Isogeometric boundary element for analyzing steady-state heat conduction problems under spatially varying conductivity and internal heat source

Isogeometric and NURBS-enhanced boundary element formulations for steady-state heat conduction with volumetric heat source and nonlinear boundary conditions

“…Volumetric heat generation is defined on a region 𝛺 𝐺 with boundary 𝛤 𝐺 . The boundary of this domain can be expressed using NURBS basis functions, and following RIM [30][31][32][33][34] with proper coordinate transformations from physical to parameter and from parameter to parent spaces, the domain integral on the right-hand side of Eq. (2.4) can be written as:…”

“…Alternatively, the domain integrals can be transformed into boundary integrals through a set of interpolation functions and particular solutions. Several different techniques have been proposed to transform domain integrals into boundary integrals such as dual reciprocity method [25,26], multiple reciprocity method [27], triple reciprocity method [28,29] and radial integration method (RIM) [30][31][32][33][34]. Among these, RIM has distinct advantages of transforming complicated domain integrals without using particular solution and removing various singularities in the domain integrals.…”

“…Among these, RIM has distinct advantages of transforming complicated domain integrals without using particular solution and removing various singularities in the domain integrals. RIM has been successfully applied to heat conduction problems with spatially varying [33,35,36] and temperature dependent thermal conductivity [37,38], and heat conduction problems with heat generation [33,34,36]. Moreover, RIM has been also combined with precise integration method to solve transient heat conduction problems including spatially varying thermal conductivity and heat source [39].…”