Numerical inverse isoparametric mapping in remeshing and nodal quantity contouring

Abstract In finite element analysis, isoparametric mapping defined as [( ξ , η ) → ( x , y ): x = N i ξ i ] is widely used. It is a one-to-one mapping and its construction is especially elegant for elements of a variable number of nodes showing its versatile applicability to model curved boundaries. In certain analyses, such as remeshing in dynamic analyses or contouring and others, the inverse of this mapping is inevitably valuable, but its determination is not so straightforward. To avoid solving a system of nonlinear equations, generally an iterative technique of order N 2 in a two-dimensional mesh is often resorted to. In the paper, this technique is improved by systematically bisecting along a predefined line that reduces the iterations to only order N . Its applications in remeshing and nodal quantity contouring are demonstrated and a possible extension for stress contouring is also discussed. The FORTRAN subroutines for the technique proposed are also given.