Fast simulation of thermoelastic problems using IGA

Thomas Elguedj (INSA-Lyon)

Abstract.
We are interested in introducing a new computational framework to decrease significantly the cost of simulation for time dependent thermal, thermoelastic and thermoelastoplastic problems that arise in particular in the simulation of welding or additive manufacturing.
For that purpose we use Isogeometric Analysis, weighted quadrature and matrix free approaches that have been introduced with other types of problems. We will focus in particular the talk on the introduction of a cheap preconditioned, based on the Fast Diagonalisation method that exploits the tensor product structure of the IGA basis functions. We will show that our preconditioner offers efficiency, cost effectiveness and simplicity in implementation. Furthermore, it exhibits robustness concerning polynomial degree and mesh size parameters.
We will address both transient heat conduction problems with variables coefficient, as well as linear elasticity with some preliminary extensions to elastoplasticity.