An integral‐collocation‐based fictitious‐domain technique for solving elliptic problems
Copyright policy )An integral‐collocation‐based fictitious‐domain technique for solving elliptic problems
AbstractThis 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. Copyright © 2007 John Wiley & Sons, Ltd.
- University of Sydney Australia
- University of Southern Queensland Australia
Boundary value problems for second-order elliptic equations, point collocation techniques, fictitious domains, Spectral, collocation and related methods for boundary value problems involving PDEs, numerical results, integrated Chebyshev polynomials, elliptic problems
Boundary value problems for second-order elliptic equations, point collocation techniques, fictitious domains, Spectral, collocation and related methods for boundary value problems involving PDEs, numerical results, integrated Chebyshev polynomials, elliptic problems
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