New variable transformations for evaluating nearly singular integrals in 2D boundary element method

A general algorithm for evaluating nearly singular integrals in anisotropic three-dimensional boundary element analysis

“…Substituting transformations (23) and (24) and the distance function (27) into the integral (22) yields…”

“…Apart from pure analytical integration, which has obvious limitations (low order elements), many other methods have been devised. The methods developed so far include, but are not limited to, element subdivision methods [15][16][17], semi-analytical methods [6,18,19] and various nonlinear transformations [20][21][22][23][24][25][26][27]. The element subdivision method is appealing, stable, and accurate but is costly because the number of sub-elements and their sizes are strongly dependent on the order of the near singularity and the dimension of the element.…”

A general algorithm for the numerical evaluation of domain integrals in 3D boundary element method for transient heat conduction

“…However, much literature focus on the nearly singular integrals [15][16][17][18][19][20] and singular integrals [21][22][23][24][25][26][27], and little literature refer to these pseudo-singular domain integrals. Gao [28,29] proposed the radial integration method which converted the domain integrals into equivalent boundary integrals.…”

Calculation of three-dimensional nearly singular boundary element integrals for steady-state heat conduction

“…Effective computation of nearly singular integrals has received intensive attention in recent years. Various numerical techniques have been developed to remove the near singularities, such as nonlinear transformations [19], Taylor series expansion algorithm [22], global regularization [6,23], optimization transformation [24], semi-analytical or analytical integral formulas [25][26][27][28][29], the sinh transformation [30][31][32][33][34], polynomial transformation [35], adaptive subdivision method [7,36], distance transformation technique [21,[38][39][40], the PART method [41][42][43], and the exponential transformation [44][45][46]. Most of them benefit from the strategies for computing singular integrals [6,22,23].…”