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Coupled Systems Mechanics
  Volume 7, Number 6, December 2018 , pages 755-774

The Iterated Ritz Method: Basis, implementation and further development
Josip Dvornik, Damir Lazarevic, Mario Uros and Marta Savor Novak

    The Ritz method is known as very successful strategy for discretizing continuous problems, but it has never been used for solving systems of algebraic equations. The Iterated Ritz Method (IRM) is a novel iterative solver based on the discretized Ritz procedure applied at each iteration step. With an appropriate choice of coordinate vectors, the method may be efficient in linear, nonlinear and optimization problems. Additionally, some iterative methods can be explained as special cases of this approach, which helps to understand advantages and limitations of these methods and gives motivation for their improvement in sense of IRM. In this paper, some ideas for generation of efficient coordinate vectors are presented. The algorithm was developed and tested independently and then implemented into the open source program FEAP. Method has been successfully applied to displacement based (even ill-conditioned) models of structural engineering practice. With this original approach, a new iterative solution strategy has been opened.
Key Words
    iterative methods; conjugate gradients; successive over-relaxation; preconditioning; Iterated Ritz Method
Josip Dvornik, Damir Lazarevic, Mario Uros and Marta Savor Novak: Department for Engineering Mechanics, Faculty of Civil Engineering, University of Zagreb, Kaciceva 26, 10 000 Zagreb, Croatia

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