The FIELD II simulation program can be used for simulating any kind of linear ultrasound fields. The program is capable of describing multi-element transducers used with any kind of excitation, apodization, and focusing. The program has been widely used in both academia and by commercial ultrasound companies for investigation novel transducer geometries and advanced linear imaging schemes. The program models transducer geometries using a division of the transducer elements into either rectangles, triangles, or bounding lines. The precision of the simulation and the simulation time is intimately linked through the choice of the fundamental elements. The rectangular elements use a far-field approximation, whereas the two other methods use the full analytic solution, leading to a higher precision at the price of a slower simulation time. The talk will describe the different compromises and solutions to obtain a fast simulation and still attain a high precision including a newly developed semi-analytic solution for a convex surface elements.