Nonlinear Equations case study

Nonlinear Equations case study - AMSC/CMSC 660 Scientific...

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AMSC/CMSC 660 Scientific Computing I Fall 2006 UNIT 4: Nonlinear Systems and the Homotopy Method Part 2 Dianne P. O’Leary c 2002,2004,2006 Case study: Octahedral variable geometry truss Note: This case study concerns solving a system of polynomial equations. As you know , we should be using a special purpose homotopy method for solving this, but just to illustrate the tools we have, we’ll use a general purpose method. Reference : This problem is taken from Layne T. Watson, “Probability-one homotopies in computational science,” J. of Computational and Applied Mathematics 140 (2002) 785-807. The problem Imagine that we have attached 3 trusses together to form a triangle ABC . This will be the base of a platform. Now take 3 more trusses and form a triangle ¯ A ¯ B ¯ C from them. But assume that these trusses have variable length . This will be the top of the platform. We will use 6 more trusses to attach the top to the bottom. Vertex A will be attached to ¯ A and ¯ C .
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