NUMERICAL METHODS FOR INTEGRAL EQUATIONS
Learning outcomes of the course unit
Introduction to modern techniques for the approximate solution of real problems modelled by boundary integral equations.
Knowledge of the fundamental notions of Numerical Analysis and of the classical approximation techniques for differential boundary value problems.
Course contents summary
Integral formulation of elliptic boundary value problems. Boundary integral operators with weakly singular, singular and hyper-singular kernels.
Approximation techniques:collocation boundary element method and Galerkin boundary element method (BEM). h-, p-, and h-p techniques.
Quadrature formulas for weakly singular integrals, Cauchy principal value integrals and Hadamard finite parts integrals. Convergence results. Algebraic reformulation of Galerkin problem. Numerical schemes for the generation of Galerkin linear system.
Introduction to Fortran programming language for scientific computation. Fortran numerical libraries: NAG, IMSL.
Development of a project of applicative interest to be fixed with students.
W. Mc Lean, Strongly Elliptic Systems and Boundary
Integral Equations, Cambridge University Press, 2000.
G. Chen, J. Zhou, Boundary Element Methods, Academic