Comparison of iterative solvers in isogeometric boundary element formulation for heat transfer problems with non-linear boundary conditions

Abstract

Boundary element method is a widely used numerical technique to solve partial differential equations (PDEs). Although the solution of linear PDEs with linear boundary conditions is straightforward, the presence of non-linearities requires additional steps which is the case for many heat transfer problems. In this study, a basis for heat transfer problems with non-linear boundary conditions is constructed by employing the isogeometric boundary element method, which leverages parametric functions used for geometry modeling to represent the field variables. The heat transfer problem with radiative and convective boundary conditions is solved with a non-linear solver in which different linear solvers are utilized. The performances of direct and iterative solvers are assessed. Preconditioners are employed to increase the convergence rate of iterative solvers. The accuracy of the proposed method is assessed by comparing the results with the analytical solution and the performance of each solver is determined by the elapsed time required for the convergence.