About Localized Boundary- Domain Integro-Differential Formulations for a Quasilinear Problem with Variable Coefficients

  • Sergey E. Mikhailov


Application of the boundary integral equation (BIE) method (boundary element method) to the solution of linear boundary value problems (BVPs) for partial differential equations (PDEs) has been intensively developed over recent decades. Using a fundamental solution of an auxiliary linear PDE, a nonlinear BVP can be reduced to a nonlinear boundary-domain integral or integro-differential equation (BDIE or BDIDE) (see, e.g., [1,2,3]). However, a fundamental solution necessary for the reduction is usually highly nonlocal, which generally leads after discretization to a system of nonlinear algebraic equations with a fully populated matrix. Moreover, the fundamental solution is generally not available if the coefficients of the auxiliary PDE are not constant.


Fundamental Solution Boundary Element Method Nonlinear Algebraic Equation Populated System Local Boundary Integral Equation 
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  1. 1.
    C.A. Brebbia, J.C.F. Telles, and L.C. Wrobel, Boundary Element Techniques, Springer-Verlag, Berlin, 1984.CrossRefMATHGoogle Scholar
  2. 2.
    P.K. Banerjee, Boundary Element Methods in Engineering, McGraw-Hill, London, 1994.Google Scholar
  3. 3.
    X.-W. Gao and T.G. Davies, Boundary Element Programming in Mechanics, Cambridge University Press, Cambridge, 2002.MATHGoogle Scholar
  4. 4.
    S.E. Mikhailov, Localized boundary-domain integral formulations for problems with variable coefficients, Engrg. Anal. with Boundary Elements 26 (2002), 681–690.CrossRefMATHGoogle Scholar
  5. 5.
    T. Zhu, J.-D. Zhang, and S.N. Atluri, A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach, Comput. Mech. 21 (1998), 223–235.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    T. Zhu, J.-D. Zhang, and S.N. Atluri, A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems, Engrg. Anal. with Boundary Elements 23 (1999), 375–389.CrossRefMATHGoogle Scholar

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© Springer Science+Business Media New York 2004

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  • Sergey E. Mikhailov

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