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Numerics of boundary-domain integral and integro-differential equations for BVP with variable coefficient in 3D

Abstract

A numerical implementation of the direct boundary-domain integral and integro-differential equations, BDIDEs for treatment of the Dirichlet problem for a scalar elliptic PDE with variable coefficient in a three-dimensional domain is discussed. The mesh-based discretisation of the BDIEs with tetrahedron domain elements in conjunction with collocation method leads to a system of linear algebraic equations (discretised BDIE). The involved fully populated matrices are approximated by means of the H-Matrix/adaptive cross approximation technique. Convergence of the method is investigated.

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Correspondence to Richards Grzhibovskis.

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Grzhibovskis, R., Mikhailov, S. & Rjasanow, S. Numerics of boundary-domain integral and integro-differential equations for BVP with variable coefficient in 3D. Comput Mech 51, 495–503 (2013). https://doi.org/10.1007/s00466-012-0777-8

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Keywords

  • Elliptic PDE
  • Variable coefficients
  • Boundary-domain integral equation
  • H-matrices