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Background to Trefftz and the Workshops

The original method presented by Erich Trefftz in 1926, titled Ein Gegenstuck zum Ritzschen Verfahren*, was driven by the desire to derive both upper and lower bounds to the global errors inherent in approximate solutions. Thus Trefftz exploited trial approximating functions with the distinctive property that they satisfied exactly the governing differential equations of the continuum within the domain or subdomains defining a problem, but they did not need to satisfy a priori the boundary conditions. The combination of such functions was determined so as to best satisfy the boundary conditions in an approximate sense. The method is thus an alternative to the more familiar Ritz method, and has given rise to alternative formulations of finite element and other methodologies in computational mechanics. Two international workshops have been held devoted to modern developments and applications of Trefftz concepts in computational mechanics; the first was held in Cracow in 1996 to coincide with the 70th anniversary of the seminal paper by Trefftz, and the second was held in 1999 in Sintra, Portugal. The latter was dedicated to Professor J.Jirousek who is a renowned proponent of the Trefftz method in finite element formulations as implemented in the SAFE software developed at EPFL Lausanne. The success of these workshops led to the decision to organise them on a three year cycle, and to widen their scope to include Trefftz-related methodologies in novel formulations and applications where high-performance is the goal.

* Translated as "A counterpart to Ritz's Method" by CADFEM.

 

Copyright 2001.
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