Localized boundary-domain integral formulations for problems with variable coefficients

• Published in: Engineering analysis with boundary elements Vol. 26; no. 8; pp. 681 - 690
• Main Author: Mikhailov, S.E.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.09.2002; Elsevier
• Subjects: Boundary element method; Boundary-domain integral equation; Boundary-domain integro-differential equation; Boundary-integral methods; Computational techniques; Domain decomposition; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Localization; Mathematical methods in physics; Mesh-based algorithm; Meshless algorithm; Parametrix; Physics; Boundary-domain integro-differential equation; Mesh-based algorithm; 35C15; Boundary-domain integral equation; 35J25; Parametrix; 65N; 35Q; Meshless algorithm; 45A05; Localization; Domain decomposition; Boundary element method; Integro-differential equations; Boundary integral method; Boundary-value problems; Numerical method; Meshless method
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/S0955-7997(02)00030-9

Specially constructed localized parametrixes are used in this paper instead of a fundamental solution to reduce a boundary value problem with variable coefficients to a localized boundary-domain integral or integro-differential equation (LBDIE or LBDIDE). After discretization, this results in a sparsely populated system of linear algebraic equations, which can be solved by well-known efficient methods. This make the method competitive with the finite element method for such problems. Some methods of the parametrix localization are discussed and the corresponding LBDIEs and LBDIDEs are introduced. Both mesh-based and meshless algorithms for the localized equations discretization are described.