Interrelated fundamental solutions for various heterogeneous potential, wave and advective-diffusive problems

• Published in: Engineering analysis with boundary elements Vol. 16; no. 1; pp. 29 - 33
• Main Authors: Shaw, Richard Paul, Steven Gipson, G.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1995; Elsevier
• Subjects: boundary element method; Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); fundamental solutions; Heterogeneous media; Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Heterogeneous media; fundamental solutions; boundary element method; Scattering; Fluid-structure interactions; Boundary integral method; Two dimensional model; Numerical method; Green function; Axial symmetry; Advection; Heterogeneous wave; Integral equations; Differential equations; Inhomogeneous materials; Boundary element method
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/0955-7997(95)00056-9

The Green's fundamental solutions for several second order elliptic partial differential equations governing various physical processes are found to be interrelated. These solutions are required for boundary integral equation formulations. Thus a solution for one such process is essentially a solution for several others. This is particularly useful for heterogeneous media where the catalog of existing fundamental solutions is meager. After a discussion of these relationships, a new class of two dimensional fundamental solutions involving axisymmetric material variations is given.