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A new technique for boundary element analysis of potential problems using a multipole expansion to obtain the solution quickly only in a target region has been developed. The capability of the present technique was verified by numerical simulations. In this technique, the multipole expansion is applied to boundary integral equations on nontarget boundaries where source points are allocated on target boundary. Those equations are expanded by multipole moments and the expansion is truncated at the term where the error bound of the higher terms is guaranteed. This technique decreases the calculation amount by introducing multipole moments as the unknown in place of the unknown in the non-target region. Boundary integral equations of the same number of multipole moments on non-target boundaries where source points are allocated on near non-target boundary are formulated. The fluxes of boundary integral equations on non-target boundaries are approximated by multipole moments using generalized inverse matrix. To demonstrate the effectiveness of the method, some example analyses were performed. When the solutions only in the target region are needed, especially in large size boundary value problems, this technique enables us to obtain them quickly and precisely.

nihon kikai gakkai ronbunshū. a

Efficient Boundary Element Method by Multipole Expansion and Generalized Inverse Matrix for Analysing Target Region : Applied for Two-Dementional Elastostatic Problems