Domain optimisation using Trefftz functions – application to free boundaries - Bouberbachene, Mohamed; Hochard, Christian; Poitou, Arnaud (Computer Assisted Methods in Engineering and Science, 2023)
Trefftz approximations are known to require very few degrees of freedom to give an order of magnitude of the solution. In this paper, we show that it is possible to take advantage of this situation in two ways: (i) we show that it is also possible to get accurate solutions (especially for the pressure) at a reasonable cost and (ii) we show that the low number of degrees of freedom needed for this accuracy allows an easy domain optimisation, which is illustrated here for the free boundary problem in extrusion. A construction of Trefftz polynomials associated with Stokes problem for plane strains is also given with some recurrence properties which is usefull for computing them at a low cost. Moreover a domain decomposition method which has shown to be efficient for compressible elastic material has been extended here to the case of incompressible linear viscous fluids.