An integral-collocation-based fictitious-domain technique for solving elliptic problems

Abstract

This paper presents a new fictitious-domain technique for numerically solving elliptic second-order partial-differential equations (PDEs) in complex geometries. The proposed technique is based on the use of integral collocation schemes and Chebyshev polynomials. The boundary conditions on the actual boundary are implemented by means of integration constants. The method works for both Dirichlet and Neumann boundary conditions. Several test problems are considered to verify the technique. Numerical results show that the present method yields spectral accuracy for smooth (analytic) problems.