
In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...
متن کاملRichardson Extrapolation Applied to the Numerical Solution of Boundary Integral Equations for a Laplace’s Equation Dirichlet Problem
Richardson extrapolation is applied to improve the accuracy of the numerical solution of boundary integral equations. The boundary integral equations arise from a direct boundary integral method for solving a Laplace’s equation interior Dirichlet problem. Specifically, the Richardson extrapolation is used to improve the accuracy of collocation. Numerical justification is provided to support the...
متن کامل