Efficient hypersingular line and surface integrals direct evaluation by complex variable differentiation method

[1]  J. Hadamard,et al.  Lectures on Cauchy's Problem in Linear Partial Differential Equations , 1924 .

[2]  S. G. Mikhlin,et al.  Multidimensional Singular Integrals and Integral Equations , 1965 .

[3]  Barry W. Ninham,et al.  Generalised functions and divergent integrals , 1966 .

[4]  H. R. Kutt On the numerical evaluation of finite-part integrals involving an algebraic singularity , 1975 .

[5]  J. Radok,et al.  Singular Integral Equations: Boundary problems of functions theory and their applications to mathematical physics , 1977 .

[6]  D. F. Paget,et al.  The numerical evaluation of Hadamard finite-part integrals , 1981 .

[7]  D. F. Paget,et al.  A quadrature rule for finite-part integrals , 1981 .

[8]  C. Schneider,et al.  Some new aspects of rational interpolation , 1986 .

[9]  Giovanni Monegato,et al.  On the weights of certain quadratures for the numerical evaluation of Cauchy principal value integrals and their derivatives , 1986 .

[10]  Mauricio Pazini Brandao,et al.  Improper integrals in theoretical aerodynamics - The problem revisited , 1987 .

[11]  Satya N. Atluri,et al.  An effective method for solving the hyper‐singular integral equations in 3‐D acoustics , 1990 .

[12]  Massimo Guiggiani,et al.  A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method , 1990 .

[13]  F. Rizzo,et al.  A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations , 1992 .

[14]  F. J. Rizzo,et al.  A weakly singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems , 1992 .

[15]  Q. Qin,et al.  Nonlinear analysis of reissner plates on an elastic foundation by the BEM , 1993 .

[16]  Q. Qin,et al.  Hybrid Trefftz finite-element approach for plate bending on an elastic foundation , 1994 .

[17]  Giovanni Monegato,et al.  Numerical evaluation of hypersingular integrals , 1994 .

[18]  M. Guiggiani,et al.  Hypersingular formulation for boundary stress evaluation , 1994 .

[19]  M. Guiggiani Hypersingular boundary integral equations have an additional free term , 1995 .

[20]  F. Rizzo,et al.  HYPERSINGULAR INTEGRALS: HOW SMOOTH MUST THE DENSITY BE? , 1996 .

[21]  H. Mittelmann,et al.  Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval , 1997 .

[22]  Qing Hua Qin,et al.  Crack growth prediction of an inclined crack in a half-plane thermopiezoelectric solid , 1997 .

[23]  Graeme Fairweather,et al.  The method of fundamental solutions for elliptic boundary value problems , 1998, Adv. Comput. Math..

[24]  Chung-Yuen Hui,et al.  EVALUATIONS OF HYPERSINGULAR INTEGRALS USING GAUSSIAN QUADRATURE , 1999 .

[25]  Qing Hua Qin,et al.  General solutions for thermopiezoelectrics with various holes under thermal loading , 2000 .

[26]  Vladimir Rokhlin,et al.  Numerical quadratures for singular and hypersingular integrals , 2001 .

[27]  B. Dembart,et al.  Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering , 2002 .

[28]  Xiao-Wei Gao,et al.  The radial integration method for evaluation of domain integrals with boundary-only discretization , 2002 .

[29]  Qing Hua Qin,et al.  BEM for crack-hole problems in thermopiezoelectric materials , 2002 .

[30]  P. Chen,et al.  Internal stresses in inelastic BEM using complex-variable differentiation , 2002 .

[31]  Qing-Hua Qin,et al.  Variational formulations for TFEM of piezoelectricity , 2003 .

[32]  Gennadi Vainikko,et al.  Hypersingular Integral Equations and Their Applications , 2003 .

[33]  Joaquim R. R. A. Martins,et al.  The complex-step derivative approximation , 2003, TOMS.

[34]  Leonard J. Gray,et al.  Direct Evaluation of Hypersingular Galerkin Surface Integrals , 2004, SIAM J. Sci. Comput..

[35]  Lloyd N. Trefethen,et al.  Barycentric Lagrange Interpolation , 2004, SIAM Rev..

[36]  H. Mittelmann,et al.  Recent Developments in Barycentric Rational Interpolation , 2005 .

[37]  Xiao-Wei Gao,et al.  A new inverse analysis approach for multi-region heat conduction BEM using complex-variable-differentiation method * , 2005 .

[38]  Qing Hua Qin,et al.  A meshless model for transient heat conduction in functionally graded materials , 2006 .

[39]  Kai Hormann,et al.  Barycentric rational interpolation with no poles and high rates of approximation , 2007, Numerische Mathematik.

[40]  Michael Carley,et al.  Numerical Quadratures for Singular and Hypersingular Integrals in Boundary Element Methods , 2007, SIAM J. Sci. Comput..

[41]  Qing Hua Qin,et al.  Green's Function and Boundary Elements of Multifield Materials , 2007 .

[42]  Jay I. Frankel Regularization of inverse heat conduction by combination of rate sensor analysis and analytic continuation , 2007 .

[43]  Alok Sutradhar,et al.  Symmetric Galerkin Boundary Element Method , 2008 .

[44]  Giovanni Monegato,et al.  Definitions, properties and applications of finite-part integrals , 2009 .

[45]  Xiao-Wei Gao,et al.  An effective method for numerical evaluation of general 2D and 3D high order singular boundary integrals , 2010 .

[46]  J. Mosig,et al.  Fast and Accurate Computation of Hypersingular Integrals in Galerkin Surface Integral Equation Formulations via the Direct Evaluation Method , 2011, IEEE Transactions on Antennas and Propagation.

[47]  Jean-Paul Berrut,et al.  Recent advances in linear barycentric rational interpolation , 2014, J. Comput. Appl. Math..

[48]  Hui Wang,et al.  Method of fundamental solutions for 3 D elasticity with body forces by coupling compactly supported radial basis functions , 2015 .

[49]  Hui Wang,et al.  Method of fundamental solutions for 3D elasticity with body forces by coupling compactly supported radial basis functions , 2015 .

[50]  Xiao-Wei Gao,et al.  An improved direct method for evaluating hypersingular stress boundary integral equations in BEM , 2015 .

[51]  Q. Qin,et al.  Special n-sided Voronoi fiber/matrix elements for clustering thermal effect in natural-hemp-fiber-filled cement composites , 2016 .

[52]  Q. Qin,et al.  Dual reciprocity boundary element method using compactly supported radial basis functions for 3D linear elasticity with body forces , 2016 .