Extrusion is a widely used process to create products with a fixed cross-sectional shape. Many applications require complex shaped cross-sections, where the dies contain sharp corners. Common requirement on the extrudate is dimensional precision. However, the shape and dimensions of the extrudate are highly influenced by a phenomenon called extrudate swell. The swelling process involves complex dynamics influenced by many parameters, such as viscoelasticity and temperature. Therefore, the optimized shape of a die, to obtain an extrudate with desired dimensions and shape, is now often obtained through trial-and-error. We developed a transient 3D finite element model, to predict extrudate swelling for extrudates containing sharp edges. This model describes the corner lines of the domain separately to obtain the positions of these lines in the two swell directions. A 2D height function is used to describe the free surfaces of the extrudate, using the positions obtained from solving the material lines to expand the domain of the height function [1]. This method is combined with a real-time active control scheme, to numerically solve the inverse problem of three-dimensional die design for extrudate swell. A feedback connection is established between the finite element method and the control scheme [2]. In this talk we show that this is a promising approach to design dies for viscoelastic extrusion flows. Furthermore, we will highlight the applicability of the developed method to model various extrusion techniques for complex materials [3].