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This paper marks the debut of a Galerkin isogeometric method for solving aFredholm integral eigenvalue problem, enabling random field discretization bymeans of the Karhunen-Loeve expansion. The method involves a Galerkinprojection onto a finite-dimensional subspace of a Hilbert space, basis splines(B-splines) and non-uniform rational B-splines (NURBS) spanning the subspace,and standard methods of eigensolutions. Compared with the existing Galerkinmethods, such as the finite-element and mesh-free methods, the NURBS-basedisogeometric method upholds exact geometrical representation of the physical orcomputational domain and exploits regularity of basis functions deliveringglobally smooth eigensolutions. Therefore, the introduction of the isogeometricmethod for random field discretization is not only new; it also offers a fewcomputational advantages over existing methods. In the big picture, the use ofNURBS for random field discretization enriches the isogeometric paradigm. As aresult, an uncertainty quantification pipeline of the future can be envisionedwhere geometric modeling, stress analysis, and stochastic simulation are allintegrated using the same building blocks of NURBS. Three numerical examples,including a three-dimensional random field discretization problem, illustratethe accuracy and convergence properties of the isogeometric method forobtaining eigensolutions.

A Galerkin Isogeometric Method for Karhunen-Loeve Approximation of Random Fields