Regularized Heaviside and Dirac delta function are used in several fields of\r\ncomputational physics and mechanics. Hence the issue of the quadrature of integrals\r\nof discontinuous and singular functions arises. In order to avoid ad-hoc quadrature\r\nprocedures, regularization of the discontinuous and the singular fields is often carried out.\r\nIn particular, weight functions of the signed distance with respect to the discontinuity\r\ninterface are exploited. Tornberg and Engquist (Journal of Scientific Computing, 2003,\r\n19: 527ââ?¬â??552) proved that the use of compact support weight function is not suitable\r\nbecause it leads to errors that do not vanish for decreasing mesh size. They proposed\r\nthe adoption of non-compact support weight functions. In the present contribution, the\r\nrelationship between the Fourier transform of the weight functions and the accuracy of the\r\nregularization procedure is exploited. The proposed regularized approach was implemented\r\nin the eXtended Finite Element Method. As a three-dimensional example, we study a slender\r\nsolid characterized by an inclined interface across which the displacement is discontinuous.\r\nThe accuracy is evaluated for varying position of the discontinuity interfaces with respect\r\nto the underlying mesh. A procedure for the choice of the regularization parameters\r\nis proposed.
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