Evaluation of nearly singular integrals in isogeometric boundary element method

Coupling Heat Conduction and Radiation by an Isogeometric Boundary Element Method in 2-D Structures

“…Ax + B T 4 􏼐 􏼑 � y, (26) where x in Equation ( 26) is the unknown temperature and the column vector composed of the heat flux of the boundary node and the internal point; y is the column vector obtained by multiplying all the known boundary quantities by the corresponding coefficients in Equation ( 26), and the column element corresponding to the boundary node with available temperature in matrix B is 0. en, we give three kinds of boundary conditions, namely, temperature boundary condition, heat flow boundary conditions, and hybrid boundary conditions, as shown in the respective equations:…”

“…Mondal and Mishra [22] combined the Boltzmann method with the finite volume method to deal with the coupled heat transfer and radiation with heat flow and temperature boundary conditions. Gu et al [23][24][25][26][27][28][29][30] studied the heat transfer of coating structure based on the isogeometric boundary element method, and they also used the isogeometric boundary element method by calculating the effective property of steady-state thermal conduction in 2D heterogeneities with a homogeneous interphase. Fu et al [31][32][33] studied the boundary collocation method for anomalous heat conduction analysis in functionally graded materials.…”

An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources

“…In recent years, with the development of IGABEM as a preferred approach, some integration schemes for nearly singular integrals in IGABEM have emerged. Gong et al [65] illustrate the necessity of evaluating the near singular integral in IGABEM, and use the exponential transformation method to remove or weaken the near singularities in potential problems. In [66], the nearly singular integrals are computed by sinh-transformation method.…”

Hybrid nearly singular integration for isogeometric boundary element analysis of coatings and other thin 2D structures

“…Similar to the sinh transformation method, an exponential transformation method has been widely used to cope with nearly singular integrals for the conventional BEM [68,[71][72][73]. In [74], the exponential transformation method was applied to deal with the nearly singular integrals arising in IGABEM. The interested reader is directed to the works [68,74] for a full description of the method.…”

“…In [74], the exponential transformation method was applied to deal with the nearly singular integrals arising in IGABEM. The interested reader is directed to the works [68,74] for a full description of the method.…”