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NBImag is a code suitable for the design and optimization of complex magnetic field configurations, such as that of a multiaperture, multistage negative ion source and accelerator. The NBImag code has been developed for the design of the ITER neutral beam injector, whose full-size prototype, MITICA, is presently under construction in Padua, Italy. The ITER injector shall produce a focused beam of neutral particles (H or D) having an energy of about 1 MeV and a total power of 16.5 MW for 3600-s continuous operation. The NBImag code is based on an integral formulation and allows an efficient calculation of any static magnetic field configuration on the basis of the geometry of the magnetic sources, with linear material and permanent magnets. NBImag also includes magnetic force and inductance calculations, based on the same formulation. Thanks to the capability of efficiently describing a large number of permanent magnets with limited computational effort, NBImag has also been integrated with different automatic optimization procedures for the solution of inverse magnetic problems. This paper describes the formulation of the code and optimization algorithms, the validation against analytical models and experimental measurements, and the application to the design of MITICA. [ABSTRACT FROM AUTHOR]