This paper presents two new hardware-assisted rendering techniques developed for interactive visualization of the terascale data generated from numerical modeling of next-generation accelerator designs. The first technique, based on a hybrid rendering approach, makes possible interactive exploration of large-scale particle data from particle beam dynamics modeling. The second technique, based on a compact texture-enhanced representation, exploits the advanced features of commodity graphics cards to achieve perceptually effective visualization of the very dense and complex electromagnetic fields produced from the modeling of reflection and transmission properties of open structures in an accelerator design. Because of the collaborative nature of the overall accelerator modeling project, the visualization technology developed is for both desktop and remote visualization settings. We have tested the techniques using both time-varying particle data sets containing up to one billion particles per time step and electromagnetic field data sets with millions of mesh elements.