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Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods. (English) Zbl 1272.74623
Summary: This paper deals with numerical experiments related with the shape of the source contour in the application of the method of fundamental solutions to the elastic torsion of prismatic rods. The following five boundary-value problems (BVPs) connected with torsion are studied: L-section, [-section, +-section, $$\rfloor\!\!\lceil$$-section and I-section. For all five BVPs examined, the region of cross-section of rods is concave. Both the local and global errors are examined for two basic shapes of the source contour. In the first case, the source contour is a circle and in the second case the source contour is geometrically similar to the boundary contour of the region under consideration. Furthermore, the optimal radius of the source contour, in the case of the circle, or the optimal distance of the source contour from the boundary in the case it is geometrically similar, are studied. An influence of the method parameters (radius of the circle or distance between contours) on the condition linear system of equation is examined. In all examples examined the values of the local and global errors of the method are smaller when the source contour is geometrically similar to the boundary of the region under consideration in comparison to the source contour with a shape of a circle.

##### MSC:
 74S30 Other numerical methods in solid mechanics (MSC2010) 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
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