On efficient preconditioners for iterative solution of a Galerkin boundary element equation for the three-dimensional exterior Helmholtz problem

• Published in: Journal of computational and applied mathematics Vol. 156; no. 2; pp. 303 - 318
• Main Authors: Harris, Paul J., Chen, Ke
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.07.2003; Elsevier
• Subjects: Boundary integral equation; Burton–Miller; CGN; Exact sciences and technology; Exterior Helmholtz; Galerkin; GMRES; Hyper-singular operators; Integral equations; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Partial differential equations; Preconditioners; Sciences and techniques of general use; Exterior Helmholtz; Boundary integral equation; GMRES; Hyper-singular operators; Preconditioners; Burton–Miller; CGN; Galerkin; Integral operator; Fast solver; Convergence of numerical methods; Three-dimensional calculations; Fredholm operator; Singular equation; Iterative method; Numerical method; Boundary condition; Partial differential equation; Numerical approximation; Quadrature; Singular integral; Approximation order; Integral; Integral equation; Collocation method; Gradient method; Boundary element method; Conjugate gradient method; Neumann problem; 2001; Helmholtz equation; Algorithm; Green function; Galerkin method; Preconditioning; Singular operator

The paper presents a Galerkin numerical method for solving the hyper-singular boundary integral equations for the exterior Helmholtz problem in three dimensions with a Neumann's boundary condition. Previous work in the topic has often dealt with the collocation method with a piecewise constant...