Zagorodnov, I. JACoW Geneva, Switzerland 978-3-95450-180-9 10.18429/JACoW-NAPAC2016-WEA1IO02 English 642-646 WEA1IO02 ion simulation electromagnetic-fields vacuum wakefield Contribution to a conference proceedings 2017 2017-01 http://dx.doi.org/10.18429/JACoW-NAPAC2016-WEA1IO02 https://jacow.org/napac2016/papers/wea1io02.pdf We discuss recent developments of numerical methods for computation of wakefields excited by short bunches in accelerators. They include a low-dispersive computational algorithm, conformal approximation of the boundaries, surface conductivity, and indirect wake potential integration. The implementation of these methods in the electromagnetic code ECHO for 2D and 3D problems are presented with a special emphasis on a new ECHO2D code for fast calculations of wakefields in rectangular geometries. Several examples of application of the code to calculation of wakefields for the European Free Electron Laser project and in the Linac Coherent Light Source (LCLS) project are considered.