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Domain decomposition in the symmetric boundary element analysis


Recent developments in the symmetric boundary element method (SBEM) have shown a clear superiority of this formulation over the collocation method. Its competitiveness has been tested in comparison to the finite element method (FEM) and is manifested in several engineering problems in which internal boundaries are present, i.e. those in which the body shows a jump in the physical characteristics of the material and in which an appropriate study of the response must be used. When we work in the ambit of the SBE formulation, the body is subdivided into macroelements characterized by some relations which link the interface boundary unknowns to the external actions. These relations, valid for each macroelement and characterized by symmetric matricial operators, are similar in type to those obtainable for the FEM. The assembly of the macroelements based on the equilibrium conditions, or on the compatibility conditions, or on both of these conditions leads to three analysis methods: displacement, force, and mixed-value methods, respectively. The use of the fundamental solutions involves the punctual satisfaction of the compatibility and of the equilibrium inside each macroelement and it causes a stringent elastic response close to the actual solution. Some examples make it possible to perform numerical checks in comparison with solutions obtainable in closed form. These checks show that the numerical solutions are floating ones when the macroelement geometry obtained by subdividing the body changes.