Modified Potentials as a Tool for Computing Green's Functions in Continuum Mechanics
Yu.A. Melnikov and M.Yu. Melnikov

doi:10.3970/cmes.2001.002.291
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 2, No. 2, pp. 291-306, 2001
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Abstract The use of potential (integral) representations is studied when computing Green's functions for boundary value problems stated for Laplace and biharmonic equations over regions of complex configuration in two dimensions. The emphasis is on the non-traditional potentials, whose observation and source points occupy different sets. Such potentials reduce the original boundary value problems to functional (integral) equations with smooth kernels. Special integral representations are studied, the ones whose kernels are built not of the fundamental solutions of governing differential equations but of the Green's functions for simply shaped regions, which are associated with boundary value problems under consideration. Such integral representations are called here the {\it modified potentials}, to the contrary of the standard potentials that are referred to as the {\it classical potentials}. Computability of different existing forms of Green's functions is discussed. Computational experiments have been conducted to analyze the relative effectiveness of both types of potentials when solving test problems.
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