Jensen and Svendsen propose a method for simulating pulsed pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers. The method is based on the Tupholme–Stepanishen approach, which calculates pulsed pressure fields and can also handle continuous wave and pulse-echo cases. The field is calculated by dividing the transducer surface into small rectangles and summing their responses. A fast calculation is achieved using the far-field approximation. The method is accurate and efficient, with examples showing its performance for various transducer geometries and apodization functions. The paper outlines the theory behind the method, which involves solving the wave equation for the velocity potential to calculate the pressure field. The solution is derived using Green's function and involves integrating over the transducer surface. The method accounts for the transducer's geometry and apodization, and the pressure field is calculated by convolving the piston velocity waveform with the apodized spatial impulse response. The method is applied to various transducer geometries, including concave and flat transducers, and is shown to produce accurate results. The simulation approach involves dividing the transducer surface into small rectangles and summing their responses. The far-field approximation is used to reduce computational complexity, and the method is validated against analytic solutions and experimental measurements. The paper also discusses the use of the method for calculating pulse-echo fields and the importance of element size in determining the accuracy of the results. The method is efficient, with calculation times in the order of a few seconds, and can handle any excitation of the transducer. The accuracy of the method is on the order of 3 to 5 percent compared to theoretical results, and the method is shown to be effective for a wide range of applications in ultrasound imaging and acoustics.Jensen and Svendsen propose a method for simulating pulsed pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers. The method is based on the Tupholme–Stepanishen approach, which calculates pulsed pressure fields and can also handle continuous wave and pulse-echo cases. The field is calculated by dividing the transducer surface into small rectangles and summing their responses. A fast calculation is achieved using the far-field approximation. The method is accurate and efficient, with examples showing its performance for various transducer geometries and apodization functions. The paper outlines the theory behind the method, which involves solving the wave equation for the velocity potential to calculate the pressure field. The solution is derived using Green's function and involves integrating over the transducer surface. The method accounts for the transducer's geometry and apodization, and the pressure field is calculated by convolving the piston velocity waveform with the apodized spatial impulse response. The method is applied to various transducer geometries, including concave and flat transducers, and is shown to produce accurate results. The simulation approach involves dividing the transducer surface into small rectangles and summing their responses. The far-field approximation is used to reduce computational complexity, and the method is validated against analytic solutions and experimental measurements. The paper also discusses the use of the method for calculating pulse-echo fields and the importance of element size in determining the accuracy of the results. The method is efficient, with calculation times in the order of a few seconds, and can handle any excitation of the transducer. The accuracy of the method is on the order of 3 to 5 percent compared to theoretical results, and the method is shown to be effective for a wide range of applications in ultrasound imaging and acoustics.